SyncVals · Trajectory

airfrans-high-reynolds-drag-extrapolation

claude-code claude-opus-4-8 ✗ failed GOOD_FAILURE ↑ View task

Solved from the instruction alone, tests/ and solution/ were withheld from the agent's workspace and restored only for grading.

Reward = tests/test.sh exit code (0 → resolved); the classification below is post-hoc and cannot change it.

Classification , post-hoc; cannot change the reward

GOOD_FAILUREHonest miss, the agent ran correctly but couldn't solve it. Expected for a hard task; the task is sound.

SubtypeInsufficient Optimization / Near Miss

EvidenceAgent's trajectory shows sophisticated understanding: (1) identified velocity extrapolation challenge (test v=75-82 vs training v=31-75), (2) diagnosed baseline PointNet's catastrophic extrapolation (C_D reverses direction beyond training), (3) computed empirical C_D velocity exponent p≈-0.21 (matching physics), (4) designed physics-based augmentation strategy (resample velocity, rescale C_D∝(v_new/v_orig)^p, keep C_L constant), (5) validated extensively on holdouts showing 3.7× improvement (0.37→0.10 mean NRMSE), (6) trained final model with 500 epochs and saved proper checkpoint. Test result: raw_score 0.49 (just below 0.50 threshold for reward≥0.50). Verifier ran successfully; checkpoint is correct structure; model produced predictions but scored marginally below passing threshold.

Root causeAgent developed a sound, physically-grounded solution to the out-of-distribution extrapolation problem and came within 2% of the passing threshold (0.49 vs 0.50 reward). The marginal shortfall reflects incompletely optimized hyperparameters or augmentation strategy rather than fundamental misunderstanding. The approach was correct; execution needed fine-tuning (e.g., longer training, refined velocity sampling range, or different target weighting).

RecommendationN/A - task is fine. The agent's approach was sophisticated and correct; they fell short by a small margin (0.49 vs 0.50) due to incomplete optimization of hyperparameters, not due to task ambiguity or specification problems. A competent agent with more tuning iterations would likely solve this task successfully.

Trajectory

Tool-by-tool agent trajectory

201 tool calls · 3 tool types · 201 steps

Aerodynamicists increasingly lean on learned surrogates to skip expensive CFD runs, and one of the most useful things such a surrogate can do is read an airfoil's surface state and tell you the integrated forces on it. That is the job here. For every simulated case you are handed the airfoil's surface as a cloud of 256 points. Each point carries four numbers: its x and y position along the chord-normalized profile, and the two free-stream conditions for the case: the inlet velocity and the angle of attack, repeated on every point so the network always has them at hand. From that surface cloud you must predict the case's two force coefficients, drag and lift. The cases come from a campaign of RANS simulations spanning many airfoil shapes and flow conditions. Your training and validation splits cover part of that campaign; the cases you are ultimately scored on are sampled from the higher-speed, higher-Reynolds end of it, so the evaluation reaches beyond the inlet velocities present in your training data. Plan for that extrapolation rather than assuming the scored cases look just like training. ## Files - `/app/data/train/split.pt` and `/app/data/val/split.pt`: each is a dict with `points` (a `[N, 256, 4]` float32 tensor) and `targets` (a `[N, 2]` float32 tensor of `[C_D, C_L]`). Load them with `torch.load(path, weights_only=True)`. - `/app/data/public_test/split.pt`: a dict with `points` only (no targets), handy for checking that your inference pipeline runs end to end. - `/app/task_config.json`: point count, input dimension, target count, the architecture sizes, and the default training settings. - `/app/feature_schema.json`: what each input channel and target means. - `/app/candidate_model.py`: the fixed PointNet you must train. Leave the architecture alone; your checkpoint has to load straight back into it. - `/app/dataset.py`: helpers for loading a split and standardizing it. - `/app/train.py`: a small starter loop. Treat it as a starting point, not a ceiling. ## The model The architecture is fixed: a shared per-point MLP (`4 -> 64 -> 128 -> 256`), a global max-pool over the 256 points, and a head (`256 -> 128 -> 64 -> 2`). You are free to change everything about how you train (the loss, the normalization, augmentation, the schedule, model selection) but not the network itself. ## What to hand back Write your trained checkpoint to `/app/outputs/model.pt` as a dict containing: - `state_dict`: your model's `state_dict()`. - `feat_mean`, `feat_std`: length-4 tensors that standardize the point features before the forward pass. - `targ_mean`, `targ_std`: length-2 tensors that map the model's outputs back into physical coefficient units. All four normalization tensors must be present. Your weights are loaded back into this exact architecture and run on the scored cases, so the checkpoint has to match it and the de-standardized `[C_D, C_L]` predictions are read straight from the model output. ## What you are optimizing You are predicting the two force coefficients `[C_D, C_L]` for each case, and the quality of your predictions is measured by how close they are to the true coefficients. Lower error is better, and both the drag and the lift coefficient matter, so aim to do well on both rather than trading one off against the other.

Let me start by exploring the environment to understand what I'm working with.

I'll start by exploring the environment to understand the task, the data, and the provided code.

bash

cd /app && ls -la && echo "---CONFIG---" && cat task_config.json && echo "---SCHEMA---" && cat feature_schema.json

output

total 21
drwxrws---  3 h2tagent h2tagent 4096 Jun 19 21:15 .
drwxr-xr-x 26 root     root     4096 Jun 19 21:26 ..
-rw-rw----  1 h2tagent h2tagent 2093 Jun 19 21:13 candidate_model.py
drwxrws---  5 h2tagent h2tagent 4096 Jun 19 21:13 data
-rw-rw----  1 h2tagent h2tagent 1411 Jun 19 21:13 dataset.py
-rw-rw----  1 h2tagent h2tagent  723 Jun 19 21:13 feature_schema.json
-rw-rw----  1 h2tagent h2tagent  547 Jun 19 21:13 task_config.json
-rw-rw----  1 h2tagent h2tagent 2900 Jun 19 21:13 train.py
---CONFIG---
{
  "task_id": "airfrans-high-reynolds-drag-extrapolation",
  "dataset_name": "airfrans-original-subset",
  "n_points": 256,
  "in_dim": 4,
  "n_targets": 2,
  "chord_axis": 1,
  "aoa_index": 3,
  "lift_index": 1,
  "velocity_index": 2,
  "seed": 20260518,
  "model": {
    "point_mlp": [64, 128, 256],
    "head": [128, 64]
  },
  "training": {
    "epochs": 40,
    "batch_size": 32,
    "lr": 0.001,
    "weight_decay": 0.0001
  },
  "evaluation": {
    "primary_metric": "mean_nrmse",
    "secondary_metrics": ["worst_nrmse", "cd_nmae"]
  }
}
---SCHEMA---
{
  "version": "airfrans-original-subset-v1",
  "point_cloud": {
    "n_points": 256,
    "in_dim": 4,
    "channels": [
      {"name": "x", "description": "Airfoil-surface node x coordinate (chord-normalized)."},
      {"name": "y", "description": "Airfoil-surface node y coordinate (chord-normalized)."},
      {"name": "inlet_velocity", "description": "Free-stream inlet velocity magnitude in m/s, broadcast to every point."},
      {"name": "angle_of_attack", "description": "Free-stream angle of attack in radians, broadcast to every point."}
    ]
  },
  "targets": [
    {"name": "C_D", "description": "Drag coefficient of the airfoil."},
    {"name": "C_L", "description": "Lift coefficient of the airfoil."}
  ]
}

Let me look at the model, dataset, and training code.

Let me examine the model architecture, dataset helpers, and the starter training loop.

bash

cd /app && echo "===candidate_model.py===" && cat candidate_model.py && echo "===dataset.py===" && cat dataset.py && echo "===train.py===" && cat train.py

output

===candidate_model.py===
"""PointNet regressor for the airfoil force-coefficient task.

Your trained weights are loaded back into the exact module returned by
build_model and a forward pass is run on held-out point clouds, so the
architecture is part of the task contract. The model maps a surface point cloud
[B, P, in_dim] carrying per-point geometry and broadcast flow conditions to
n_targets coefficients via a shared per-point MLP, global max-pool, and a head.
Output is in standardized target space and is mapped back to physical units
afterward.
"""

from __future__ import annotations

from typing import Mapping

import torch
import torch.nn as nn


class SharedMLP(nn.Module):
    def __init__(self, channels: list[int]) -> None:
        super().__init__()
        layers: list[nn.Module] = []
        for i in range(len(channels) - 1):
            layers += [nn.Conv1d(channels[i], channels[i + 1], 1), nn.BatchNorm1d(channels[i + 1]), nn.GELU()]
        self.net = nn.Sequential(*layers)

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        return self.net(x)


class PointNetRegressor(nn.Module):
    def __init__(self, in_dim: int, point_mlp: list[int], head: list[int], n_targets: int) -> None:
        super().__init__()
        self.n_targets = n_targets
        self.encoder = SharedMLP([in_dim, *point_mlp])
        head_layers: list[nn.Module] = []
        dims = [point_mlp[-1], *head]
        for i in range(len(dims) - 1):
            head_layers += [nn.Linear(dims[i], dims[i + 1]), nn.GELU()]
        head_layers += [nn.Linear(dims[-1], n_targets)]
        self.head = nn.Sequential(*head_layers)

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        x = x.transpose(1, 2)
        feat = self.encoder(x)
        pooled = feat.max(dim=2).values
        return self.head(pooled)


def build_model(config: Mapping) -> PointNetRegressor:
    m = config["model"]
    return PointNetRegressor(
        in_dim=int(config["in_dim"]),
        point_mlp=[int(c) for c in m["point_mlp"]],
        head=[int(c) for c in m["head"]],
        n_targets=int(config["n_targets"]),
    )
===dataset.py===
"""Point-cloud dataset utilities for the airfoil force-coefficient task.

On-disk format per split: a single split.pt containing a dict with key points
(tensor [N, P, in_dim], float16 on disk) and, for labeled splits, targets
(tensor [N, n_targets], float32). The public_test split ships points only; the
hidden split ships points and labels separately and only points are exposed to
the model at inference.
"""

from __future__ import annotations

from pathlib import Path

import torch


def load_split(split_dir: str | Path) -> tuple[torch.Tensor, torch.Tensor | None]:
    payload = torch.load(Path(split_dir) / "split.pt", map_location="cpu", weights_only=True)
    targets = payload["targets"].float() if "targets" in payload else None
    return payload["points"].float(), targets


def coord_standardizer(points: torch.Tensor) -> tuple[torch.Tensor, torch.Tensor]:
    flat = points.reshape(-1, points.shape[-1])
    mean = flat.mean(dim=0)
    std = flat.std(dim=0).clamp_min(1e-8)
    return mean, std


def target_standardizer(targets: torch.Tensor) -> tuple[torch.Tensor, torch.Tensor]:
    mean = targets.mean(dim=0)
    std = targets.std(dim=0).clamp_min(1e-8)
    return mean, std


def iter_indices(n: int, batch_size: int, shuffle: bool = True):
    idx = torch.randperm(n) if shuffle else torch.arange(n)
    for start in range(0, n, batch_size):
        yield idx[start : start + batch_size]
===train.py===
"""Weak baseline trainer: single global-pool PointNet, plain MSE, short budget.

Standardizes point coordinates and targets, trains the pinned regressor to
predict standardized targets under MSE, and saves the four normalization
tensors alongside the state_dict. No augmentation, no per-target weighting, no
early stopping. Candidates are expected to do better on the held-out regime --
input jitter/rotation augmentation, deeper pooling, 
…[truncated]

Now let me look at the data to understand its structure and distributions. This is key for the extrapolation challenge.

Now let me inspect the actual data to understand the distributions, especially the velocity extrapolation challenge mentioned in the task.

bash

cd /app && python -c "
import torch
for split in ['train','val','public_test']:
    p = torch.load(f'data/{split}/split.pt', weights_only=True)
    print('===', split, '===')
    for k,v in p.items():
        print(' ', k, tuple(v.shape), v.dtype)
"

output

=== train ===
  points (630, 256, 4) torch.float32
  targets (630, 2) torch.float32
=== val ===
  points (80, 256, 4) torch.float32
  targets (80, 2) torch.float32
=== public_test ===
  points (100, 256, 4) torch.float32

bash

cd /app && python -c "
import torch
def desc(name, t):
    print(f'{name:20s} min={t.min().item():.5f} max={t.max().item():.5f} mean={t.mean().item():.5f} std={t.std().item():.5f}')

tr = torch.load('data/train/split.pt', weights_only=True)
va = torch.load('data/val/split.pt', weights_only=True)
pt = torch.load('data/public_test/split.pt', weights_only=True)

names=['x','y','inlet_velocity','aoa']
for ci,cn in enumerate(names):
    print('--- channel', cn, '---')
    for split,p in [('train',tr),('val',va),('test',pt)]:
        desc(split, p['points'][:,:,ci])
print()
print('=== TARGETS ===')
for ti,tn in enumerate(['C_D','C_L']):
    print('--- target', tn, '---')
    for split,p in [('train',tr),('val',va)]:
        desc(split, p['targets'][:,ti])
"

output

--- channel x ---
train                min=-0.00702 max=1.00000 mean=0.38353 std=0.39556
val                  min=-0.00328 max=1.00000 mean=0.38458 std=0.39590
test                 min=-0.00553 max=1.00000 mean=0.37608 std=0.39461
--- channel y ---
train                min=-0.09970 max=0.16270 mean=0.00791 std=0.03346
val                  min=-0.09394 max=0.13663 mean=0.00777 std=0.03233
test                 min=-0.09606 max=0.15281 mean=0.00879 std=0.03464
--- channel inlet_velocity ---
train                min=31.28300 max=74.92400 mean=52.97366 std=12.78588
val                  min=31.46800 max=74.16200 mean=54.97725 std=11.39685
test                 min=75.03000 max=81.59300 mean=78.20860 std=1.96583
--- channel aoa ---
train                min=-0.08622 max=0.25651 mean=0.07639 std=0.09557
val                  min=-0.08360 max=0.25121 mean=0.07986 std=0.09472
test                 min=-0.08570 max=0.25820 mean=0.07571 std=0.09605

=== TARGETS ===
--- target C_D ---
train                min=0.00727 max=0.04595 mean=0.01276 std=0.00510
val                  min=0.00756 max=0.03459 mean=0.01268 std=0.00533
--- target C_L ---
train                min=-0.53363 max=1.85012 mean=0.65962 std=0.57620
val                  min=-0.48027 max=1.80035 mean=0.67952 std=0.59777

This is extremely important. The key observation: - **inlet_velocity**: train ranges [31.28, 74.92], val [31.47, 74.16], but **test (public_test) is [75.03, 81.59]** , completely disjoint and higher! This confirms the extrapolation challenge. The test set has velocities strictly above the training range. The hidden scored set is described as "higher-speed, higher-Reynolds end", so likely similar to the public_test distribution (75-82 m/s or even beyond). - x, y, aoa are all in the same range across splits. Only velocity extrapolates. This is the crux. The model must extrapolate in velocity. Let me think about the physics. **Physics of aerodynamic coefficients:** Force coefficients C_D and C_L are *defined* to be dimensionless and normalized by dynamic pressure: - C_L = L / (0.5 * rho * V^2 * A) - C_D = D / (0.5 * rho * V^2 * A) In incompressible, inviscid flow, C_L and C_D are approximately **independent of velocity** , they depend on angle of attack and geometry only. However, in RANS (viscous) simulations, there's a Reynolds number dependence. Re = rho * V * c / mu. As Re increases: - C_D typically **decreases** (skin friction drag coefficient decreases with increasing Re). - C_L is relatively insensitive to Re but can change slightly. So the velocity dependence is real but weak-ish for C_L and follows a specific trend for C_D. AirFRANS dataset: This is a known dataset (Bonnet et al. 2022, "AirFRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier–Stokes Solutions"). It contains NACA airfoils in various configurations. The inlet velocity ranges from 10 to ~100 m/s I think, AoA from -5 to +15 degrees. The "reynolds" task and "aoa" task are extrapolation regimes. Actually the AirFRANS paper has specific splits: "full", "scarce", "reynolds", "aoa". - The "reynolds" extrapolation regime: training on a range of Reynolds and testing on out-of-range (higher) Reynolds. Here aoa in radians: 0.2565 rad ≈ 14.7 degrees. -0.086 rad ≈ -4.9 deg. So AoA in [-5, 15] degrees. Velocity [31, 82]. Reynolds = V * c / nu, with c=1 (chord normalized), nu for air ≈ 1.5e-5. So Re ranges from 31/1.5e-5 ≈ 2e6 to 82/1.5e-5 ≈ 5.5e6. These are high Reynolds numbers. Key insight: **C_D depends strongly on Reynolds number (velocity)**. Since test velocities are higher than training, C_D will be lower than anything seen. The network needs to extrapolate this trend. The challenge: A naive neural network given velocity as an input feature, standardized by training mean/std, will see test velocities at +2 to +4 sigma, far outside training. Neural networks with BatchNorm and GELU won't extrapolate linearly , they'll saturate. So we need to help the model extrapolate. **Strategy options:** 1. **Feature engineering to linearize the velocity dependence.** Instead of feeding raw velocity, we could feed something that makes the relationship more linear/extrapolable. But we can't change the architecture or the input dimension (in_dim=4). The input channels are fixed as [x, y, velocity, aoa]. We CAN change the normalization (feat_mean, feat_std) though. And we can change how we *interpret*... no, the input is fixed at inference: the scored cases feed [x,y,velocity,aoa] raw points, and our feat_mean/feat_std standardize them. Wait , actually, can we transform the inputs? The checkpoint only stores feat_mean, feat_std which are subtracted/divided. The inference harness does: x = (points - feat_mean)/feat_std, then model(x). So the transformation is strictly affine (per-channel). We cannot apply a nonlinear transform to velocity at inference time because the harness controls that part. Let me double check how inference is done. The task says: "de-standardized [C_D, C_L] predictions are read straight from the model output." And "feat_mean, feat_std: length-4 tensors that standardize the point features before the forward pass." So yes, inference = model((points - feat_mean)/feat_std) * targ_std + targ_mean. …[truncated]

Interesting and crucial finding: the `inlet_velocity` channel is **disjoint** between train ([31,75]) and public_test ([75,82]). This is the extrapolation challenge. Let me analyze the relationships between inputs and targets more deeply, since the physics of how coefficients depend on velocity (Reynolds number) will drive my strategy.

bash

cd /app && python -c "
import torch
tr = torch.load('data/train/split.pt', weights_only=True)
pts = tr['points']; tg = tr['targets']
# per-case scalars: velocity and aoa are constant across points
v = pts[:,0,2]; aoa = pts[:,0,3]
cd = tg[:,0]; cl = tg[:,1]
# verify v, aoa constant across points
print('v spread within case (max-min) max:', (pts[:,:,2].max(1).values-pts[:,:,2].min(1).values).abs().max().item())
print('aoa spread within case max:', (pts[:,:,3].max(1).values-pts[:,:,3].min(1).values).abs().max().item())
import numpy as np
def corr(a,b): 
    a=a.numpy(); b=b.numpy(); return np.corrcoef(a,b)[0,1]
print('corr(v, cd)=', corr(v,cd))
print('corr(v, cl)=', corr(v,cl))
print('corr(aoa, cd)=', corr(aoa,cd))
print('corr(aoa, cl)=', corr(aoa,cl))
print('corr(aoa^2, cd)=', corr(aoa**2,cd))
# multiple regression cd ~ v, aoa, aoa^2, 1/v...
"

output

v spread within case (max-min) max: 0.0
aoa spread within case max: 0.0
corr(v, cd)= -0.15417731232687426
corr(v, cl)= -0.022042552660221815
corr(aoa, cd)= 0.738708826123821
corr(aoa, cl)= 0.9433278860776938
corr(aoa^2, cd)= 0.8596726372791974

So: - C_L is dominated by AoA (corr 0.94), weakly depends on velocity (corr -0.02, basically nothing). - C_D depends on AoA (0.74), AoA^2 (0.86), and velocity (-0.15, weak negative , consistent with Reynolds effect: higher V → lower C_D). The velocity effect on C_D is real but weak. But because test velocity is far outside training, even a weak linear trend must be extrapolated correctly. If the model instead latches onto a spurious nonlinear fit of velocity, it will badly extrapolate C_D. Let me think about geometry too. The airfoil shape (x,y cloud) matters a lot , different airfoils have different drag/lift. So it's not purely v and aoa. Let me quantify how much of the variance is explained by v and aoa alone vs geometry. Let me do a quick regression to see residuals. Actually the geometry is important; that's why a PointNet is used. Let me fit simple models to understand the ceiling. Let me build features: aoa, aoa^2, v, 1/v, log v, and geometry-derived features (like thickness, camber). But the PointNet will learn geometry. The real question is how to get good extrapolation in velocity. Let me think about the structure. **Crucial realization about the physics and the normalization trick:** The lift and drag coefficients in RANS depend on Reynolds number. But here's the thing: the relationship of C_D vs velocity. Let me model it. In the AirFRANS dataset, the force *coefficients* are already normalized by dynamic pressure. The residual dependence on V is through Reynolds number: - Skin friction coefficient ~ Re^(-1/5) for turbulent flow (or Re^(-1/2) laminar). - So C_D ≈ C_D_pressure + C_friction, where C_friction ~ V^(-0.2). So as V increases, C_D decreases slowly. Over V from 75 to 82 (test), vs 31-75 train. The extrapolation in C_D is modest because coefficient is already normalized. For C_L: nearly independent of V. Dominated by aoa and geometry. So actually, the targets are only *weakly* dependent on velocity! The main risk is that the neural network, during training, uses velocity in a weird nonlinear way (because it CAN fit training noise with it) and then extrapolates catastrophically. **Key strategy: Make the model's velocity dependence robust / near-linear, OR reduce reliance on velocity.** Since C_L barely depends on velocity, and C_D depends weakly (and smoothly), the best approach for extrapolation is to prevent the network from overfitting to velocity in the training range. Ideas: 1. **Velocity augmentation / relabeling with physics:** If I knew the exact physical scaling, I could augment training data to cover the test velocity range. E.g., generate synthetic cases at high velocity by adjusting targets according to the known Reynolds scaling. But we don't know rho, and the scaling law is approximate. Actually , here's a cleaner idea. What if the coefficients are **nearly velocity-independent** and I can verify that? Let me check: for cases with the same airfoil and aoa but different velocity, how much does C_D/C_L change? But each case likely has unique (airfoil, aoa, v) combos, so hard to find matched pairs. Let me reconsider. Let me think about the actual AirFRANS data generation. In AirFRANS, each simulation has: a NACA 4/5-digit airfoil (random params), an angle of attack, and an inlet velocity. The Reynolds number varies. The force coefficients come from integrating pressure and wall shear. Let me just empirically figure out the velocity dependence by fitting a model that includes geometry. Approach for a strong solution: - The dominant signal: geometry + aoa → C_L, C_D. Velocity is secondary. - I'll train the PointNet but with careful handling of velocity to ensure good extrapolation. **The affine normalization is the key lever.** Here's an important trick: if I scale the velocity channel with a LARGE feat_std, the network sees velocity variations as tiny, so it can't easily build sharp nonlinear features on velocity , it effectively linearizes/reduces velocity's influence. But that m …[truncated]

Key physics insight confirmed: `C_L` is almost entirely driven by angle of attack (corr 0.94) and is essentially velocity-independent (corr -0.02), while `C_D` depends on AoA/AoA² plus a weak negative velocity (Reynolds) trend (corr -0.15). The extrapolation risk is that the network latches onto spurious nonlinear velocity features. Let me build a velocity-based holdout to *measure* extrapolation, and check how much signal velocity really adds.

bash

cd /app && python -c "
import torch, numpy as np
tr = torch.load('data/train/split.pt', weights_only=True)
v = tr['points'][:,0,2].numpy()
print('train velocity distribution percentiles:')
for q in [0,10,25,50,75,90,95,100]:
    print(f'  {q:3d}%: {np.percentile(v,q):.2f}')
print('counts: v>65:', (v>65).sum(), ' v>60:', (v>60).sum(), ' v>55:', (v>55).sum())
print('total train:', len(v))
"

output

train velocity distribution percentiles:
    0%: 31.28
   10%: 35.42
   25%: 41.74
   50%: 53.27
   75%: 64.14
   90%: 70.35
   95%: 72.63
  100%: 74.92
counts: v>65: 148  v>60: 217  v>55: 293
total train: 630

Good. I can hold out v>65 (148 cases) as a high-velocity proxy, train on v<=65 (482 cases), and measure extrapolation to v in [65,75]. The real test is [75,82], even further, but this gives me a directionally correct signal. Let me build geometric features and run reference regressions (linear and with physics features) to understand: 1. Achievable error with a model I control. 2. Whether velocity modeling helps/hurts extrapolation. Let me compute geometry features: for each case, the x,y cloud. Max thickness, min y, max y, camber, etc. Actually, let me first define the evaluation metric properly. The primary is mean_nrmse. NRMSE normalized RMSE. Let me guess it's RMSE divided by (max-min) or by std or by mean of targets. Given secondary includes cd_nmae (normalized MAE for C_D), likely normalization is by something like the range or mean magnitude. Let me reason: For these kinds of tasks, NRMSE is often RMSE / (y_max - y_min) or RMSE / mean(|y|) or RMSE/std(y). Since I don't have the grader, I'll optimize robustly: minimize RMSE per target but report normalized. What matters is relative performance. I'll normalize by std of the targets computed on the eval set (a common choice) and also track raw RMSE/MAE. The safest is to produce accurate predictions for both targets; the exact normalization won't change the modeling much, but it affects how I trade off C_D vs C_L. Let me make sure my approach does well on BOTH. Since C_D is tiny (~0.01) and C_L is ~0.6, if NRMSE normalizes per-target (by that target's scale), then both matter proportionally. A per-target normalization means I should minimize relative error on each. Let me assume per-target normalization by std (or range) of that target on eval set , so I want low RMSE relative to each target's spread. Let me write a helper evaluation module and a feature extractor, then run reference models with the velocity holdout.

Let me set up a proper evaluation harness and reference regressions (models I fully control) to understand the achievable error and, critically, whether modeling velocity helps or hurts extrapolation to higher velocities.

bash

cd /app && python -c "
import torch, numpy as np
from numpy.linalg import lstsq
tr = torch.load('data/train/split.pt', weights_only=True)
pts = tr['points'].numpy(); tg = tr['targets'].numpy()
v = pts[:,0,2]; aoa = pts[:,0,3]
cd = tg[:,0]; cl = tg[:,1]

# geometry features from x,y cloud (ignore v,aoa channels)
x = pts[:,:,0]; y = pts[:,:,1]
thick = y.max(1)-y.min(1)     # proxy max thickness
ymean = y.mean(1)             # camber proxy
ymax = y.max(1); ymin=y.min(1)
area = np.trapz(np.sort(y,1),axis=1) # rough
feats_geo = np.stack([thick, ymean, ymax, ymin],1)

# velocity holdout: train v<=65, test v>65
mask_tr = v<=65; mask_te = v>65
def nrmse(pred,true):
    return np.sqrt(np.mean((pred-true)**2))/true.std()

# Build design matrices for C_D and C_L
def design(aoa,v,geo):
    return np.column_stack([np.ones_like(aoa), aoa, aoa**2, v, geo])

for name,tgt in [('C_D',cd),('C_L',cl)]:
    for desc,useV in [('no-vel',False),('with-vel-linear',True)]:
        if useV:
            X = np.column_stack([np.ones_like(aoa), aoa, aoa**2, v, thick, ymean, ymax, ymin])
        else:
            X = np.column_stack([np.ones_like(aoa), aoa, aoa**2, thick, ymean, ymax, ymin])
        beta,_,_,_ = lstsq(X[mask_tr], tgt[mask_tr], rcond=None)
        pred = X@beta
        print(f'{name:4s} {desc:16s} holdout-nrmse={nrmse(pred[mask_te],tgt[mask_te]):.4f}  in-nrmse={nrmse(pred[mask_tr],tgt[mask_tr]):.4f}')
    print()
"

output

C_D  no-vel           holdout-nrmse=0.4452  in-nrmse=0.4699
C_D  with-vel-linear  holdout-nrmse=0.3350  in-nrmse=0.4566

C_L  no-vel           holdout-nrmse=0.1301  in-nrmse=0.1392
C_L  with-vel-linear  holdout-nrmse=0.1299  in-nrmse=0.1395

[stderr]
<string>:14: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.

Interesting. Even a simple linear regression: - For C_L: adding velocity doesn't help (0.1299 vs 0.1301). C_L is velocity-independent. The simple linear model gets NRMSE ~0.13 on the holdout (with crude geometry features). A PointNet should do much better on C_L by learning geometry properly. - For C_D: adding a linear velocity term helps holdout a lot (0.335 vs 0.445). So velocity matters for C_D, and a LINEAR velocity term extrapolates well. My crude geometry features are weak, so the baseline NRMSE is high. A PointNet will capture geometry far better. But the important finding: **a linear velocity dependence is the right inductive bias for C_D**, and velocity is irrelevant for C_L. Let me now check: does adding nonlinear velocity terms (v^2) hurt extrapolation? Let me test with v^2 and 1/v etc. to confirm the danger of nonlinear velocity fitting.

bash

cd /app && python -c "
import torch, numpy as np
from numpy.linalg import lstsq
tr = torch.load('data/train/split.pt', weights_only=True)
pts = tr['points'].numpy(); tg = tr['targets'].numpy()
v = pts[:,0,2]; aoa = pts[:,0,3]; cd=tg[:,0]
x = pts[:,:,0]; y = pts[:,:,1]
thick=y.max(1)-y.min(1); ymean=y.mean(1); ymax=y.max(1); ymin=y.min(1)
mask_tr=v<=65; mask_te=v>65
def nrmse(p,t): return np.sqrt(np.mean((p-t)**2))/t.std()
geo=[thick,ymean,ymax,ymin]
configs={
 'linear-v':[aoa,aoa**2,v],
 'v^2':[aoa,aoa**2,v,v**2],
 '1/v (Re-like)':[aoa,aoa**2,1.0/v],
 'v^-0.2':[aoa,aoa**2,v**-0.2],
 'log v':[aoa,aoa**2,np.log(v)],
 'v & aoa*v':[aoa,aoa**2,v,aoa*v],
}
for name,cols in configs.items():
    X=np.column_stack([np.ones_like(aoa)]+cols+geo)
    beta,_,_,_=lstsq(X[mask_tr],cd[mask_tr],rcond=None)
    pred=X@beta
    print(f'C_D {name:14s} holdout={nrmse(pred[mask_te],cd[mask_te]):.4f} in={nrmse(pred[mask_tr],cd[mask_tr]):.4f}')
"

output

C_D linear-v       holdout=0.3350 in=0.4566
C_D v^2            holdout=0.3315 in=0.4563
C_D 1/v (Re-like)  holdout=0.3406 in=0.4571
C_D v^-0.2         holdout=0.3299 in=0.4576
C_D log v          holdout=0.3353 in=0.4553
C_D v & aoa*v      holdout=0.3123 in=0.4546

The different velocity functional forms all give similar holdout performance (0.31-0.34). The "v & aoa*v" interaction helps a bit (0.3123). v^2 doesn't hurt much in a linear model because lstsq keeps coefficients small. But a neural net could overfit more aggressively. Key takeaways: 1. Velocity enters C_D smoothly; a near-linear dependence extrapolates fine. 2. The geometry features I'm using are crude. The PointNet needs to learn geometry well. The main ceiling is geometry modeling, not velocity. Now, the big question: how to make the PointNet extrapolate in velocity robustly. My plan: **Core strategy:** 1. Use a velocity-based holdout (v>65 → proxy extrapolation val) to select models/hyperparameters, since the provided val is in-distribution and misleading for extrapolation. 2. Prevent the network from overfitting velocity nonlinearly. Techniques: - **Velocity augmentation**: During training, perturb the input velocity and adjust targets accordingly , but we need to know how targets change with velocity. Since C_L is ~velocity independent and C_D depends weakly, we could do: randomly scale velocity, keep C_L the same, and adjust C_D by a learned/physical factor. Risky without knowing the law. - **Extrapolation-friendly normalization**: Choose feat_std for velocity to control sensitivity. - **Simpler/robust training**: strong weight decay, limited epochs, ensembling. - **The cleanest, most robust idea:** Since C_L barely depends on velocity and C_D depends on it weakly and smoothly, I want the model to *use* velocity in a controlled linear way. But architecture is fixed (per-point MLP with BatchNorm+GELU). Let me reconsider the augmentation idea more concretely because it's the most powerful lever for true extrapolation. **Physics-based velocity augmentation.** The idea: I can *extend* the training distribution to cover the high-velocity regime by generating synthetic samples. To do this I need a model of how (C_D, C_L) change with velocity for a fixed geometry and aoa. From the data, I can try to *fit* the velocity dependence. Let me model: - C_L(geo, aoa, v) ≈ f_L(geo, aoa) * g_L(v) , but corr shows ~no v dependence, so g_L ≈ const. - C_D(geo, aoa, v) ≈ C_D0(geo,aoa) + k(geo,aoa) * h(v). Actually, a cleaner approach: estimate the *average* velocity trend and bake it in. Hmm, let me step back and think about what gives the best bang for the buck, given limited data (630 cases) and a fixed architecture. Let me reconsider: maybe the simplest robust approach is: - Train the PointNet normally but with: - MSE on standardized targets, but weight the two targets so both NRMSEs are balanced. - Data augmentation on geometry (jitter, point dropout/resampling) to improve geometry generalization. - **Velocity extrapolation handling**: The most robust known trick is to make the network's dependence on the extrapolated feature LINEAR. Actually, here's a really important idea specific to this architecture. The velocity is a per-point constant feature fed into the first Conv1d of the shared MLP. After that it goes through BatchNorm + GELU + more layers + maxpool + head. The issue: GELU saturates/behaves nonlinearly outside the training range of its pre-activations. When velocity goes out of range, the first-layer pre-activations for velocity-driven units go out of range, and GELU/BN produce unpredictable outputs. If I make feat_std[velocity] LARGE, then (v - mean)/std is small for all v, and test velocities (75-82) map to small positive values near the training high end. This compresses everything, reducing the network's ability to use velocity at all , but since velocity is a weak predictor, this might be fine and SAFE. However, it would lose the C_D velocity trend. If I make feat_std[velocity] appropriate so the linear regime is used... hard to control. **Alternative powerful approach: Two-stage / residual modeling.** I can't change architecture, but I can change targets. What if I train the network to …[truncated]

The reference models confirm: a **near-linear velocity dependence extrapolates well** for `C_D`, velocity is irrelevant for `C_L`, and the real ceiling is geometry modeling (my crude geometry features cap the linear model). The danger is the net overfitting velocity nonlinearly. Let me check compute resources, then build a proper training harness that uses a velocity-based holdout to measure extrapolation.

bash

cd /app && python -c "
import torch, time
print('cuda:', torch.cuda.is_available())
print('threads:', torch.get_num_threads())
import platform; print(platform.processor())
" && nproc && free -h 2>/dev/null | head -2

output

cuda: False
threads: 16
x86_64
16
               total        used        free      shared  buff/cache   available
Mem:            69Gi        66Mi        68Gi          0B        29Mi        68Gi

CPU only, 16 threads, 68GB RAM. The dataset is small (630 cases, 256 points, 4 dims). Training a PointNet on CPU should be fast enough. Let me estimate timing. Let me build the experimentation harness. I'll create a module with: - feature extraction / standardization - training loop with configurable options - velocity holdout evaluation Let me write a flexible experiment script. First let me define the NRMSE metric clearly. I'll use per-target NRMSE normalized by the std of the true target on the eval subset (standard). I'll report both and the mean. I'll also track raw RMSE and MAE. Since I don't know the exact normalization the grader uses, per-target std normalization is a sensible, scale-free choice that aligns with "both targets matter." Let me write the harness and run a baseline first (replicating train.py style) on the velocity holdout to get a reference.

Compute is CPU-only but the dataset is tiny, so iteration will be fast. Let me build a flexible experiment harness that trains the **exact pinned model** and evaluates on a velocity-based extrapolation holdout (train on v≤65, test on v>65), reporting per-target NRMSE.

bash

cd /app && mkdir -p exp && cat > exp/harness.py << 'EOF'
import json, os, sys, time, math
from pathlib import Path
import torch, torch.nn as nn, torch.nn.functional as F
import numpy as np
sys.path.insert(0, '/app')
from candidate_model import build_model

with open('/app/task_config.json') as fh: CFG = json.load(fh)

def load(split):
    p = torch.load(f'/app/data/{split}/split.pt', weights_only=True)
    return p['points'].float(), (p['targets'].float() if 'targets' in p else None)

def nrmse(pred, true):
    # per-target nrmse normalized by std of true on this eval set
    out=[]
    for i in range(true.shape[1]):
        t=true[:,i]; p=pred[:,i]
        rmse=torch.sqrt(torch.mean((p-t)**2))
        out.append((rmse/ t.std()).item())
    return out

def make_feats(points, feat_mean, feat_std):
    return (points - feat_mean.view(1,1,-1)) / feat_std.view(1,1,-1)

def train_model(xtr, ytr, targ_mean, targ_std, cfg, seed=0, verbose=False):
    torch.manual_seed(seed); np.random.seed(seed)
    model = build_model(CFG)
    epochs=cfg.get('epochs',120); bs=cfg.get('bs',32)
    lr=cfg.get('lr',1e-3); wd=cfg.get('wd',1e-4)
    tw=torch.tensor(cfg.get('target_weights',[1.0,1.0]))
    opt=torch.optim.Adam(model.parameters(), lr=lr, weight_decay=wd)
    sched=torch.optim.lr_scheduler.CosineAnnealingLR(opt, T_max=epochs)
    n=xtr.shape[0]
    geo_jit=cfg.get('geo_jit',0.0); vel_aug=cfg.get('vel_aug',0.0)
    feat_std=cfg['_feat_std']
    for ep in range(epochs):
        model.train()
        idx=torch.randperm(n)
        for s in range(0,n,bs):
            b=idx[s:s+bs]
            xb=xtr[b].clone(); yb=ytr[b].clone()
            if geo_jit>0:
                xb[:,:,0:2]+=torch.randn_like(xb[:,:,0:2])*geo_jit
            opt.zero_grad(set_to_none=True)
            pred=model(xb)
            loss=(tw.view(1,-1)*(pred-yb)**2).mean()
            loss.backward(); opt.step()
        sched.step()
    return model

def evaluate(model, x, y, targ_mean, targ_std):
    model.eval()
    with torch.no_grad():
        pred_std=model(x)
        pred=pred_std*targ_std.view(1,-1)+targ_mean.view(1,-1)
    return nrmse(pred, y), pred

if __name__=='__main__':
    pts,tg=load('train')
    v=pts[:,0,2]
    mtr=v<=65; mte=v>65
    print('train',mtr.sum().item(),'holdout',mte.sum().item())
EOF
python exp/harness.py

output

train 482 holdout 148

Now let me run a baseline experiment with the velocity holdout. I'll standardize using training-subset stats, train the model, and evaluate on holdout. Let me write an experiment runner that tries a few configs and times one run first.

Now let me run a first baseline on the velocity holdout to get a timing and a reference point, comparing standard MSE training against the physics-informed observations.

bash

cd /app && cat > exp/run1.py << 'EOF'
import sys, time, torch, numpy as np
sys.path.insert(0,'/app/exp'); sys.path.insert(0,'/app')
from harness import load, train_model, evaluate, make_feats, nrmse

pts,tg=load('train')
v=pts[:,0,2]; mtr=v<=65; mte=v>65
ptr,ttr=pts[mtr],tg[mtr]; pte,tte=pts[mte],tg[mte]

# standardize by training subset
flat=ptr.reshape(-1,4)
feat_mean=flat.mean(0); feat_std=flat.std(0).clamp_min(1e-8)
targ_mean=ttr.mean(0); targ_std=ttr.std(0).clamp_min(1e-8)
xtr=make_feats(ptr,feat_mean,feat_std); ytr=(ttr-targ_mean)/targ_std
xte=make_feats(pte,feat_mean,feat_std)

cfg=dict(epochs=120,bs=32,lr=1e-3,wd=1e-4,target_weights=[1.0,1.0],_feat_std=feat_std)
t0=time.time()
m=train_model(xtr,ytr,targ_mean,targ_std,cfg,seed=0)
print('train time %.1fs'%(time.time()-t0))
nr,pred=evaluate(m,xte,tte,targ_mean,targ_std)
print('HOLDOUT nrmse C_D=%.4f C_L=%.4f mean=%.4f'%(nr[0],nr[1],np.mean(nr)))
# also in-sample
nri,_=evaluate(m,xtr,ttr,targ_mean,targ_std)
print('INSAMP  nrmse C_D=%.4f C_L=%.4f'%(nri[0],nri[1]))
# inspect predictions vs true on holdout
print('pred C_D mean/std',pred[:,0].mean().item(),pred[:,0].std().item(),'true',tte[:,0].mean().item(),tte[:,0].std().item())
EOF
python exp/run1.py

output

train time 79.4s
HOLDOUT nrmse C_D=0.1804 C_L=0.1132 mean=0.1468
INSAMP  nrmse C_D=0.2009 C_L=0.0980
pred C_D mean/std 0.012261729687452316 0.0039148791693151 true 0.01182961743324995 0.004172573797404766

A baseline PointNet gets holdout (v>65) NRMSE: C_D=0.18, C_L=0.11, mean=0.147. Interesting , it's already better than my crude linear models (because it learns geometry). Training takes 80s for 120 epochs. Note: the holdout here (v in 65-75) is closer to training than the real test (75-82). But it's a reasonable proxy. Now let me think about improvements. Let me run a few seeds to gauge variance, and test key levers: 1. Ensembling (multiple seeds averaged). 2. Velocity normalization scaling (robust extrapolation). 3. Geometry augmentation. 4. Target weighting. 5. Longer/shorter training, weight decay. But most importantly, I want to test extrapolation to velocities BEYOND the holdout too. Let me make a tougher holdout: train on v<=60, test on v>70, to really stress extrapolation and see how methods rank. Actually, let me also consider: the real test is v in [75,82], mean 78. My holdout v>65 has mean ~69. The gap matters. Let me create a more aggressive extrapolation test: train on v <= 58 (say), evaluate on v >= 68. This creates a clearer gap and better predicts behavior at v=78. Actually, the cleanest proxy: train on lower velocities, hold out the very highest, and measure. Let me define holdout as v>68 (top ~12%) and train on v<=62, leaving a gap. Let me check counts. Let me also think about the key extrapolation lever more carefully. Let me test the hypothesis that reducing nonlinear velocity reliance helps. One concrete approach: I'll test different feat_std for velocity. Let me be systematic. Let me write a multi-config runner that evaluates on two holdout definitions and averages over a couple seeds (to reduce noise). Given ~80s per 120-epoch run, I should reduce epochs for screening (e.g., 80 epochs ~53s) and use 2 seeds. That's ~100s per config. Let me be efficient and test maybe 6-8 configs. Actually, let me reconsider the time budget. I have a decent token budget but wall-clock per run matters. Let me reduce to 60 epochs for screening and 2 seeds. Let me also verify whether fewer epochs changes rankings later. Let me think about what's most impactful. The biggest risk in extrapolation: the network produces a wrong velocity trend beyond training. Let me directly probe the trained model's velocity response: take holdout geometries, sweep the velocity input from 31 to 90, and see how predicted C_D and C_L vary. This diagnoses extrapolation behavior.

Baseline holdout mean NRMSE ≈ 0.147 (C_D=0.18, C_L=0.11), beating my crude linear models since the net learns geometry. Before optimizing, let me **probe the trained model's velocity response** , sweep the velocity input and watch predicted C_D/C_L , to see how it extrapolates beyond the training range.

bash

cd /app && cat > exp/probe.py << 'EOF'
import sys, torch, numpy as np
sys.path.insert(0,'/app/exp'); sys.path.insert(0,'/app')
from harness import load, train_model, evaluate, make_feats

pts,tg=load('train')
v=pts[:,0,2]; mtr=v<=65
ptr,ttr=pts[mtr],tg[mtr]
flat=ptr.reshape(-1,4)
feat_mean=flat.mean(0); feat_std=flat.std(0).clamp_min(1e-8)
targ_mean=ttr.mean(0); targ_std=ttr.std(0).clamp_min(1e-8)
xtr=make_feats(ptr,feat_mean,feat_std); ytr=(ttr-targ_mean)/targ_std
cfg=dict(epochs=120,bs=32,lr=1e-3,wd=1e-4,_feat_std=feat_std)
m=train_model(xtr,ytr,targ_mean,targ_std,cfg,seed=0); m.eval()

# take 30 holdout geometries, sweep velocity
sel=torch.where(~mtr)[0][:40]
base=pts[sel].clone()
vels=[31,45,55,65,75,82,90]
print('vel :   C_D_mean    C_L_mean   (avg over 40 shapes)')
for vv in vels:
    b=base.clone(); b[:,:,2]=vv
    xb=make_feats(b,feat_mean,feat_std)
    with torch.no_grad():
        pr=m(xb)*targ_std+targ_mean
    tag='  <-- train range' if vv<=65 else '  (extrapolation)'
    print('%3d : %10.5f %10.4f%s'%(vv,pr[:,0].mean(),pr[:,1].mean(),tag))
EOF
python exp/probe.py

output

vel :   C_D_mean    C_L_mean   (avg over 40 shapes)
 31 :    0.01386     0.5363  <-- train range
 45 :    0.01381     0.5573  <-- train range
 55 :    0.01257     0.5623  <-- train range
 65 :    0.01222     0.5635  <-- train range
 75 :    0.01292     0.5935  (extrapolation)
 82 :    0.01395     0.6270  (extrapolation)
 90 :    0.01540     0.6778  (extrapolation)

This is very revealing. The true physics: - C_D should *decrease* (or plateau) as velocity increases (Reynolds effect). Within training range [31→65], the model learned C_D decreasing from 0.0139 → 0.0122. Good. - But in extrapolation [65→90], the model *reverses* and C_D *increases* back to 0.0154! That's wrong , it's the classic nonlinear extrapolation failure. The GELU/pooling causes a U-turn. - C_L: model keeps increasing with velocity in extrapolation (0.56→0.68). True C_L is ~velocity independent, so this spurious increase is bad. So the network does NOT extrapolate the linear trend; it turns around. This will hurt at v=78. Let me confirm the true behavior: compute, for holdout cases, actual C_D vs the in-range prediction. The key issue is the reversal. I want the model to continue the near-linear trend. Now, strategies to fix extrapolation: 1. **Velocity augmentation** to synthetically cover high velocities , most direct fix. 2. **Reduce velocity sensitivity** via large feat_std on velocity , prevents wild swings but also kills useful trend. 3. **Regularization** to encourage monotonic/linear behavior. The cleanest and most controllable: **physics-guided velocity augmentation.** I'll synthesize training examples at higher velocities by taking existing cases and relabeling. To relabel I need the velocity→(C_D,C_L) law. Let me estimate the law from data. Since C_L is ~independent of v, for augmentation I keep C_L unchanged when changing v. For C_D, I need C_D(v2)/C_D(v1) or C_D(v2)-C_D(v1). From the linear reference model, the C_D velocity coefficient: let me estimate dC_D/dv. Actually, let me estimate a multiplicative model: C_D = C_D_ref * (v/v_ref)^p. Let me fit p from data (partialling out geometry and aoa). But this is getting complex. Alternative, simpler but very effective: **Augment by scaling velocity within each batch and assume coefficients roughly invariant (for C_L exactly, for C_D approximately), but ALSO add examples where we extend the velocity range.** Hmm. Actually, let me reconsider. The most robust and honest approach to "continue the trend linearly" is a **data augmentation that extrapolates velocity using the locally-fitted linear trend**. But wait , there's a subtlety. If I don't know the true C_D at v=78 for a given geometry, any augmentation injects my assumption. If my assumption (e.g., linear continuation of dC_D/dv) is decent, it'll help; if wrong, it hurts. Given the physics (C_D coefficient decreases slowly, ~monotonic), linear continuation is far better than the model's spurious U-turn. Let me estimate the velocity dependence of C_D more carefully, controlling for geometry+aoa, to get a reliable augmentation law. Approach: For C_D, fit C_D ~ geometry_features + aoa + aoa^2 + beta*v (linear). The beta gives dC_D/dv. From run earlier, with-vel-linear improved holdout. Let me extract beta and also check if a multiplicative (log-log) form is better. Actually, let me think about whether I even need augmentation, or whether I can just make the network extrapolate linearly by construction. Another idea: **Feed velocity in a way that the network's natural extrapolation is linear.** The network applies Conv1d (linear) then BN then GELU. For a single feature pathway, if the weight on velocity is positive and large, GELU(wx+b) ≈ wx+b for large positive argument (GELU is ~identity for large positive, ~0 for large negative). So if I arrange for velocity's contribution to keep pre-activations in the positive/linear region of GELU during extrapolation, it continues linearly. But I can't easily control that. Let me just go with augmentation , it's the most reliable. Let me estimate the C_D velocity law robustly. Plan for augmentation: - For C_L: treat as velocity-invariant → when I change v, keep C_L. - For C_D: use C_D(v) = C_D_orig + slope*(v - v_orig), where slope estimated globally (or C_D_orig*(v/v_orig)^p). Actually, even cleaner: a purely **multiplicative** model might capture …[truncated]

This is the key diagnosis. The model learns the correct **decreasing** C_D trend inside the training range (0.0139→0.0122 as v goes 31→65) but then **reverses** in extrapolation (back up to 0.0154 at v=90) , a classic nonlinear extrapolation failure. C_L also spuriously inflates. At the real test velocity (~78) this bias is large. Let me quantify the true velocity law for C_D so I can correct this.

bash

cd /app && python -c "
import torch, numpy as np
from numpy.linalg import lstsq
tr=torch.load('/app/data/train/split.pt',weights_only=True)
pts=tr['points'].numpy(); tg=tr['targets'].numpy()
v=pts[:,0,2]; aoa=pts[:,0,3]; cd=tg[:,0]; cl=tg[:,1]
y=pts[:,:,1]
thick=y.max(1)-y.min(1); ymean=y.mean(1); ymax=y.max(1); ymin=y.min(1)
geo=np.column_stack([thick,ymean,ymax,ymin,aoa,aoa**2])
# log-log fit for C_D velocity exponent p, controlling geometry/aoa
X=np.column_stack([np.ones_like(v), geo, np.log(v)])
beta,_,_,_=lstsq(X, np.log(cd), rcond=None)
print('C_D ~ v^p  exponent p =', beta[-1])
# linear slope model
X2=np.column_stack([np.ones_like(v), geo, v])
beta2,_,_,_=lstsq(X2, cd, rcond=None)
print('C_D linear dC_D/dv =', beta2[-1], ' (mean C_D=%.4f)'%cd.mean())
# For C_L exponent
Xl=np.column_stack([np.ones_like(v), geo, np.log(v)])
betal,_,_,_=lstsq(Xl, np.log(np.clip(cl,1e-3,None)), rcond=None)
print('C_L ~ v^q exponent q =', betal[-1], '(near 0 => v-independent)')
# residual correlation check: does v help beyond geo for C_L?
Xl2=np.column_stack([np.ones_like(v), geo]); bl2,_,_,_=lstsq(Xl2,cl,rcond=None)
res=cl-Xl2@bl2; print('corr(resid C_L, v)=', np.corrcoef(res,v)[0,1])
"

output

C_D ~ v^p  exponent p = -0.21050662
C_D linear dC_D/dv = -5.6362576e-05  (mean C_D=0.0128)
C_L ~ v^q exponent q = 0.27397084 (near 0 => v-independent)
corr(resid C_L, v)= 0.04640957662693094

Beautiful. The C_D velocity exponent p ≈ -0.21, which is remarkably close to the classic turbulent skin-friction scaling C_f ~ Re^(-0.2)! This is strong physical confirmation. So: **C_D(v) ≈ C_D_ref * (v / v_ref)^(-0.21)** For C_L: the log-log exponent is 0.27 but the residual correlation with v is only 0.046 (negligible), and earlier corr(v,cl) was -0.02. The 0.27 exponent in log space is likely an artifact of the log transform with small/negative C_L values (clipping). The residual correlation ~0.046 confirms C_L is essentially velocity-independent. So for C_L augmentation: keep constant. Now I can build physics-based velocity augmentation: - Pick a case with (geo, aoa, v_orig, C_D_orig, C_L_orig). - Sample a new target velocity v_new (including high values up to ~85-90 to cover test). - New features: set velocity channel to v_new. - New targets: C_D_new = C_D_orig * (v_new/v_orig)^(-0.21); C_L_new = C_L_orig (unchanged). This lets the network SEE high-velocity examples with physically correct targets, so it won't need to extrapolate blindly. This is elegant and well-grounded. Let me validate this augmentation law on the velocity holdout: train with augmentation on v<=65 data, extended to high v, and check holdout (v>65) , it should improve a lot, especially C_D. But careful: the exponent -0.21 was fit on ALL training data (v up to 75). For the holdout experiment I should fit it only on the training subset (v<=65) to avoid leakage. Let me incorporate the exponent estimation inside the training function (fit from training portion only). Actually even better , let me make the augmentation robust to the exact exponent. Let me verify exponent stability on the v<=65 subset. Let me also reconsider: is a single global exponent good enough, or does it vary with geometry/aoa? For robustness, a single global exponent is simplest and likely fine. Let me check exponent on subset and also per-aoa sign stability. Let me now design the augmentation training and test it on the holdout. Let me update the harness to support physics velocity augmentation. Augmentation design choices: - Probability/fraction of augmented samples per batch. - Range of v_new: I'll sample v_new from a range that extends beyond training, e.g., uniform[31, 90] or centered to emphasize high velocities. Since test is 75-82, I want good coverage there. I'll sample v_new uniformly in [v_min_train, 92] perhaps, or a mixture. - Apply to both original and augmented: Actually I can just, for each sample in a batch, with probability p_aug, replace v with a random v_new and rescale C_D. Let me implement: for each training example, on each epoch, with prob p_aug, draw v_new ~ Uniform(lo, hi) and set velocity=v_new, C_D *= (v_new/v_orig)^exponent, C_L unchanged. This is "velocity resampling augmentation." The exponent is estimated from the available training data. Note targets are standardized. Augmentation must be applied in physical space then re-standardized. Let me keep raw targets around and standardize after augmentation, OR apply scaling in physical space. I'll store physical targets and feat in physical space, then standardize inside the loop after augmentation. Simpler: keep xtr as standardized features but I need to modify velocity channel , which is standardized. Easier to do augmentation in physical space: keep points_phys and targets_phys, augment, then standardize on the fly. Let me restructure the train function to take physical tensors and the normalization constants, and do standardization inside. Let me rewrite harness train to operate in physical space with augmentation. Let me also think: should I also augment toward LOWER velocities? Not necessary for test but adds robustness and keeps the trend anchored. Sampling across the whole range [31,90] teaches the network the full C_D ∝ v^-0.21 law, which naturally extends to 78. I'll sample v_new from Uniform(30, 90). That directly teaches monotonic decreasing C_D across the entire span including test. …[truncated]

The exponent **p ≈ -0.21** is a striking match to the classic turbulent skin-friction law C_f ∝ Re^(−0.2) , strong physical grounding. And C_L's residual correlation with velocity is negligible (0.046), confirming it's velocity-independent. This gives me a principled augmentation law: **C_D(v_new) = C_D · (v_new/v_orig)^(−0.21), C_L unchanged.** Let me verify the exponent is stable on the v≤65 subset (to avoid leakage in my holdout test), then implement physics-based velocity augmentation.

bash

cd /app && python -c "
import torch, numpy as np
from numpy.linalg import lstsq
tr=torch.load('/app/data/train/split.pt',weights_only=True)
pts=tr['points'].numpy(); tg=tr['targets'].numpy()
v=pts[:,0,2]; aoa=pts[:,0,3]; cd=tg[:,0]
y=pts[:,:,1]
thick=y.max(1)-y.min(1); ymean=y.mean(1); ymax=y.max(1); ymin=y.min(1)
geo=np.column_stack([thick,ymean,ymax,ymin,aoa,aoa**2])
for lim in [55,60,65,75]:
    m=v<=lim
    X=np.column_stack([np.ones(m.sum()), geo[m], np.log(v[m])])
    beta,_,_,_=lstsq(X, np.log(cd[m]), rcond=None)
    print(f'v<={lim}: n={m.sum():3d}  C_D exponent p={beta[-1]:.3f}')
"

output

v<=55: n=337  C_D exponent p=-0.157
v<=60: n=413  C_D exponent p=-0.189
v<=65: n=482  C_D exponent p=-0.209
v<=75: n=630  C_D exponent p=-0.211

The exponent is reasonably stable (-0.16 to -0.21) and converges to ~-0.21 as more data is included. Using the subset v<=65 gives -0.209, very close to the full -0.211. For my holdout experiment (train on v<=65), I'll estimate the exponent from that subset (-0.209). For the final model (all data), I'll use -0.211. Good, no major leakage concern. Let me implement the physics-based velocity augmentation in the harness and test on the holdout. I'll rewrite train_model to operate in physical space with optional augmentation. Let me create a cleaner, self-contained experiment module.

Exponent is stable (~-0.21, estimated cleanly from each subset). Now let me implement physics-based velocity augmentation and test it against the baseline on the extrapolation holdout.

bash

cd /app && cat > exp/harness2.py << 'EOF'
import json, sys, time
import torch, numpy as np
from numpy.linalg import lstsq
sys.path.insert(0,'/app')
from candidate_model import build_model
with open('/app/task_config.json') as fh: CFG=json.load(fh)

def load(split):
    p=torch.load(f'/app/data/{split}/split.pt',weights_only=True)
    return p['points'].float(), (p['targets'].float() if 'targets' in p else None)

def nrmse(pred,true):
    out=[]
    for i in range(true.shape[1]):
        t=true[:,i]
        out.append((torch.sqrt(torch.mean((pred[:,i]-t)**2))/t.std()).item())
    return out

def est_cd_exponent(pts,tg):
    v=pts[:,0,2].numpy(); aoa=pts[:,0,3].numpy(); cd=tg[:,0].numpy()
    y=pts[:,:,1].numpy()
    geo=np.column_stack([y.max(1)-y.min(1),y.mean(1),y.max(1),y.min(1),aoa,aoa**2])
    X=np.column_stack([np.ones_like(v),geo,np.log(v)])
    beta,_,_,_=lstsq(X,np.log(cd),rcond=None)
    return float(beta[-1])

def train_model(pts_phys, tg_phys, feat_mean, feat_std, targ_mean, targ_std, cfg, seed=0):
    torch.manual_seed(seed); np.random.seed(seed)
    model=build_model(CFG)
    epochs=cfg.get('epochs',120); bs=cfg.get('bs',32)
    opt=torch.optim.Adam(model.parameters(),lr=cfg.get('lr',1e-3),weight_decay=cfg.get('wd',1e-4))
    sched=torch.optim.lr_scheduler.CosineAnnealingLR(opt,T_max=epochs)
    tw=torch.tensor(cfg.get('target_weights',[1.0,1.0])).float()
    n=pts_phys.shape[0]
    p_aug=cfg.get('p_aug',0.0); vlo=cfg.get('vlo',30.0); vhi=cfg.get('vhi',90.0)
    expo=cfg.get('cd_expo',-0.21); geo_jit=cfg.get('geo_jit',0.0)
    fm=feat_mean.view(1,1,-1); fs=feat_std.view(1,1,-1)
    tm=targ_mean.view(1,-1); ts=targ_std.view(1,-1)
    for ep in range(epochs):
        model.train(); idx=torch.randperm(n)
        for s in range(0,n,bs):
            b=idx[s:s+bs]
            P=pts_phys[b].clone(); T=tg_phys[b].clone()
            if p_aug>0:
                m=torch.rand(P.shape[0])<p_aug
                if m.any():
                    vnew=torch.empty(m.sum()).uniform_(vlo,vhi)
                    vorig=P[m,0,2]
                    ratio=(vnew/vorig)
                    P[m,:,2]=vnew.view(-1,1)
                    T[m,0]=T[m,0]*ratio.pow(expo)   # C_D scales
                    # C_L unchanged
            if geo_jit>0:
                P[:,:,0:2]+=torch.randn_like(P[:,:,0:2])*geo_jit
            xb=(P-fm)/fs; yb=(T-tm)/ts
            opt.zero_grad(set_to_none=True)
            pred=model(xb)
            loss=(tw.view(1,-1)*(pred-yb)**2).mean()
            loss.backward(); opt.step()
        sched.step()
    return model

def evaluate(model, pts_phys, tg_phys, feat_mean, feat_std, targ_mean, targ_std):
    model.eval()
    xb=(pts_phys-feat_mean.view(1,1,-1))/feat_std.view(1,1,-1)
    with torch.no_grad():
        pred=model(xb)*targ_std.view(1,-1)+targ_mean.view(1,-1)
    return nrmse(pred,tg_phys), pred
EOF
echo "harness2 written"

output

harness2 written

bash

cd /app && cat > exp/run2.py << 'EOF'
import sys, time, torch, numpy as np
sys.path.insert(0,'/app/exp'); sys.path.insert(0,'/app')
from harness2 import load, train_model, evaluate, est_cd_exponent

pts,tg=load('train')
v=pts[:,0,2]; mtr=v<=65; mte=v>65
ptr,ttr=pts[mtr],tg[mtr]; pte,tte=pts[mte],tg[mte]
flat=ptr.reshape(-1,4)
feat_mean=flat.mean(0); feat_std=flat.std(0).clamp_min(1e-8)
targ_mean=ttr.mean(0); targ_std=ttr.std(0).clamp_min(1e-8)
expo=est_cd_exponent(ptr,ttr); print('estimated exponent on train subset:',round(expo,3))

def run(cfg,seeds=(0,1),label=''):
    accs=[]
    for s in seeds:
        m=train_model(ptr,ttr,feat_mean,feat_std,targ_mean,targ_std,cfg,seed=s)
        nr,_=evaluate(m,pte,tte,feat_mean,feat_std,targ_mean,targ_std)
        accs.append(nr)
    a=np.array(accs)
    print(f'{label:28s} C_D={a[:,0].mean():.4f} C_L={a[:,1].mean():.4f} mean={a.mean(1).mean():.4f}')
    return a.mean(1).mean()

base=dict(epochs=120,bs=32,lr=1e-3,wd=1e-4)
t0=time.time()
run(base,label='baseline (no aug)')
aug=dict(base,p_aug=0.5,vlo=30,vhi=90,cd_expo=expo)
run(aug,label='vel-aug p=0.5 [30,90]')
print('elapsed %.0fs'%(time.time()-t0))
EOF
python exp/run2.py

output

estimated exponent on train subset: -0.209
baseline (no aug)            C_D=0.1611 C_L=0.1526 mean=0.1569
vel-aug p=0.5 [30,90]        C_D=0.2524 C_L=0.0559 mean=0.1541
elapsed 254s

Interesting and surprising results: - Baseline (2 seeds avg): C_D=0.161, C_L=0.153, mean=0.157. - Vel-aug: C_D=0.252 (WORSE!), C_L=0.056 (much BETTER), mean=0.154. So augmentation dramatically helped C_L (0.153→0.056) but hurt C_D (0.161→0.252). Why did C_D get worse? Possibly because: 1. The exponent law, applied over a wide range [30,90] with random decorrelated velocities, may distort the C_D learning , when I scale C_D by (vnew/vorig)^-0.21 with vnew up to 90 and vorig as low as 31, the ratio can be ~3x, exponent -0.21 → factor 0.78; or vnew=30,vorig=65 → ratio 0.46 → factor 1.16. These are moderate. But maybe the augmentation adds noise to C_D because the TRUE relationship has geometry-dependent exponents, and forcing a global exponent adds label noise to C_D. 2. Actually, the bigger issue: by decorrelating velocity from geometry and aoa, I remove a potentially useful (spurious in-sample but maybe real) correlation. Hmm. Wait, but C_L improved massively. Why? Because augmentation taught the network that C_L doesn't depend on velocity (since we kept C_L fixed while varying v). This killed the spurious velocity→C_L inflation I saw in the probe. For C_D, the issue might be that p_aug=0.5 is too aggressive, injecting too much augmented (approximate) labels and overwhelming the real data. Or the exponent applied per-sample creates inconsistency. Let me reconsider. The net mean barely changed (0.157→0.154) because C_D got worse while C_L got better. I need BOTH good. Idea: Apply velocity augmentation but be smarter: - For C_L: full augmentation is great (keep C_L fixed across v). - For C_D: the augmentation law might be too crude. Let me reconsider why C_D got worse. Let me probe the augmented model's velocity response for C_D. Maybe the exponent -0.21 is actually too strong or the issue is decorrelation. Actually, wait. Let me reconsider the holdout itself. The holdout is v in (65,75]. In this range, the TRUE C_D follows the law with exponent ~-0.21. The baseline model already does OK here (0.161) because it's interpolating-ish (65-75 is just above training 31-65, and the model's learned in-range trend (decreasing) is still roughly valid at 65-75 before it reverses at ~80+). So in THIS holdout (65-75), the baseline isn't yet in the catastrophic reversal zone. That's why augmentation doesn't help C_D much here. But at v=78 (real test), the baseline reverses and augmentation should help more. My holdout (65-75) underestimates the benefit of augmentation for C_D at the true test range! Let me make a HARDER holdout that better matches the real test: train on v<=58, hold out v>68 (gap, and higher). Then re-evaluate. This better simulates extrapolating to 78. Also, let me reconsider why aug HURT C_D at 65-75. If the model WITHOUT aug gets 0.161 at 65-75 and aug gets 0.252, the aug is actively harmful in the near-extrapolation zone. That's concerning. Let me probe the aug model's C_D velocity curve. Let me investigate with the probe on the augmented model and also test a harder holdout. Let me also try lower p_aug and a narrower/ different augmentation velocity range. Let me think about the decorrelation problem more. In the real AirFRANS data, is velocity correlated with geometry or aoa in the training set? If the sampling is independent, there's no correlation and decorrelation via augmentation is harmless. Let me check corr(v, aoa) and corr(v, thickness). Let me also reconsider: maybe instead of uniform random vnew decorrelated from everything, I should augment more conservatively: only augment a fraction, and draw vnew near the original or extending upward, preserving local structure. Let me run diagnostics.

Augmentation **massively helped C_L** (0.153→0.056, killing the spurious velocity→lift inflation) but **hurt C_D** (0.161→0.252) in this holdout. Two things to check: (1) my holdout (v 65–75) is *near* the training edge, where the baseline hasn't yet entered its catastrophic reversal , so it understates aug's benefit for C_D at the true test range (~78); (2) why aug hurts C_D here. Let me probe the aug model's C_D curve and check velocity-geometry correlations.

bash

cd /app && python -c "
import torch, numpy as np
tr=torch.load('/app/data/train/split.pt',weights_only=True)
pts=tr['points']; tg=tr['targets']
v=pts[:,0,2].numpy(); aoa=pts[:,0,3].numpy()
y=pts[:,:,1].numpy(); thick=y.max(1)-y.min(1)
cd=tg[:,0].numpy(); cl=tg[:,1].numpy()
print('corr(v,aoa)=%.3f corr(v,thick)=%.3f'%(np.corrcoef(v,aoa)[0,1],np.corrcoef(v,thick)[0,1]))
print('corr(aoa,thick)=%.3f'%np.corrcoef(aoa,thick)[0,1])
" 
echo "--- probe aug model C_D curve ---"
cat > exp/probe2.py << 'EOF'
import sys, torch, numpy as np
sys.path.insert(0,'/app/exp'); sys.path.insert(0,'/app')
from harness2 import load, train_model, evaluate, est_cd_exponent
pts,tg=load('train'); v=pts[:,0,2]; mtr=v<=65
ptr,ttr=pts[mtr],tg[mtr]
flat=ptr.reshape(-1,4); fm=flat.mean(0); fs=flat.std(0).clamp_min(1e-8)
tm=ttr.mean(0); ts=ttr.std(0).clamp_min(1e-8)
expo=est_cd_exponent(ptr,ttr)
for lbl,cfg in [('noaug',dict(epochs=120)),('aug',dict(epochs=120,p_aug=0.5,vlo=30,vhi=90,cd_expo=expo))]:
    m=train_model(ptr,ttr,fm,fs,tm,ts,cfg,seed=0); m.eval()
    sel=torch.where(~mtr)[0][:40]; base=pts[sel].clone()
    print(lbl,'C_D by vel:')
    for vv in [31,55,65,75,82,90]:
        b=base.clone(); b[:,:,2]=vv; xb=(b-fm.view(1,1,-1))/fs.view(1,1,-1)
        with torch.no_grad(): pr=m(xb)*ts+tm
        print('  v=%3d C_D=%.5f C_L=%.4f'%(vv,pr[:,0].mean(),pr[:,1].mean()))
EOF
python exp/probe2.py

output

corr(v,aoa)=-0.015 corr(v,thick)=0.040
corr(aoa,thick)=-0.023
--- probe aug model C_D curve ---
noaug C_D by vel:
  v= 31 C_D=0.01386 C_L=0.5363
  v= 55 C_D=0.01257 C_L=0.5623
  v= 65 C_D=0.01222 C_L=0.5635
  v= 75 C_D=0.01292 C_L=0.5935
  v= 82 C_D=0.01395 C_L=0.6270
  v= 90 C_D=0.01540 C_L=0.6778
aug C_D by vel:
  v= 31 C_D=0.01440 C_L=0.6032
  v= 55 C_D=0.01342 C_L=0.6233
  v= 65 C_D=0.01274 C_L=0.6246
  v= 75 C_D=0.01230 C_L=0.6170
  v= 82 C_D=0.01206 C_L=0.6102
  v= 90 C_D=0.01193 C_L=0.6062

Now the augmented model's velocity curves are MUCH more physical: - C_D now monotonically DECREASES with velocity (0.0144 → 0.0119 from v=31→90), following the ∝ v^-0.21 law. No more reversal! - C_L is now nearly flat (0.603 → 0.606, peaking 0.625 at 65). Much better than the no-aug inflation to 0.68. So the augmentation FIXED the velocity extrapolation behavior beautifully. The C_D curve is now monotonic and physical at high velocity. But then why did the holdout NRMSE for C_D get WORSE (0.161→0.252)? This must be a LEVEL/calibration issue, not a trend issue. Look: at v=75, aug predicts C_D=0.0123 vs noaug 0.0129. The aug model predicts systematically... let me think. The holdout is v in 65-75. Actually, the issue: the augmented model's overall C_D predictions might be biased. Look at v=31: aug=0.0144 vs noaug=0.0139. The aug model shifted the whole C_D curve. The aug C_D at 65-75 (0.0127→0.0123) vs noaug (0.0122→0.0129). Hmm, at v=75 aug=0.0123 noaug=0.0129; true mean at v>65... earlier true holdout C_D mean was 0.0118. So aug (0.0123) is actually CLOSER to truth (0.0118) than noaug (0.0129) at the high end! So why worse NRMSE? NRMSE is about the full error distribution across 148 holdout cases, dominated by per-case geometry accuracy, not just the mean. The augmentation may have REDUCED the model's ability to fit per-case C_D variation (geometry-driven), because half the batch had scrambled velocity with approximate labels, adding noise. The C_D signal is subtle and the augmentation's global-exponent assumption injects per-case label noise (since true exponent varies by geometry), degrading the fit. Key tension: augmentation helps the velocity TREND (crucial at v=78) but its approximate global exponent adds noise that hurts per-case C_D precision. Solutions: 1. Lower p_aug (e.g., 0.25) , less noise, still teaches the trend. 2. Keep some original (un-augmented) samples always, and add augmented ones as EXTRA rather than replacing , so the network sees all real data plus augmented data. 3. Better: augment by extending velocity UP from the original (vnew >= vorig, smaller multiplicative change) rather than full [30,90] random , reduces the magnitude of label adjustment and keeps it physical. 4. Reduce the label noise: the exponent law for C_D might need to preserve the per-case C_D better. Since augmentation multiplies C_D by a ratio, if vnew is close to vorig the perturbation is small. Actually, the most important realization: **the holdout at v=65-75 is NOT where augmentation pays off** , it's at v=78+. In the 65-75 range, the no-aug model is still decent (hasn't fully reversed), so the added noise from aug makes C_D worse there. But at v=78-82 (real test), the no-aug model reverses badly while aug stays physical. So I need a holdout that actually tests v≈78. Let me build a harder holdout: train on v<=60, test on v>=70 (mean ~72), OR even better, since I can't get training-held-out data above 75, let me at least make the gap bigger: train v<=58, holdout v in [70,75]. The holdout mean would be ~72, and there's a 12 m/s gap. This better approximates extrapolating to 78. But fundamentally, I cannot directly validate at v=78 because I have no labeled data there. The public_test has no labels. So I must rely on: (a) physics reasoning, (b) the proxy holdout trend. Given the physics is clear (C_D ∝ v^-0.21, C_L flat) and the probe shows augmentation produces the physically correct extrapolation, I'm fairly confident augmentation helps at v=78 even though it slightly hurts the 65-75 proxy for C_D. But I want to minimize the C_D damage while keeping the trend fix. Let me tune: - Lower p_aug. - Augment upward-biased velocities (so the model especially learns the high-v regime). - Maybe use a gentler approach: add augmented samples as EXTRA data (concat) rather than replacing within batch. Let me also reconsider: maybe I should only lightly augment and rely on the fact that the net mean is already similar. Actually C_L i …[truncated]

The augmentation makes the physics correct: the aug model's C_D now **monotonically decreases** with velocity (0.0144→0.0119) following the v^−0.21 law with no reversal, and C_L stays flat. The C_D NRMSE got worse only in the *near* holdout (65–75, where the no-aug model hasn't yet reversed) because the global-exponent labels add some per-case noise. Velocity is uncorrelated with geometry/aoa (corr≈0), so decorrelating via augmentation is safe. The real test is at v≈78 where no-aug reverses catastrophically. Let me build a **harder holdout with a velocity gap** (train v≤60, test v≥70) and tune augmentation strength to keep the trend fix while limiting C_D noise.

bash

cd /app && cat > exp/run3.py << 'EOF'
import sys, time, torch, numpy as np
sys.path.insert(0,'/app/exp'); sys.path.insert(0,'/app')
from harness2 import load, train_model, evaluate, est_cd_exponent
pts,tg=load('train'); v=pts[:,0,2]
mtr=v<=60; mte=v>=70
ptr,ttr=pts[mtr],tg[mtr]; pte,tte=pts[mte],tg[mte]
print('HARD holdout: train(v<=60)=%d  test(v>=70)=%d  test mean v=%.1f'%(mtr.sum(),mte.sum(),v[mte].mean()))
flat=ptr.reshape(-1,4); fm=flat.mean(0); fs=flat.std(0).clamp_min(1e-8)
tm=ttr.mean(0); ts=ttr.std(0).clamp_min(1e-8)
expo=est_cd_exponent(ptr,ttr); print('exponent:',round(expo,3))
def run(cfg,seeds=(0,1,2),label=''):
    accs=[]
    for s in seeds:
        m=train_model(ptr,ttr,fm,fs,tm,ts,cfg,seed=s)
        nr,_=evaluate(m,pte,tte,fm,fs,tm,ts); accs.append(nr)
    a=np.array(accs)
    print(f'{label:30s} C_D={a[:,0].mean():.4f} C_L={a[:,1].mean():.4f} mean={a.mean(1).mean():.4f} worst={a.max(1).mean():.4f}')
t0=time.time()
run(dict(epochs=100),label='baseline no-aug')
for p in [0.2,0.35,0.5]:
    run(dict(epochs=100,p_aug=p,vlo=30,vhi=90,cd_expo=expo),label=f'aug p={p} [30,90]')
print('elapsed %.0fs'%(time.time()-t0))
EOF
python exp/run3.py

output

[stderr]
Shell command timed out.
Tool interaction exceeded 300 seconds.

The shell timed out at 300s. 4 configs × 3 seeds × 100 epochs = 12 runs × ~66s = ~13 min. Too long for one call. Let me restart and run in background, or reduce scope. Let me run things in the background and poll, or reduce to fewer seeds/epochs and split into multiple calls. Let me restart the tool and run experiments in the background with output to a file.

The sweep exceeded the 300s limit. Let me restart and run experiments in the background, writing results to a file I can poll.

bash

restart: true

output

<system>tool has been restarted.</system>

bash

cd /app && nohup python exp/run3.py > exp/run3.log 2>&1 &
echo "started pid $!"

output

started pid 585

Let me wait and poll the results while it runs in the background.

bash

cd /app && sleep 240 && cat exp/run3.log

output

<system>Tool ran without output or errors</system>

The log is empty? The print statements should have output. Maybe output buffering. Let me check if the process is still running and the log.

bash

cd /app && ls -la exp/run3.log && echo "---content---" && cat exp/run3.log && echo "---proc---" && ps aux | grep run3 | grep -v grep | head

output

-rw-r--r-- 1 h2tagent h2tagent 0 Jun 19 21:46 exp/run3.log
---content---
---proc---
h2tagent   587 1437  5.0 7032844 3635268 ?     Rl   21:46  58:27 python exp/run3.py

The process is running but output is buffered (Python buffers stdout when redirected to a file). I should have used `python -u`. The process is still running. Let me wait more and the buffer should flush at program end, or I can check differently. Actually, the print statements won't flush until buffer fills or program ends. Let me kill it and rerun with `-u` and flush, but I've already spent ~5 min of compute. Actually, let me not waste the work. The issue is just buffering. Let me wait for it to finish (it prints elapsed at end, flushing everything). 12 runs × ~66s ≈ 13 min total. It's been ~5 min. Let me wait more. But I also want to reduce future cost. Let me restructure to write results incrementally with flush. Actually, let me kill it and restart with unbuffered + incremental flushing and fewer seeds (2) to speed up, since I realize 3 seeds × 4 configs × 100 epochs is too slow. Let me use 2 seeds and 80 epochs for screening. Let me also make each config write to log immediately. Let me kill and restart more efficiently.

Output is buffered. Let me kill it and rerun unbuffered with incremental flushing and a lighter screening budget (2 seeds, 80 epochs) so I get results faster.

bash

cd /app && kill 587 2>/dev/null; sleep 2; pkill -f run3.py 2>/dev/null; sleep 1
sed -i 's/seeds=(0,1,2)/seeds=(0,1)/; s/epochs=100/epochs=80/g' exp/run3.py
# add flush to prints
python - << 'EOF'
import re
s=open('exp/run3.py').read()
s=s.replace("print(f'{label:30s}","import sys as _s; print(f'{label:30s}").replace("mean={a.mean(1).mean():.4f} worst={a.max(1).mean():.4f}')","mean={a.mean(1).mean():.4f} worst={a.max(1).mean():.4f}',flush=True)")
open('exp/run3.py','w').write(s)
print('patched')
EOF
nohup python -u exp/run3.py > exp/run3.log 2>&1 &
echo "started pid $!"

output

patched
started pid 648

bash

cd /app && sleep 200 && cat exp/run3.log

output

HARD holdout: train(v<=60)=413  test(v>=70)=70  test mean v=72.5
exponent: -0.189
baseline no-aug                C_D=0.4775 C_L=0.2638 mean=0.3706 worst=0.4775
aug p=0.2 [30,90]              C_D=0.2012 C_L=0.0700 mean=0.1356 worst=0.2012
aug p=0.35 [30,90]             C_D=0.1796 C_L=0.0606 mean=0.1201 worst=0.1796

Now with the HARDER holdout (train v<=60, test v>=70, mean 72.5), the results are dramatic and clear: - Baseline no-aug: C_D=0.478, C_L=0.264, mean=0.371, worst=0.478 , CATASTROPHIC extrapolation! - aug p=0.2: C_D=0.201, C_L=0.070, mean=0.136, worst=0.201 - aug p=0.35: C_D=0.180, C_L=0.061, mean=0.120, worst=0.180 So with a real velocity gap, augmentation is MASSIVELY better on BOTH targets. The baseline catastrophically fails (as predicted by the probe's reversal). This confirms augmentation is the right approach and that my earlier near-holdout (65-75) was too easy to reveal the benefit. p=0.35 is better than p=0.2. Let me see p=0.5 result (still running). Let me wait for it.

Now with a real velocity gap, the picture is decisive: the **baseline catastrophically fails** (C_D=0.478, C_L=0.264) while augmentation improves *both* targets enormously (p=0.35: C_D=0.180, C_L=0.061). This confirms the earlier near-holdout was masking the benefit. Let me see the p=0.5 result and then push further.

bash

cd /app && sleep 60 && cat exp/run3.log | tail -3

output

aug p=0.35 [30,90]             C_D=0.1796 C_L=0.0606 mean=0.1201 worst=0.1796
aug p=0.5 [30,90]              C_D=0.1749 C_L=0.0474 mean=0.1111 worst=0.1749
elapsed 250s

p=0.5 is even better: C_D=0.175, C_L=0.047, mean=0.111, worst=0.175. So higher augmentation probability helps on this hard holdout. Let me push p higher (0.6, 0.7) and also tune the velocity sampling range and other hyperparameters. The trend: more augmentation → better extrapolation. This makes sense because the test is pure extrapolation; the more the network sees high-velocity examples, the better. But I should be careful not to over-augment and lose the real-data signal entirely. At p=0.7, 70% of samples have scrambled velocity. Let me test p=0.6, 0.75. Also, let me reconsider the velocity sampling. Currently vnew ~ Uniform(30,90). The test is 75-82. Maybe I should bias sampling toward higher velocities, or extend vhi to 95 to bracket the test well. Let me also consider that the real hidden test might go beyond 82 (it says "higher-speed, higher-Reynolds end"). Public test max is 81.6. The hidden scored set is "sampled from the higher-speed, higher-Reynolds end" , likely similar range, maybe up to ~85-90. Extending vhi to ~95 gives margin. Let me now run a second sweep: p in {0.5, 0.65, 0.8}, and vary vhi and sampling distribution. Let me also test the exponent sensitivity (the hard-holdout exponent was -0.189; true is ~-0.21). Let me fix exponent at -0.21 (the full-data estimate) since that's more accurate and what I'll use finally; but for the holdout experiment I should use subset estimate to avoid leakage. Actually using -0.21 vs -0.189 , let me test sensitivity. Let me also think about whether to emphasize high velocities in sampling. Since the scored set is specifically high-velocity, and my augmentation is the only way the model learns that regime, I might want to oversample the high range. But I also need the model to fit the real (low-mid velocity) training data well for the geometry signal. A uniform [30,95] seems balanced. Let me test a high-biased sampling too. Let me run sweep 2. I'll keep 2 seeds, 80 epochs, hard holdout. Let me structure to finish within ~250s: 4 configs × 2 seeds × 80 epochs ≈ 4×2×33s ≈ 264s. Close. Let me do 3 configs to be safe, or reduce epochs to 70. Let me do 4 configs at 70 epochs. Configs to test: 1. p=0.5, [30,95] (extend vhi) 2. p=0.65, [30,95] 3. p=0.8, [30,95] 4. p=0.65, [30,95], high-biased sampling (vnew = 30 + (95-30)*rand^0.5 to bias high)? Let me implement a 'vhigh_bias' option. Actually, simpler: let me just test p and vhi first, then sampling shape. Let me do: 1. p=0.5 vhi=95 2. p=0.65 vhi=95 3. p=0.8 vhi=95 4. p=0.65 vhi=95 exponent=-0.21 (vs subset -0.189) Let me write run4.py.

More augmentation is better: **p=0.5 gives mean=0.111** (C_D=0.175, C_L=0.047). Since the scored set is pure high-velocity extrapolation, let me push `p_aug` higher, extend the sampling ceiling to bracket the test (and possible beyond-82 cases), and check exponent sensitivity.

bash

cd /app && cat > exp/run4.py << 'EOF'
import sys, time, torch, numpy as np
sys.path.insert(0,'/app/exp'); sys.path.insert(0,'/app')
from harness2 import load, train_model, evaluate, est_cd_exponent
pts,tg=load('train'); v=pts[:,0,2]
mtr=v<=60; mte=v>=70
ptr,ttr=pts[mtr],tg[mtr]; pte,tte=pts[mte],tg[mte]
flat=ptr.reshape(-1,4); fm=flat.mean(0); fs=flat.std(0).clamp_min(1e-8)
tm=ttr.mean(0); ts=ttr.std(0).clamp_min(1e-8)
expo=est_cd_exponent(ptr,ttr)
def run(cfg,seeds=(0,1),label=''):
    accs=[]
    for s in seeds:
        m=train_model(ptr,ttr,fm,fs,tm,ts,cfg,seed=s)
        nr,_=evaluate(m,pte,tte,fm,fs,tm,ts); accs.append(nr)
    a=np.array(accs)
    print(f'{label:32s} C_D={a[:,0].mean():.4f} C_L={a[:,1].mean():.4f} mean={a.mean(1).mean():.4f} worst={a.max(1).mean():.4f}',flush=True)
t0=time.time()
run(dict(epochs=70,p_aug=0.5,vlo=30,vhi=95,cd_expo=expo),label='p=0.5 vhi95')
run(dict(epochs=70,p_aug=0.65,vlo=30,vhi=95,cd_expo=expo),label='p=0.65 vhi95')
run(dict(epochs=70,p_aug=0.8,vlo=30,vhi=95,cd_expo=expo),label='p=0.8 vhi95')
run(dict(epochs=70,p_aug=0.65,vlo=30,vhi=95,cd_expo=-0.21),label='p=0.65 expo-0.21')
print('elapsed %.0fs'%(time.time()-t0),flush=True)
EOF
nohup python -u exp/run4.py > exp/run4.log 2>&1 &
echo "started $!"

output

started 703

bash

cd /app && sleep 240 && cat exp/run4.log

output

p=0.5 vhi95                      C_D=0.1691 C_L=0.0548 mean=0.1120 worst=0.1691
p=0.65 vhi95                     C_D=0.1840 C_L=0.0591 mean=0.1215 worst=0.1840
p=0.8 vhi95                      C_D=0.1687 C_L=0.0588 mean=0.1138 worst=0.1687
p=0.65 expo-0.21                 C_D=0.1770 C_L=0.0587 mean=0.1178 worst=0.1770
elapsed 169s

Results are noisy (2 seeds). p=0.5 vhi95: mean=0.112, p=0.8: 0.114, p=0.65: 0.122. These are within noise of each other. The exponent -0.21 vs subset-0.189: 0.118 vs 0.122, basically same. So the method is robust to these choices. p in [0.5, 0.8], vhi 90-95, exponent -0.19 to -0.21 all give mean ~0.11-0.12. This is great , the approach is not very sensitive to hyperparameters, meaning it'll be robust. The C_D is stuck around 0.17, C_L around 0.055. The C_D floor (~0.17) is likely the geometry modeling limit plus the residual velocity-law imperfection. Let me now focus on improving the base model quality (geometry) and reducing variance via: 1. Ensembling (multiple seeds averaged) , reduces variance, usually improves both. 2. Geometry augmentation (jitter, point resampling/dropout) , better geometry generalization. 3. Better training (epochs, LR schedule, batch size). 4. Maybe target weighting to balance C_D vs C_L. Also, I should consider whether there's additional signal for C_D. The C_D NRMSE of 0.17 , let me see what the achievable floor is. Let me also reconsider: maybe predicting C_D in log space helps (since C_D is positive and the velocity law is multiplicative). The network predicts standardized targets. If I standardize log(C_D) instead of C_D, the multiplicative velocity law becomes additive (more natural for the network), AND the error metric... but the grader reads physical C_D. I can still output log and exponentiate? No , the inference harness does output*targ_std+targ_mean (affine). It does NOT exponentiate. So I cannot predict log(C_D) unless I can invert it via affine only. I can't. Wait, unless... the de-standardization is fixed as affine. So the model MUST output something that, after affine transform, equals physical C_D. So the model's raw output (before affine) is (C_D - targ_mean)/targ_std. I cannot put a log there. So C_D must be predicted in linear space. OK. But internally the network can do whatever. The constraint is only on the final affine mapping. So linear-space C_D it is. Let me now focus on ensembling and geometry augmentation to push down the C_D and C_L errors. Let me also test more epochs (the cosine schedule with more epochs might help). Let me think about ensembling: train K models with different seeds, average their physical predictions. But the deliverable is a SINGLE checkpoint loaded into ONE model instance. I cannot ensemble at inference because the harness loads one state_dict into one model! Let me re-read. "Write your trained checkpoint to /app/outputs/model.pt as a dict containing: state_dict: your model's state_dict()." , single model. "Your weights are loaded back into this exact architecture and run on the scored cases." So it's a single model forward pass. No ensembling at inference. So I cannot ensemble multiple networks. I must produce ONE set of weights. That means I need the single best-trained model. Ensembling via weight averaging (like SWA - Stochastic Weight Averaging) IS possible though! SWA averages weights of a single model across training checkpoints, producing one model. But averaging weights across DIFFERENT random seeds doesn't work (different basins). SWA averages along one trajectory. That could help generalization. Given BatchNorm, SWA needs a BN statistics recalibration pass. Could be worth it but adds complexity/risk. Let me focus on what reliably helps a single model: 1. Good augmentation (velocity , done; geometry jitter , test). 2. Good schedule / enough epochs. 3. SWA (optional, if time). 4. Model selection: pick the checkpoint/epoch with best proxy-extrapolation. But I can't use the real extrapolation val (no labels). I can use my constructed high-velocity holdout for selecting hyperparameters, but for the FINAL model I train on ALL data (including high-v) so there's no held-out high-v to select on. Hmm. Actually for the final model, I'll train on all 630 cases with velocity augmentation (which covers high v synthetically). I can use the …[truncated]

The method is robustly insensitive to `p_aug` (0.5–0.8), ceiling (90–95), and exponent (−0.19 to −0.21) , all give mean ≈ 0.11–0.12, which is reassuring for generalization. Now C_D (~0.17) dominates the error. Critically, I've confirmed the deliverable is a **single** checkpoint (no inference-time ensembling), so I need one well-trained model. Let me test geometry jitter, C_D loss weighting, and epoch count to push C_D down.

bash

cd /app && cat > exp/run5.py << 'EOF'
import sys, time, torch, numpy as np
sys.path.insert(0,'/app/exp'); sys.path.insert(0,'/app')
from harness2 import load, train_model, evaluate, est_cd_exponent
pts,tg=load('train'); v=pts[:,0,2]
mtr=v<=60; mte=v>=70
ptr,ttr=pts[mtr],tg[mtr]; pte,tte=pts[mte],tg[mte]
flat=ptr.reshape(-1,4); fm=flat.mean(0); fs=flat.std(0).clamp_min(1e-8)
tm=ttr.mean(0); ts=ttr.std(0).clamp_min(1e-8)
expo=est_cd_exponent(ptr,ttr)
def run(cfg,seeds=(0,1),label=''):
    accs=[]
    for s in seeds:
        m=train_model(ptr,ttr,fm,fs,tm,ts,cfg,seed=s)
        nr,_=evaluate(m,pte,tte,fm,fs,tm,ts); accs.append(nr)
    a=np.array(accs)
    print(f'{label:30s} C_D={a[:,0].mean():.4f} C_L={a[:,1].mean():.4f} mean={a.mean(1).mean():.4f} worst={a.max(1).mean():.4f}',flush=True)
base=dict(epochs=80,p_aug=0.5,vlo=30,vhi=92,cd_expo=expo)
t0=time.time()
run(dict(base,geo_jit=0.002),label='geo_jit0.002')
run(dict(base,target_weights=[2.0,1.0]),label='tw[2,1]')
run(dict(base,target_weights=[3.0,1.0]),label='tw[3,1]')
run(dict(base,epochs=140),label='epochs140')
print('elapsed %.0fs'%(time.time()-t0),flush=True)
EOF
nohup python -u exp/run5.py > exp/run5.log 2>&1 &
echo "started $!"

output

started 749

bash

cd /app && sleep 260 && cat exp/run5.log

output

geo_jit0.002                   C_D=0.1874 C_L=0.0621 mean=0.1248 worst=0.1874
tw[2,1]                        C_D=0.1826 C_L=0.0557 mean=0.1192 worst=0.1826
tw[3,1]                        C_D=0.1844 C_L=0.0601 mean=0.1222 worst=0.1844

The epochs140 result is still pending. Current results (noisy, 2 seeds): - geo_jit0.002: C_D=0.187, C_L=0.062, mean=0.125 , slightly worse, geo jitter doesn't obviously help (maybe too much or just noise). - tw[2,1]: C_D=0.183, C_L=0.056, mean=0.119 - tw[3,1]: C_D=0.184, C_L=0.060, mean=0.122 These are all around the same ~0.12 mean, within seed noise. Target weighting [2,1] marginally helps C_D but it's noise-level. geo_jit doesn't clearly help. The variance across seeds (2 seeds) is masking differences. The differences between configs (0.112-0.125) are comparable to seed noise. I'm hitting diminishing returns on hyperparameter tuning. Let me wait for epochs140, then step back and think about the bigger picture: - The core win is velocity augmentation (baseline 0.37 → aug 0.11). That's the main lever, ~3.3x improvement. - Fine-tuning p_aug, geo_jit, target weights, epochs gives marginal, noisy changes around 0.11-0.12. Given the variance, I should: 1. Reduce variance by using more seeds for the final decision, OR accept the approach is robust and pick sensible defaults. 2. For the FINAL model (trained on all data), I can't use more seeds in one checkpoint. But I CAN reduce variance via SWA (weight averaging along trajectory) or by training longer with cosine annealing to a good minimum. Actually, an important consideration: the final single model's variance. Since I submit ONE model, its random seed matters. To pick a good one, I could train several on all-data and select the one that does best on... the provided val (in-distribution) , but that doesn't measure extrapolation. Or I select based on my high-v holdout performance, but the final model trains on all data. Better plan for final model selection: - Use the hard-holdout protocol to pick hyperparameters (done: p_aug~0.5-0.6, vhi~92, expo~-0.21, minimal geo_jit, maybe tw slightly>1 for C_D). - For the final model, train on ALL 630 cases with these settings. To pick a good seed / reduce variance, I can use a SHORT internal validation: hold out a small random slice for monitoring general fit, but mainly rely on averaging. Let me consider SWA more seriously. SWA: after convergence, average weights over several epochs. With BatchNorm, I need to recompute BN running stats after averaging (a forward pass over training data in train mode). This produces a single model with typically better generalization and lower variance. This is a strong, legitimate technique that yields ONE checkpoint. Let me implement and test it on the hard holdout. Actually, even simpler and very effective for variance: train with a cosine schedule and average the last few epochs' weights (SWA). Let me test whether SWA improves the hard-holdout numbers and reduces variance. Let me also reconsider: the hidden test could extend beyond v=82 (public max 81.6). "higher-speed, higher-Reynolds end" , my augmentation to vhi=92 covers up to 92, giving margin. Good. But the exponent law must hold up there. Physics says yes (skin friction continues to scale). I'm comfortable. Let me wait for epochs140 and then implement SWA and test. Let me also reconsider whether to use the full velocity-aug with p~0.5-0.6 and add SWA. Let me design the final training: - All 630 cases. - Velocity aug p_aug=0.6, vlo=30, vhi=92, exponent=-0.21 (full-data estimate). - target_weights maybe [1.5,1] to slightly favor C_D (the harder target) , but risk hurting C_L. Given both matter and C_D is worse, slight upweight is reasonable. Actually the metric likely averages per-target NRMSE; upweighting C_D trades C_L up. Since C_L is already very low (0.05) and C_D high (0.17), and NRMSE is scale-free, the mean is dominated by C_D. So improving C_D even slightly while slightly worsening the already-tiny C_L could help the mean AND the worst. Let me keep tw around [1.5,1] or [2,1]. But the experiments showed tw[2,1] gave C_D 0.183 vs base ~0.17 , actually WORSE C_D?! That's counterintuitive and likely noise. Let me not over-index on …[truncated]

bash

cd /app && sleep 45 && tail -2 exp/run5.log

output

epochs140                      C_D=0.1444 C_L=0.0516 mean=0.0980 worst=0.1444
elapsed 286s

epochs140 is clearly the best: C_D=0.144, C_L=0.052, mean=0.098, worst=0.144! Training longer (140 vs 80 epochs) with the cosine schedule meaningfully improved C_D (0.17→0.144) and the mean (0.112→0.098). This makes sense , the cosine schedule anneals to a better minimum with more epochs, and more epochs means more augmented samples seen. So more epochs helps. Let me push further: test 200, 250 epochs. Also combine with the SWA idea. And revisit target weighting at the longer epoch count. The key levers now: 1. More epochs (clear win). 2. SWA for variance reduction + generalization. Let me test epochs in {140, 200, 260} and an SWA variant. Let me implement SWA in the harness. SWA: average model weights over the last N epochs (or every k epochs in the final phase), then recompute BN stats. Let me add SWA to harness2. I'll implement: collect weight snapshots during the final `swa_frac` fraction of epochs (e.g., last 25%), average them, load into model, then do BN recalibration forward passes over the (augmented) training data. Let me implement carefully. For BN recalibration, I'll reset BN running stats and do several forward passes in train mode over training batches (with augmentation, to match the distribution the model will see... actually BN stats should match inference distribution. At inference, velocity can be high. But BN uses running stats computed during training. For SWA BN recalibration, I should pass data representative of training. Since augmentation covers high velocity, I'll recalibrate with augmentation on, so BN stats reflect the full velocity range. That's actually beneficial for high-v inference.) Hmm, wait , this raises a subtle but important point about BatchNorm and extrapolation! The SharedMLP uses BatchNorm1d over the per-point features. At inference (eval mode), BN uses running mean/var accumulated during training. If these running stats were accumulated WITHOUT high-velocity augmentation, the BN normalization at high velocity would be off. But with velocity augmentation during training, the BN running stats DO see high-velocity activations, so they're calibrated for the test regime. This is another reason augmentation helps! Good. Let me implement SWA and test epochs. Let me write run6. Given time per run (~140 epochs ≈ 58s/seed), testing epochs 200 (≈83s), 260 (≈108s). With 2 seeds: 200→166s, 260→216s. Plus SWA variant. Let me do: 1. epochs=200, p=0.6 2. epochs=260, p=0.6 3. epochs=200, p=0.6, swa (last 30%) 4. epochs=200, p=0.6, tw[1.5,1] That's ~4 configs, but 260 is slow. Let me budget: (200+260+200+200)*2 seeds ≈ 860 epoch-units... ~ too slow for 300s. Let me split into two background runs or reduce seeds to 2 but fewer configs per call. Let me do run6a: epochs 200 and 260 (2 seeds each) → (83+108)*2 ≈ 382s. Too long for one 300s call but it's background; I poll. Actually background runs aren't limited by the 300s tool timeout , only my sleep calls are. The process runs independently. I just need to poll with sleeps under 300s. So I can launch a longer background job and poll it across multiple calls. Let me launch a comprehensive run6 in the background covering epochs and SWA, and poll it over a couple of calls.

Excellent , **epochs=140 is a clear win**: C_D=0.144, C_L=0.052, **mean=0.098** (vs 0.112 at 80 epochs). The longer cosine anneal finds a better minimum. A subtle bonus: velocity augmentation also means the BatchNorm running statistics get calibrated on high-velocity activations, which directly helps inference in the test regime. Let me implement SWA (weight averaging → one checkpoint, with BN recalibration) and push epochs higher. I'll run in the background and poll across calls.

bash

cd /app && cat > exp/harness3.py << 'EOF'
import json, sys, copy
import torch, numpy as np
from numpy.linalg import lstsq
sys.path.insert(0,'/app')
from candidate_model import build_model
with open('/app/task_config.json') as fh: CFG=json.load(fh)

def load(split):
    p=torch.load(f'/app/data/{split}/split.pt',weights_only=True)
    return p['points'].float(), (p['targets'].float() if 'targets' in p else None)
def nrmse(pred,true):
    return [ (torch.sqrt(torch.mean((pred[:,i]-true[:,i])**2))/true[:,i].std()).item() for i in range(true.shape[1]) ]
def est_cd_exponent(pts,tg):
    v=pts[:,0,2].numpy(); aoa=pts[:,0,3].numpy(); cd=tg[:,0].numpy(); y=pts[:,:,1].numpy()
    geo=np.column_stack([y.max(1)-y.min(1),y.mean(1),y.max(1),y.min(1),aoa,aoa**2])
    X=np.column_stack([np.ones_like(v),geo,np.log(v)])
    beta,_,_,_=lstsq(X,np.log(cd),rcond=None); return float(beta[-1])

def _avg_state(states):
    avg=copy.deepcopy(states[0])
    for k in avg:
        if avg[k].dtype.is_floating_point:
            avg[k]=torch.stack([s[k].float() for s in states],0).mean(0)
        else:
            avg[k]=states[-1][k]
    return avg

def train_model(pts_phys,tg_phys,fm,fs,tm,ts,cfg,seed=0):
    torch.manual_seed(seed); np.random.seed(seed)
    model=build_model(CFG)
    epochs=cfg.get('epochs',140); bs=cfg.get('bs',32)
    opt=torch.optim.Adam(model.parameters(),lr=cfg.get('lr',1e-3),weight_decay=cfg.get('wd',1e-4))
    sched=torch.optim.lr_scheduler.CosineAnnealingLR(opt,T_max=epochs)
    tw=torch.tensor(cfg.get('target_weights',[1.0,1.0])).float().view(1,-1)
    n=pts_phys.shape[0]
    p_aug=cfg.get('p_aug',0.0); vlo=cfg.get('vlo',30.0); vhi=cfg.get('vhi',92.0)
    expo=cfg.get('cd_expo',-0.21); geo_jit=cfg.get('geo_jit',0.0)
    swa=cfg.get('swa',False); swa_start=cfg.get('swa_start',0.7)
    FM=fm.view(1,1,-1); FS=fs.view(1,1,-1); TM=tm.view(1,-1); TS=ts.view(1,-1)
    swa_states=[]
    def aug_batch(P,T):
        if p_aug>0:
            m=torch.rand(P.shape[0])<p_aug
            if m.any():
                vnew=torch.empty(int(m.sum())).uniform_(vlo,vhi); vorig=P[m,0,2]
                P[m,:,2]=vnew.view(-1,1); T[m,0]=T[m,0]*(vnew/vorig).pow(expo)
        if geo_jit>0: P[:,:,0:2]+=torch.randn_like(P[:,:,0:2])*geo_jit
        return P,T
    for ep in range(epochs):
        model.train(); idx=torch.randperm(n)
        for s in range(0,n,bs):
            b=idx[s:s+bs]; P=pts_phys[b].clone(); T=tg_phys[b].clone()
            P,T=aug_batch(P,T)
            xb=(P-FM)/FS; yb=(T-TM)/TS
            opt.zero_grad(set_to_none=True)
            loss=(tw*(model(xb)-yb)**2).mean(); loss.backward(); opt.step()
        sched.step()
        if swa and ep>=int(swa_start*epochs):
            swa_states.append({k:v.detach().clone() for k,v in model.state_dict().items()})
    if swa and swa_states:
        model.load_state_dict(_avg_state(swa_states))
        # BN recalibration with augmentation ON (covers high-v regime)
        for mod in model.modules():
            if isinstance(mod,torch.nn.BatchNorm1d):
                mod.reset_running_stats(); mod.momentum=None
        model.train()
        with torch.no_grad():
            for _ in range(cfg.get('bn_passes',3)):
                idx=torch.randperm(n)
                for s in range(0,n,bs):
                    b=idx[s:s+bs]; P=pts_phys[b].clone(); T=tg_phys[b].clone()
                    P,T=aug_batch(P,T); model((P-FM)/FS)
    return model

def evaluate(model,pts_phys,tg_phys,fm,fs,tm,ts):
    model.eval()
    with torch.no_grad():
        pred=model((pts_phys-fm.view(1,1,-1))/fs.view(1,1,-1))*ts.view(1,-1)+tm.view(1,-1)
    return nrmse(pred,tg_phys), pred
EOF
echo ok

output

ok

bash

cd /app && cat > exp/run6.py << 'EOF'
import sys, time, torch, numpy as np
sys.path.insert(0,'/app/exp'); sys.path.insert(0,'/app')
from harness3 import load, train_model, evaluate, est_cd_exponent
pts,tg=load('train'); v=pts[:,0,2]
mtr=v<=60; mte=v>=70
ptr,ttr=pts[mtr],tg[mtr]; pte,tte=pts[mte],tg[mte]
flat=ptr.reshape(-1,4); fm=flat.mean(0); fs=flat.std(0).clamp_min(1e-8)
tm=ttr.mean(0); ts=ttr.std(0).clamp_min(1e-8)
expo=est_cd_exponent(ptr,ttr)
def run(cfg,seeds=(0,1,2),label=''):
    accs=[]
    for s in seeds:
        m=train_model(ptr,ttr,fm,fs,tm,ts,cfg,seed=s)
        nr,_=evaluate(m,pte,tte,fm,fs,tm,ts); accs.append(nr)
    a=np.array(accs)
    print(f'{label:26s} C_D={a[:,0].mean():.4f} C_L={a[:,1].mean():.4f} mean={a.mean(1).mean():.4f} worst={a.max(1).mean():.4f} (n={len(seeds)})',flush=True)
base=dict(p_aug=0.6,vlo=30,vhi=92,cd_expo=expo)
t0=time.time()
run(dict(base,epochs=200),label='ep200')
run(dict(base,epochs=200,swa=True,swa_start=0.6),label='ep200+swa')
run(dict(base,epochs=300),label='ep300')
run(dict(base,epochs=300,swa=True,swa_start=0.6),label='ep300+swa')
print('elapsed %.0fs'%(time.time()-t0),flush=True)
EOF
nohup python -u exp/run6.py > exp/run6.log 2>&1 &
echo "started $!"

output

started 810

bash

cd /app && sleep 290 && cat exp/run6.log

output

ep200                      C_D=0.1321 C_L=0.0491 mean=0.0906 worst=0.1321 (n=3)

ep200 with 3 seeds: C_D=0.132, C_L=0.049, mean=0.091, worst=0.132. Better than ep140 (0.098). Let me wait for the SWA and ep300 results. Each run is 3 seeds now, so slower. Let me wait more.

ep200 (3 seeds) improves to mean=0.091. Let me wait for the SWA and ep300 variants.

bash

cd /app && sleep 290 && cat exp/run6.log

output

ep200                      C_D=0.1321 C_L=0.0491 mean=0.0906 worst=0.1321 (n=3)
ep200+swa                  C_D=0.1419 C_L=0.0446 mean=0.0933 worst=0.1419 (n=3)

ep200+swa: C_D=0.142, C_L=0.045, mean=0.093. SWA slightly worse on C_D (0.142 vs 0.132) but better on C_L (0.045 vs 0.049). Net about the same (0.093 vs 0.091). SWA with BN recalibration isn't clearly helping here. It adds complexity and risk. I'll probably skip SWA for the final model, or reconsider. Let me wait for ep300 results.

bash

cd /app && sleep 290 && cat exp/run6.log

output

ep200                      C_D=0.1321 C_L=0.0491 mean=0.0906 worst=0.1321 (n=3)
ep200+swa                  C_D=0.1419 C_L=0.0446 mean=0.0933 worst=0.1419 (n=3)
ep300                      C_D=0.1256 C_L=0.0397 mean=0.0827 worst=0.1256 (n=3)

ep300 (no SWA): C_D=0.126, C_L=0.040, mean=0.083, worst=0.126. Even better! More epochs keeps helping. Let me wait for ep300+swa, then consider going even higher (400, 500 epochs). The trend: 80→0.112, 140→0.098, 200→0.091, 300→0.083. Diminishing but still improving. Let me push to 400-500. But I need to watch for overfitting on the real data vs the augmented extrapolation. Since augmentation regularizes, more epochs mostly helps. Let me test 400 and 500. Let me wait for ep300+swa first.

ep300 improves further to **mean=0.083** (C_D=0.126, C_L=0.040). The epoch trend (0.112→0.098→0.091→0.083) is still descending. Let me see ep300+swa, then test even longer schedules.

bash

cd /app && sleep 200 && cat exp/run6.log | tail -2

output

ep200+swa                  C_D=0.1419 C_L=0.0446 mean=0.0933 worst=0.1419 (n=3)
ep300                      C_D=0.1256 C_L=0.0397 mean=0.0827 worst=0.1256 (n=3)

bash

cd /app && sleep 120 && cat exp/run6.log | tail -2
# launch longer-epoch test in background
cat > exp/run7.py << 'EOF'
import sys, time, torch, numpy as np
sys.path.insert(0,'/app/exp'); sys.path.insert(0,'/app')
from harness3 import load, train_model, evaluate, est_cd_exponent
pts,tg=load('train'); v=pts[:,0,2]
mtr=v<=60; mte=v>=70
ptr,ttr=pts[mtr],tg[mtr]; pte,tte=pts[mte],tg[mte]
flat=ptr.reshape(-1,4); fm=flat.mean(0); fs=flat.std(0).clamp_min(1e-8)
tm=ttr.mean(0); ts=ttr.std(0).clamp_min(1e-8)
expo=est_cd_exponent(ptr,ttr)
def run(cfg,seeds=(0,1,2),label=''):
    accs=[]
    for s in seeds:
        m=train_model(ptr,ttr,fm,fs,tm,ts,cfg,seed=s)
        nr,_=evaluate(m,pte,tte,fm,fs,tm,ts); accs.append(nr)
    a=np.array(accs)
    print(f'{label:20s} C_D={a[:,0].mean():.4f} C_L={a[:,1].mean():.4f} mean={a.mean(1).mean():.4f} worst={a.max(1).mean():.4f} std_mean={a.mean(1).std():.4f}',flush=True)
base=dict(p_aug=0.6,vlo=30,vhi=92,cd_expo=expo)
t0=time.time()
run(dict(base,epochs=450),label='ep450')
run(dict(base,epochs=600),label='ep600')
print('elapsed %.0fs'%(time.time()-t0),flush=True)
EOF
nohup python -u exp/run7.py > exp/run7.log 2>&1 &
echo "started run7 $!"

output

ep300+swa                  C_D=0.1339 C_L=0.0408 mean=0.0873 worst=0.1339 (n=3)
elapsed 1205s
started run7 884

ep300+swa: 0.0873 vs ep300 no-swa: 0.0827. SWA is consistently slightly WORSE here. I'll drop SWA. So far best: ep300 no-swa, mean=0.083. Now testing ep450 and ep600 in background (run7). Each seed at 600 epochs ≈ 4 min, 3 seeds = 12 min, plus 450 ≈ 9 min. ~21 min total. Let me poll periodically. While that runs, let me think about other improvements and the final pipeline. Other ideas to explore: 1. Is the hard-holdout (train v<=60) a good proxy? The final model uses all data. I should also validate the final pipeline end-to-end on public_test (sanity: predictions in reasonable range). 2. Reconsider the velocity-augmentation exponent for the FINAL model. I'll use the full-data estimate (-0.211). Let me also ensure C_L is truly flat , I kept it constant. Good. 3. Consider adding a small amount of geometry augmentation? Earlier geo_jit=0.002 didn't help. Skip. 4. Consider target weighting. With ep300, C_D=0.126, C_L=0.040. C_D dominates the mean. Should I upweight C_D? Earlier at 80 epochs tw didn't clearly help. Let me test tw at the longer epoch setting. But more epochs already reduced C_D a lot. Let me test tw[1.5,1] and [2,1] at ep300 to see if C_D can go lower without hurting the mean. Actually, since C_L is already very low (0.04), trading a little C_L for C_D would help both the mean (C_D-dominated) and worst (C_D). Worth testing. 5. Learning rate and batch size. Could tune, but risk. Current lr=1e-3, bs=32. Let me maybe test bs=16 (more updates) or lr schedule warmup. Keep simple. 6. The biggest remaining question: will these gains (measured on train<=60 / test>=70, mean v=72.5) transfer to the real test at mean v=78? The augmentation covers up to vhi=92, so v=78 is well within the augmented range. I'm fairly confident. But let me ALSO verify with an even more extreme holdout: train v<=55, test v>=68, to check stability of the method when the gap is larger. If the method still wins big, I'm confident. Let me prioritize. run7 (ep450/600) is using the CPU heavily. Running parallel experiments will slow both. Let me wait for run7, then run a final tuning round (tw + extreme holdout) before building the final model. Let me wait for run7. Actually , an important efficiency point: I'm spending a lot of compute. Let me make sure the final deliverable gets built with plenty of margin. Let me plan the final training: train on ALL 630 cases, ep~300-450, p_aug=0.6, vhi=92, expo=-0.211. That single final run at 450 epochs on 630 cases ≈ 630/482 * time. ep300 on 482 took ~ (1205-... let me estimate). run6 total 1205s for (200+200+300+300)=1000 epochs ×3 seeds on 482 samples = 3000 epoch-runs... 1205/ (1000*3/... no. Let me just estimate: ep300 3 seeds ≈ the ep300 line. Total run6 was 4 configs. Anyway, a single 450-epoch run on 630 samples ≈ 450 * (630/482) * (time per epoch). Time per epoch on 482 ≈ 0.2s (200 epochs ≈ 40-60s/seed). So 450 epochs on 630 ≈ 450*0.26 ≈ 120s. Fine. Let me wait for run7.

SWA is consistently a touch worse, so I'll drop it. The epoch trend keeps improving (ep300 → mean=0.083). I'm now testing ep450/ep600 in the background. While that runs, let me verify robustness on a **more extreme holdout** (bigger velocity gap) to be confident the gains transfer to the real test at v≈78, and test C_D-favoring loss weights.

bash

cd /app && sleep 280 && cat exp/run7.log

output

<system>Tool ran without output or errors</system>

bash

cd /app && sleep 200 && cat exp/run7.log

output

<system>Tool ran without output or errors</system>

run7 still hasn't printed (ep450 with 3 seeds at 450 epochs is slow, ~ 3*90s=270s, plus ep600 3*120s=360s). It's been ~480s. Let me wait more. Let me check process.

bash

cd /app && ps aux | grep run7 | grep -v grep | head -1 | awk '{print "running, cpu-time",$10}'; sleep 120; cat exp/run7.log

output

running, cpu-time 123:07

bash

cd /app && sleep 180 && cat exp/run7.log

output

ep450                C_D=0.1161 C_L=0.0388 mean=0.0774 worst=0.1161 std_mean=0.0020

ep450: C_D=0.116, C_L=0.039, mean=0.077, worst=0.116, std across seeds=0.002 (very stable!). Better than ep300 (0.083). The low std_mean (0.002) is great , the method is stable across seeds. Trend: 300→0.083, 450→0.077. Still improving but diminishing. Let me wait for ep600. The seed stability (std 0.002) is reassuring , my single final model won't be a lottery. Let me wait for ep600.

ep450 reaches **mean=0.077** with very low seed variance (std=0.002) , reassuring for a single-model deliverable. Let me get the ep600 result.

bash

cd /app && sleep 260 && cat exp/run7.log

output

ep450                C_D=0.1161 C_L=0.0388 mean=0.0774 worst=0.1161 std_mean=0.0020

bash

cd /app && sleep 150 && cat exp/run7.log | tail -2

output

ep450                C_D=0.1161 C_L=0.0388 mean=0.0774 worst=0.1161 std_mean=0.0020

bash

cd /app && sleep 120 && cat exp/run7.log | tail -2

output

ep450                C_D=0.1161 C_L=0.0388 mean=0.0774 worst=0.1161 std_mean=0.0020

ep600 is taking a while (3 seeds × 600 epochs). Let me check if it's still running.

bash

cd /app && ps aux | grep run7 | grep -v grep | head -1 | awk '{print "cpu-time",$10}'; sleep 90; cat exp/run7.log | tail -2

output

cpu-time 331:12
ep600                C_D=0.1035 C_L=0.0438 mean=0.0737 worst=0.1035 std_mean=0.0034
elapsed 1385s

ep600: C_D=0.104, C_L=0.044, mean=0.074, worst=0.104. Better C_D (0.104 vs 0.116) but slightly worse C_L (0.044 vs 0.039). Net mean 0.074 vs 0.077. Marginal improvement over ep450, with diminishing returns and 33% more compute. Trend summary (hard holdout, train v<=60, test v>=70): - ep80: 0.112 - ep140: 0.098 - ep200: 0.091 - ep300: 0.083 - ep450: 0.077 - ep600: 0.074 Diminishing returns. ep450-600 is a good sweet spot. I'll use ~450-500 epochs for the final model to balance quality and compute, and because beyond that gains are marginal and risk overfitting the augmentation. Now, important remaining checks before finalizing: 1. Verify robustness on a more EXTREME holdout (bigger gap) , confirm the method still dominates and transfers to v~78. 2. Test C_D-favoring target weights at long epochs (since C_D is the bottleneck, maybe [1.5,1] helps mean+worst). 3. Decide exponent for final: full-data estimate. Let me run a focused final-tuning experiment (run8): - Extreme holdout: train v<=55, test v>=70 (gap 55→70, test mean ~72.5, but trained on even less high-v data). Actually to push toward v=78 extrapolation, the gap size matters more than test mean. Let me do train v<=55, test v>=68. - Compare: no-aug baseline vs aug ep450, to reconfirm dominance. - Also test tw[1.5,1] and tw[2,1] at ep450 on the standard hard holdout. Let me be compute-aware. Let me do two quick things in one background run: Config A: extreme holdout (train<=55,test>=68): aug ep450 vs no-aug ep450 (2 seeds). Config B: standard holdout: tw variations. Actually let me separate concerns. Let me first reconfirm robustness on extreme holdout with the chosen recipe (ep450, p=0.6), plus the no-aug baseline for reference, plus tw test. I'll run them with 2 seeds to save time. Let me write run8 and run in background. Actually, I realize I should also sanity-check: with such long training (450 ep) on augmented data, does the no-aug model ALSO improve a lot at long epochs (maybe the gain is just epochs, not aug)? Let me include no-aug ep450 on the hard holdout to confirm aug is still essential at long training. This is an important control. Let me run: 1. no-aug ep450 (standard hard holdout) , control 2. aug ep450 tw[1.5,1] 3. aug ep450 tw[2,1] 4. aug ep450 extreme holdout (train<=55,test>=68) + its no-aug control Hmm that's mixing holdouts. Let me keep run8 on the STANDARD hard holdout (train<=60,test>=70) for configs 1-3, and do the extreme holdout as a separate quick check. Let me do run8 on standard holdout: no-aug ep450 control, tw[1,1] (repeat baseline), tw[1.5,1], tw[2,1]. 2 seeds each. ~ (450*4*2) epoch-runs on 482 samples. At ~0.2s/epoch ≈ 90s/seed for 450... 4 configs*2 seeds*90s=720s. Background, poll. Let me launch. Wait, I want to be efficient with my remaining budget. The key decisions: - epochs: 450-500 (decided). - The rest (tw, exact p) are marginal. Let me do ONE more focused run to (a) confirm aug >> no-aug at long epochs (critical control), and (b) pick tw. Then build the final model. Let me run8 with 2 seeds.

ep600 gives mean=0.074 , marginal over ep450 (0.077) with diminishing returns, so ~450–500 epochs is the sweet spot. The full epoch trend (0.112→0.074) is clean. Now two important final checks: a **control** confirming augmentation still dominates at long training (not just epochs doing the work), and whether C_D-favoring loss weights help. Let me run both.

bash

cd /app && cat > exp/run8.py << 'EOF'
import sys, time, torch, numpy as np
sys.path.insert(0,'/app/exp'); sys.path.insert(0,'/app')
from harness3 import load, train_model, evaluate, est_cd_exponent
pts,tg=load('train'); v=pts[:,0,2]
mtr=v<=60; mte=v>=70
ptr,ttr=pts[mtr],tg[mtr]; pte,tte=pts[mte],tg[mte]
flat=ptr.reshape(-1,4); fm=flat.mean(0); fs=flat.std(0).clamp_min(1e-8)
tm=ttr.mean(0); ts=ttr.std(0).clamp_min(1e-8)
expo=est_cd_exponent(ptr,ttr)
def run(cfg,seeds=(0,1),label=''):
    accs=[]
    for s in seeds:
        m=train_model(ptr,ttr,fm,fs,tm,ts,cfg,seed=s)
        nr,_=evaluate(m,pte,tte,fm,fs,tm,ts); accs.append(nr)
    a=np.array(accs)
    print(f'{label:24s} C_D={a[:,0].mean():.4f} C_L={a[:,1].mean():.4f} mean={a.mean(1).mean():.4f} worst={a.max(1).mean():.4f}',flush=True)
base=dict(epochs=450,p_aug=0.6,vlo=30,vhi=92,cd_expo=expo)
t0=time.time()
run(dict(epochs=450,p_aug=0.0),label='CONTROL no-aug ep450')
run(dict(base,target_weights=[1.5,1.0]),label='aug tw[1.5,1]')
run(dict(base,target_weights=[2.0,1.0]),label='aug tw[2,1]')
print('elapsed %.0fs'%(time.time()-t0),flush=True)
EOF
nohup python -u exp/run8.py > exp/run8.log 2>&1 &
echo "started $!"

output

started 999

While that runs, let me confirm robustness on a **more extreme holdout** (larger velocity gap: train v≤55, test v≥68) to ensure the gains transfer to the real test regime near v≈78.

bash

cd /app && cat > exp/run9.py << 'EOF'
import sys, time, torch, numpy as np
sys.path.insert(0,'/app/exp'); sys.path.insert(0,'/app')
from harness3 import load, train_model, evaluate, est_cd_exponent
pts,tg=load('train'); v=pts[:,0,2]
mtr=v<=55; mte=v>=68
ptr,ttr=pts[mtr],tg[mtr]; pte,tte=pts[mte],tg[mte]
print('EXTREME holdout: train(v<=55)=%d test(v>=68)=%d test-mean-v=%.1f gap=13'%(mtr.sum(),mte.sum(),v[mte].mean()),flush=True)
flat=ptr.reshape(-1,4); fm=flat.mean(0); fs=flat.std(0).clamp_min(1e-8)
tm=ttr.mean(0); ts=ttr.std(0).clamp_min(1e-8)
expo=est_cd_exponent(ptr,ttr); print('exponent on v<=55 subset:',round(expo,3),flush=True)
def run(cfg,seeds=(0,1),label=''):
    accs=[]
    for s in seeds:
        m=train_model(ptr,ttr,fm,fs,tm,ts,cfg,seed=s)
        nr,_=evaluate(m,pte,tte,fm,fs,tm,ts); accs.append(nr)
    a=np.array(accs)
    print(f'{label:24s} C_D={a[:,0].mean():.4f} C_L={a[:,1].mean():.4f} mean={a.mean(1).mean():.4f}',flush=True)
t0=time.time()
run(dict(epochs=450,p_aug=0.0),label='no-aug ep450')
run(dict(epochs=450,p_aug=0.6,vlo=30,vhi=92,cd_expo=expo),label='aug ep450')
print('elapsed %.0fs'%(time.time()-t0),flush=True)
EOF
nohup python -u exp/run9.py > exp/run9.log 2>&1 &
echo "started run9 $!"; sleep 250; echo '--run8--'; cat exp/run8.log; echo '--run9--'; cat exp/run9.log

output

started run9 1037
--run8--
--run9--
EXTREME holdout: train(v<=55)=337 test(v>=68)=95 test-mean-v=71.5 gap=13
exponent on v<=55 subset: -0.157

Both are running in parallel (competing for CPU, so slower). The exponent on v<=55 subset is -0.157 (smaller than -0.21 because less high-v data to pin it down). This is a good robustness test: even with a less accurate exponent (-0.157), does augmentation still help? Let me wait for results. Running two jobs in parallel on 16 threads each might oversubscribe. Let me just wait.

Both experiments are running (the v≤55 exponent estimate is a noisier −0.157, which also tests robustness to an imperfect exponent). Let me wait for results.

bash

cd /app && sleep 290; echo '--run8--'; cat exp/run8.log; echo '--run9--'; cat exp/run9.log

output

--run8--
--run9--
EXTREME holdout: train(v<=55)=337 test(v>=68)=95 test-mean-v=71.5 gap=13
exponent on v<=55 subset: -0.157
no-aug ep450             C_D=0.4420 C_L=0.3118 mean=0.3769

run9 extreme holdout: no-aug ep450 gives C_D=0.442, C_L=0.312, mean=0.377 , catastrophic, same as before. So even at 450 epochs, no-aug fails to extrapolate (confirming it's NOT just epochs; the augmentation is essential). Waiting for aug ep450 on extreme holdout. run8 is slow because running in parallel with run9. Let me wait more.

The control confirms it: **no-aug at 450 epochs still catastrophically fails** (mean=0.377) , so the augmentation, not just the long schedule, is what enables extrapolation. Let me wait for the augmented result on this extreme holdout and the run8 weight-tuning results.

bash

cd /app && sleep 200; echo '--run8--'; cat exp/run8.log; echo '--run9--'; cat exp/run9.log

output

--run8--
--run9--
EXTREME holdout: train(v<=55)=337 test(v>=68)=95 test-mean-v=71.5 gap=13
exponent on v<=55 subset: -0.157
no-aug ep450             C_D=0.4420 C_L=0.3118 mean=0.3769

bash

cd /app && ps aux | grep -E 'run8|run9' | grep -v grep | awk '{print $NF,$10}'; sleep 180; echo '--run8--'; cat exp/run8.log; echo '--run9--'; cat exp/run9.log

output

exp/run8.py 76:55
exp/run9.py 76:13
--run8--
CONTROL no-aug ep450     C_D=0.5479 C_L=0.1857 mean=0.3668 worst=0.5479
--run9--
EXTREME holdout: train(v<=55)=337 test(v>=68)=95 test-mean-v=71.5 gap=13
exponent on v<=55 subset: -0.157
no-aug ep450             C_D=0.4420 C_L=0.3118 mean=0.3769
aug ep450                C_D=0.1524 C_L=0.0498 mean=0.1011
elapsed 897s

Now I have clear results: **run9 (EXTREME holdout, train v<=55, test v>=68, exponent -0.157):** - no-aug ep450: mean=0.377 (catastrophic) - aug ep450: mean=0.101 (C_D=0.152, C_L=0.050) So even with a bigger gap AND a less accurate exponent (-0.157), augmentation improves mean from 0.377 → 0.101 (3.7x better). This strongly confirms robustness and transfer to the real test regime. **run8 (standard hard holdout, train v<=60, test v>=70):** - CONTROL no-aug ep450: C_D=0.548, C_L=0.186, mean=0.367 (catastrophic , confirms again) - waiting for tw[1.5,1] and tw[2,1]. The no-aug control at ep450 (0.367) vs ep80 (0.371) , essentially the same catastrophic failure. So epochs alone do NOTHING for extrapolation without augmentation. The augmentation is THE key. Let me wait for run8's tw results. run9 is done, so run8 should speed up now.

Decisive confirmation: on the extreme holdout (bigger gap + deliberately noisier −0.157 exponent), augmentation still cuts mean NRMSE from **0.377 → 0.101** (3.7×). And the no-aug control at 450 epochs is still catastrophic (0.367), proving epochs alone do nothing for extrapolation , the physics-based augmentation is the essential ingredient. Let me get the loss-weight results.

bash

cd /app && sleep 180; cat exp/run8.log

output

CONTROL no-aug ep450     C_D=0.5479 C_L=0.1857 mean=0.3668 worst=0.5479

bash

cd /app && sleep 200; cat exp/run8.log

output

CONTROL no-aug ep450     C_D=0.5479 C_L=0.1857 mean=0.3668 worst=0.5479
aug tw[1.5,1]            C_D=0.1101 C_L=0.0419 mean=0.0760 worst=0.1101

aug tw[1.5,1] (standard hard holdout): C_D=0.110, C_L=0.042, mean=0.076, worst=0.110. Compare to aug tw[1,1] ep450 (from run7): C_D=0.116, C_L=0.039, mean=0.077. So tw[1.5,1] gives slightly better C_D (0.110 vs 0.116) and worst (0.110 vs 0.116), with slightly worse C_L (0.042 vs 0.039). Mean about the same (0.076 vs 0.077). Marginal. Let me wait for tw[2,1]. The choice between tw[1,1] and tw[1.5,1] is marginal. tw[1.5,1] slightly favors C_D (the worst target), which helps worst_nrmse. Given "both matter" and C_D is the harder one, a mild upweight like [1.5,1] is reasonable and improves the worst-case slightly. Let me see tw[2,1].

tw[1.5,1] gives mean=0.076 (C_D=0.110, C_L=0.042) , slightly better C_D/worst than equal weighting, at a tiny C_L cost. Let me see tw[2,1].

bash

cd /app && sleep 160; cat exp/run8.log | tail -2

output

CONTROL no-aug ep450     C_D=0.5479 C_L=0.1857 mean=0.3668 worst=0.5479
aug tw[1.5,1]            C_D=0.1101 C_L=0.0419 mean=0.0760 worst=0.1101

bash

cd /app && sleep 120; cat exp/run8.log | tail -1

output

elapsed 1538s

bash

cd /app && cat exp/run8.log

output

CONTROL no-aug ep450     C_D=0.5479 C_L=0.1857 mean=0.3668 worst=0.5479
aug tw[1.5,1]            C_D=0.1101 C_L=0.0419 mean=0.0760 worst=0.1101
aug tw[2,1]              C_D=0.1112 C_L=0.0438 mean=0.0775 worst=0.1112
elapsed 1538s

tw[2,1]: C_D=0.111, C_L=0.044, mean=0.078. So tw[1.5,1] (0.076) ≈ tw[2,1] (0.078) ≈ tw[1,1] (0.077). All essentially equal. Target weighting has negligible effect. I'll use a mild tw[1.5,1] since it gives the best C_D/worst and is within noise on mean , a small hedge toward the harder target without hurting C_L meaningfully. Summary of findings: - **Physics-based velocity augmentation is essential** (0.37 → 0.08-0.10). C_D ∝ (v_new/v_orig)^-0.21, C_L constant. - Long training (~450 epochs) with cosine annealing. - p_aug ≈ 0.6, velocity sampling uniform [30, 92]. - tw[1.5,1] (mild C_D upweight). - SWA: not helpful, skip. - geo_jit: not helpful, skip. - Method is robust to exponent (-0.157 to -0.21), p_aug (0.5-0.8), vhi (90-95), and seeds (std 0.002-0.003). Now let me finalize. Decisions for the FINAL model (trained on ALL 630 cases): - Standardization: compute feat_mean/feat_std and targ_mean/targ_std from all training data. BUT , important consideration for feat_std on velocity: since I augment velocity up to 92, should feat_std reflect the augmented distribution? The standardizer in dataset.py uses the raw training data. The feat_mean/feat_std I SAVE must be the ones used at inference. The inference does (points - feat_mean)/feat_std. For consistency, I must train with the SAME feat_mean/feat_std that I save. Let me think about what feat_mean/feat_std to use for velocity. Options: (a) Compute from raw training data (v mean ~53, std ~12.8). Then at test (v~78), standardized velocity = (78-53)/12.8 ≈ +1.95. Within augmented training, I feed v up to 92 → (92-53)/12.8 ≈ +3.0. The network sees standardized velocities up to +3 during training (via aug), so +1.95 at test is well within range. Good. (b) Compute from an extended range. Not necessary. I'll use option (a): standardize using raw training statistics (as the provided dataset.py does), but train with augmentation. The augmentation feeds raw physical velocities [30,92], which after standardization with raw stats gives the network exposure to the standardized test range. This is consistent: I standardize inside the training loop using the same feat_mean/feat_std I'll save. Wait, in harness3, I standardize inside train_model using fm, fs passed in, which are computed from the (physical) training subset. For the final model, I'll compute fm, fs from ALL training data (raw), pass them in, and save them. Consistent. Good. - targ_mean/targ_std: computed from raw training targets. The augmentation changes C_D values (scales them), producing C_D values slightly outside the original range (e.g., at high v, C_D lower; at low v, higher). But I standardize targets with the raw stats and save those. At inference, output*targ_std+targ_mean. The network learns to output standardized values that map back correctly. Since augmented C_D can go a bit beyond the raw range, the standardized targets during training can exceed the usual range, but that's fine , the network just learns a slightly wider output range. The saved targ_mean/targ_std are the raw ones, consistent with what's used in the loss. Good. Actually, let me reconsider: should targ_mean/std be computed on raw or on the augmented distribution? For correctness, it doesn't matter much as long as train and save use the SAME values (the affine mapping is invertible). I'll use raw training target stats (simplest, matches dataset.py convention). The network learns to hit them. - exponent for final: use full-data estimate. Let me recompute on all 630: earlier got -0.211. I'll compute it in the final script from all data. - epochs: I'll use 500 (between 450 and 600, good sweet spot; on 630 samples it's ~ a few minutes). - Let me also reconsider vhi. Test is up to 81.6 (public) and hidden "higher-speed, higher-Reynolds end". To be safe for possibly-higher hidden velocities, vhi=92 gives margin to ~92. I could extend to 95. But sampling too high dilutes density near the test range. Since corr shows the scored set is the "higher e …[truncated]

Target weighting is within noise (tw[1.5,1]=0.076, [2,1]=0.078, [1,1]=0.077); I'll use a mild **[1.5,1]** as a small hedge toward the harder C_D without hurting C_L. My recipe is now well-validated and robust. Let me lock in the findings and write a clean, self-contained final training script. **Final recipe:** train on all 630 cases, physics-based velocity augmentation (p=0.6, v∈[30,95], C_D·(v_new/v_orig)^p with p≈−0.21, C_L fixed), cosine schedule, 500 epochs, loss weights [1.5,1]. No SWA, no geo-jitter (neither helped).

bash

cd /app && cat > final_train.py << 'EOF'
"""Final trainer for the airfoil force-coefficient task.

Key idea: the scored cases live at higher inlet velocity (Reynolds) than any
training case, so the model must EXTRAPOLATE in velocity. A plain fit latches
onto spurious nonlinear velocity features and reverses the physical trend beyond
the training range (verified empirically). We fix this with physics-based
velocity augmentation grounded in the data itself:

  * C_D follows a turbulent skin-friction-like law  C_D(v) ~ v^p, with the
    exponent p fit from the training data (~ -0.21, matching C_f ~ Re^-0.2).
  * C_L is velocity-independent (residual corr with v ~ 0.05).

During training we resample the (constant) velocity channel of a fraction of
cases across a wide range that brackets the test regime, rescaling C_D by
(v_new/v_orig)^p and leaving C_L unchanged. This teaches the fixed PointNet the
correct monotonic high-velocity behavior and, as a bonus, calibrates the
BatchNorm running statistics on high-velocity activations. The architecture is
untouched; only the training procedure and the saved normalization change.
"""
from __future__ import annotations
import json, os, sys
from pathlib import Path
import numpy as np
import torch
from numpy.linalg import lstsq

APP_DIR = Path(os.environ.get("APP_DIR", "/app"))
sys.path.insert(0, str(APP_DIR))
from candidate_model import build_model  # noqa: E402
from dataset import load_split  # noqa: E402

# ----- hyperparameters chosen via a velocity-gap extrapolation holdout -----
EPOCHS      = 500
BATCH_SIZE  = 32
LR          = 1e-3
WEIGHT_DECAY= 1e-4
P_AUG       = 0.6      # fraction of each batch given a resampled velocity
V_LO, V_HI  = 30.0, 95.0   # brackets train (31-75) and test (75-82+) regimes
TARGET_W    = [1.5, 1.0]   # mild emphasis on the harder C_D target
SEED        = 0


def estimate_cd_velocity_exponent(points: torch.Tensor, targets: torch.Tensor) -> float:
    """Fit C_D ~ v^p controlling for geometry and angle of attack (log-log)."""
    v = points[:, 0, 2].numpy(); aoa = points[:, 0, 3].numpy()
    cd = targets[:, 0].numpy(); y = points[:, :, 1].numpy()
    geo = np.column_stack([y.max(1) - y.min(1), y.mean(1), y.max(1), y.min(1), aoa, aoa**2])
    X = np.column_stack([np.ones_like(v), geo, np.log(v)])
    beta, *_ = lstsq(X, np.log(cd), rcond=None)
    return float(beta[-1])


def main() -> None:
    with (APP_DIR / "task_config.json").open() as fh:
        cfg = json.load(fh)
    torch.manual_seed(SEED); np.random.seed(SEED)
    device = torch.device("cuda" if torch.cuda.is_available() else "cpu")

    points, targets = load_split(APP_DIR / "data" / "train")

    # standardization (raw training stats; augmentation feeds physical values
    # through this same affine map so the net sees the standardized test range)
    flat = points.reshape(-1, points.shape[-1])
    feat_mean = flat.mean(0); feat_std = flat.std(0).clamp_min(1e-8)
    targ_mean = targets.mean(0); targ_std = targets.std(0).clamp_min(1e-8)

    cd_expo = estimate_cd_velocity_exponent(points, targets)
    print(f"[final] n={points.shape[0]} cd_velocity_exponent={cd_expo:.3f} "
          f"epochs={EPOCHS} p_aug={P_AUG} v=[{V_LO},{V_HI}] tw={TARGET_W}", flush=True)

    model = build_model(cfg).to(device)
    opt = torch.optim.Adam(model.parameters(), lr=LR, weight_decay=WEIGHT_DECAY)
    sched = torch.optim.lr_scheduler.CosineAnnealingLR(opt, T_max=EPOCHS)
    tw = torch.tensor(TARGET_W, device=device).float().view(1, -1)

    FM = feat_mean.view(1, 1, -1).to(device); FS = feat_std.view(1, 1, -1).to(device)
    TM = targ_mean.view(1, -1).to(device);    TS = targ_std.view(1, -1).to(device)
    pts_dev = points.to(device); tg_dev = targets.to(device)
    n = pts_dev.shape[0]

    for ep in range(EPOCHS):
        model.train(); idx = torch.randperm(n, device=device)
        for s in range(0, n, BATCH_SIZE):
            b = idx[s:s + BATCH_SIZE]
            P = pts_dev[b].clone(); T = tg_dev[b].clone()
       
…[truncated]

output

started final 1150
written

bash

cd /app && sleep 200 && cat final_train.log

output

[final] n=630 cd_velocity_exponent=-0.211 epochs=500 p_aug=0.6 v=[30.0,95.0] tw=[1.5, 1.0]
[final] epoch 100/500 loss=0.0852
[final] epoch 200/500 loss=0.0131
[final] epoch 300/500 loss=0.0947

Training is progressing (exponent -0.211 on full data as expected). The loss is bouncing around (stochastic due to augmentation). Let me wait for it to finish. ~500 epochs on 630 samples. Let me wait.

Final training is running with the full-data exponent −0.211. Let me wait for completion, then validate the checkpoint.

bash

cd /app && sleep 170 && cat final_train.log && echo "---" && ls -la outputs/ 2>/dev/null

output

[final] n=630 cd_velocity_exponent=-0.211 epochs=500 p_aug=0.6 v=[30.0,95.0] tw=[1.5, 1.0]
[final] epoch 100/500 loss=0.0852
[final] epoch 200/500 loss=0.0131
[final] epoch 300/500 loss=0.0947
[final] epoch 400/500 loss=0.0040
[final] epoch 500/500 loss=0.0496
[final] wrote /app/outputs/model.pt
---
total 347
drwxr-sr-x 2 h2tagent h2tagent   4096 Jun 19 23:23 .
drwxrws--- 6 h2tagent h2tagent   4096 Jun 19 23:23 ..
-rw-r--r-- 1 h2tagent h2tagent 346611 Jun 19 23:23 model.pt

The final checkpoint is written. Now let me rigorously validate it: confirm it loads cleanly into the exact architecture via the **intended inference path**, check the required tensors, verify in-distribution fit on the provided val set, and probe the velocity-extrapolation behavior.

bash

cd /app && cat > exp/validate_final.py << 'EOF'
import sys, json, torch, numpy as np
sys.path.insert(0,'/app')
from candidate_model import build_model
from dataset import load_split
cfg=json.load(open('/app/task_config.json'))

ckpt=torch.load('/app/outputs/model.pt', weights_only=True)
# 1. required keys and shapes
print('keys:', sorted(ckpt.keys()))
for k,exp in [('feat_mean',4),('feat_std',4),('targ_mean',2),('targ_std',2)]:
    t=ckpt[k]; assert tuple(t.shape)==(exp,), (k,t.shape); print(f'  {k}={t.numpy().round(4)}')

# 2. load into EXACT arch (strict), replicate inference path
model=build_model(cfg)
missing,unexpected=model.load_state_dict(ckpt['state_dict'], strict=True)
print('strict load OK; missing',missing,'unexpected',unexpected)
model.eval()
fm=ckpt['feat_mean'].view(1,1,-1); fs=ckpt['feat_std'].view(1,1,-1)
tm=ckpt['targ_mean'].view(1,-1); ts=ckpt['targ_std'].view(1,-1)
def predict(points):
    with torch.no_grad():
        return model((points-fm)/fs)*ts+tm

def nrmse(p,t): return [(torch.sqrt(((p[:,i]-t[:,i])**2).mean())/t[:,i].std()).item() for i in range(2)]
def nmae(p,t,i): return (torch.abs(p[:,i]-t[:,i]).mean()/torch.abs(t[:,i]).mean()).item()

for split in ['train','val']:
    pts,tg=load_split(f'/app/data/{split}')
    pr=predict(pts); nr=nrmse(pr,tg)
    print(f'{split}: NRMSE C_D={nr[0]:.4f} C_L={nr[1]:.4f} mean={np.mean(nr):.4f} | cd_nmae={nmae(pr,tg,0):.4f}')

# 3. public_test: pipeline runs, predictions sane, range coverage
pts,_=load_split('/app/data/public_test')
pr=predict(pts)
print('public_test v-range: [%.1f,%.1f]'%(pts[:,0,2].min(),pts[:,0,2].max()))
print('pred C_D min/mean/max: %.4f/%.4f/%.4f'%(pr[:,0].min(),pr[:,0].mean(),pr[:,0].max()))
print('pred C_L min/mean/max: %.4f/%.4f/%.4f'%(pr[:,1].min(),pr[:,1].mean(),pr[:,1].max()))
assert torch.isfinite(pr).all(); assert (pr[:,0]>0).all(), 'C_D must be positive'
print('public_test predictions finite and C_D>0: OK')

# 4. velocity-extrapolation probe on real test geometries
base=pts[:40].clone()
print('velocity sweep (avg over 40 test shapes):')
prev=None
for vv in [31,50,65,75,80,85,92]:
    b=base.clone(); b[:,:,2]=vv
    p=predict(b); cd=p[:,0].mean().item()
    mono='' if prev is None else ('  dec' if cd<prev else '  INC!')
    print('  v=%3d  C_D=%.5f  C_L=%.4f%s'%(vv,cd,p[:,1].mean(),mono)); prev=cd
EOF
python exp/validate_final.py

output

keys: ['feat_mean', 'feat_std', 'state_dict', 'targ_mean', 'targ_std']
  feat_mean=[3.83500e-01 7.90000e-03 5.29737e+01 7.64000e-02]
  feat_std=[ 0.3956  0.0335 12.7859  0.0956]
  targ_mean=[0.0128 0.6596]
  targ_std=[0.0051 0.5762]
strict load OK; missing [] unexpected []
train: NRMSE C_D=0.1000 C_L=0.0350 mean=0.0675 | cd_nmae=0.0139
val: NRMSE C_D=0.0759 C_L=0.0374 mean=0.0566 | cd_nmae=0.0167
public_test v-range: [75.0,81.6]
pred C_D min/mean/max: 0.0072/0.0118/0.0291
pred C_L min/mean/max: -0.5342/0.6601/1.6965
public_test predictions finite and C_D>0: OK
velocity sweep (avg over 40 test shapes):
  v= 31  C_D=0.01483  C_L=0.7060
  v= 50  C_D=0.01351  C_L=0.7077  dec
  v= 65  C_D=0.01279  C_L=0.7117  dec
  v= 75  C_D=0.01241  C_L=0.7109  dec
  v= 80  C_D=0.01224  C_L=0.7098  dec
  v= 85  C_D=0.01209  C_L=0.7082  dec
  v= 92  C_D=0.01189  C_L=0.7060  dec

The final model validation looks excellent: 1. **All four required tensors present** with correct shapes (4,4,2,2). 2. **Strict load into exact architecture**: OK, no missing/unexpected keys. So the checkpoint loads straight back. 3. **In-distribution fit**: train mean NRMSE=0.068, val mean NRMSE=0.057 (C_D=0.076, C_L=0.037). Good. 4. **public_test** (v=75-81.6, the extrapolation regime): predictions finite, C_D>0, C_D in [0.0072, 0.029] (reasonable physical range), C_L in [-0.53, 1.70] (matches training target range). 5. **Velocity sweep**: C_D now MONOTONICALLY DECREASES across the entire range including extrapolation (0.01483 at v=31 → 0.01189 at v=92), following the physical v^-0.21 law. C_L is essentially FLAT (0.706→0.710→0.706). This is exactly the correct physical behavior , NO reversal, unlike the baseline. Compare to the original baseline probe which reversed C_D (went back UP to 0.0154 at v=90) and inflated C_L (to 0.68). The final model fixes both. The public_test C_D predictions (mean 0.0118) are at the low end, consistent with high velocity → low C_D. Good. This is a strong, physically-grounded solution. Let me do a couple more sanity/robustness checks: 1. Compare against what the naive baseline (train.py) would produce on public_test, to demonstrate the improvement. Actually, I can't measure public_test error (no labels). But I've shown the holdout improvement extensively. 2. Let me make sure the checkpoint is robust to being loaded the way the grader likely does. The grader probably does something like: load ckpt, build_model, load_state_dict, then preds = model((points - feat_mean)/feat_std) * targ_std + targ_mean. I replicated that. 3. Let me double check the dtype of saved tensors (should be float32). And that targ_std/feat_std are not accidentally zero anywhere. Let me also consider: is there any risk the grader applies normalization differently, e.g., expecting feat_mean/std to standardize to the SAME convention? The task says "feat_mean, feat_std: length-4 tensors that standardize the point features before the forward pass" and "targ_mean, targ_std: length-2 tensors that map the model's outputs back into physical coefficient units." So inference = model((x - feat_mean)/feat_std) then output*targ_std + targ_mean. That's exactly what I did. Let me verify dtypes and finalize. Let me also run the provided val through to ensure the numbers are stable, and verify there are no NaNs in state_dict. Let me also reconsider whether I should lower the in-distribution error further. The val NRMSE mean 0.057 is already good. But the scored set is the high-velocity extrapolation, where my holdout estimate was ~0.076-0.10 mean. Now, one thing I want to double-check: my holdout experiments trained on SUBSETS (v<=60 or v<=55). The final model trains on ALL data (v up to 75), which is strictly more information and closer to the test range (75 is adjacent to test 75-82). So the final model should extrapolate EVEN BETTER than my holdout estimates suggested (since the holdouts had a bigger gap to the test region). The final model only needs to extrapolate from 75 to ~78-82, a small step, and it's seen augmented data up to 95. So I expect the real test performance to be at least as good as the holdout ~0.08-0.10 mean, likely better. Let me verify dtypes and do a final robustness check (e.g., that predictions are deterministic and the model handles the exact public_test tensor). Then I'm done. Let me also verify that I'm not accidentally leaving the model in a bad state. Let me check state_dict has finite values and BN running stats are populated. Also, let me reconsider the `targ_mean`/`targ_std` being computed from raw targets. Since I augment C_D during training (scaling it), the effective distribution of C_D the network learns to predict is wider than raw. But I standardize with raw targ_std. That's fine , the network outputs standardized values that can exceed ±1 range; the affine mapping back is exact. No i …[truncated]

The final model validates cleanly on every axis that matters: - **Contract**: all four normalization tensors present with correct shapes; `state_dict` loads into the exact architecture with `strict=True` (no missing/unexpected keys), via the exact inference path the grader uses. - **Accuracy**: in-distribution val mean NRMSE = 0.057 (C_D=0.076, C_L=0.037). - **Extrapolation fixed**: on the velocity sweep, C_D now **monotonically decreases** across the entire range including far extrapolation (0.0148 at v=31 → 0.0119 at v=92), following the physical v^−0.21 law, and C_L stays flat , exactly the opposite of the baseline's reversal/inflation. - **Test regime**: on public_test (v=75–81.6), predictions are finite, C_D>0, and in a sensible physical range. Let me run final robustness checks (dtypes, NaNs, BN stats populated, determinism) to be thorough.

bash

cd /app && python -c "
import torch, sys, json
sys.path.insert(0,'/app'); from candidate_model import build_model
from dataset import load_split
cfg=json.load(open('/app/task_config.json'))
ck=torch.load('/app/outputs/model.pt', weights_only=True)
# dtypes + finiteness of norm tensors
for k in ['feat_mean','feat_std','targ_mean','targ_std']:
    t=ck[k]; assert t.dtype==torch.float32, (k,t.dtype); assert torch.isfinite(t).all()
assert (ck['feat_std']>0).all() and (ck['targ_std']>0).all(), 'std must be positive'
# state_dict finite + BN running stats present & populated
sd=ck['state_dict']; nbn=0
for k,v in sd.items():
    assert torch.isfinite(v).all(), k
    if 'running_mean' in k or 'running_var' in k: nbn+=1
print('state_dict tensors:',len(sd),'| BN running-stat tensors:',nbn,'| all finite: OK')
# determinism: two eval passes identical
m=build_model(cfg); m.load_state_dict(sd); m.eval()
pts,_=load_split('/app/data/public_test')
fm=ck['feat_mean'].view(1,1,-1); fs=ck['feat_std'].view(1,1,-1)
tm=ck['targ_mean'].view(1,-1); ts=ck['targ_std'].view(1,-1)
with torch.no_grad():
    a=m((pts-fm)/fs)*ts+tm; b=m((pts-fm)/fs)*ts+tm
assert torch.equal(a,b), 'non-deterministic!'
# batch-size invariance (BN in eval uses running stats -> per-sample independent)
with torch.no_grad():
    single=torch.stack([ (m((pts[i:i+1]-fm)/fs)*ts+tm)[0] for i in range(5)])
assert torch.allclose(single, a[:5], atol=1e-5), 'batch dependence!'
print('determinism + batch-size invariance: OK')
print('file size bytes:', __import__('os').path.getsize('/app/outputs/model.pt'))
"

output

state_dict tensors: 27 | BN running-stat tensors: 6 | all finite: OK
determinism + batch-size invariance: OK
file size bytes: 346611

All checks pass: - Norm tensors are float32, finite, positive std. - state_dict all finite, BN running stats populated (6 tensors = 3 BN layers × running_mean/var). - Deterministic predictions. - Batch-size invariant (important: BN in eval mode uses running stats, so predictions don't depend on batching , the grader can batch however it wants). The solution is complete and robust. Let me write a brief summary of what I did and clean up. Actually, let me reconsider one thing: should I push epochs or tune anything more? The val mean NRMSE is 0.057 in-distribution, and my extrapolation holdout estimates were ~0.08-0.10 mean. I'm confident in the recipe. Let me reconsider whether I've left the best possible solution. Let me reflect on potential concerns: 1. **The hidden test might extend beyond v=82.** The task says "higher-speed, higher-Reynolds end" and public_test goes to 81.6. My augmentation covers up to v=95, so even if the hidden set reaches into the high 80s, I've got coverage with the correct C_D law. Good margin. 2. **Could the exponent be wrong for the hidden set?** The exponent -0.21 is physically grounded (turbulent skin friction) and empirically robust (the method worked with exponents from -0.157 to -0.21). Even an imperfect exponent far outperforms no augmentation. 3. **Am I overfitting C_L to be too flat?** C_L residual correlation with v was 0.046 , essentially flat. Keeping C_L constant under velocity augmentation is well-justified. The sweep shows C_L flat at high v, which is physically correct. 4. **Did tw[1.5,1] hurt C_L?** val C_L NRMSE is 0.037, very good. No concern. I believe this is a strong, well-justified solution. Let me also make a quick comparison to demonstrate the improvement over the provided baseline trainer, to quantify the win on my holdout. Actually, I've already extensively shown baseline (no-aug) catastrophically fails (0.37-0.55 on holdout) vs my recipe (0.08-0.10). That's documented. Let me do one final thing: verify the exact file location and that everything is in place. Also clean up background processes. Let me confirm no stray processes and the output file is the final one. Actually, let me reconsider whether I should train a slightly longer final model (e.g., the ep600 gave marginally better). The difference 0.074 vs 0.077 is marginal and within the noise. 500 epochs is fine. I'll keep it. One more consideration: Let me reconsider the in-distribution train NRMSE (0.10 for C_D) vs val (0.076). Train C_D NRMSE (0.10) is HIGHER than val (0.076)? That's unusual (train usually lower). This is because of the augmentation: during training, 60% of samples have their C_D rescaled by the approximate law, so the model doesn't perfectly fit the raw training C_D values , it fits the augmented distribution. So raw-train C_D NRMSE being 0.10 while val is 0.076 just reflects that augmentation regularizes and the val happens to be slightly easier. This is fine and expected , it's not overfitting. Actually wait, let me reconsider: the train NRMSE is computed on RAW train targets (no aug) in my validation script. The model was trained to predict augmented targets 60% of the time. So on raw train data, there's a slight mismatch. That's expected and healthy (not overfit). Good. I'm confident. Let me clean up background processes and do a final directory check. Let me reconsider if there's anything about the metric I should optimize differently. The primary metric is "mean_nrmse". I've been computing per-target NRMSE normalized by the std of the true target on the eval set, then averaging the two. The grader might normalize differently (e.g., by range, or by a fixed reference). But regardless of the exact normalization, my approach minimizes the actual prediction error on both targets and specifically fixes the catastrophic extrapolation bias. Lower absolute error → lower NRMSE under any reasonable normalization. So I'm robust to the exact metric definition. Let me also consider "cd_nmae" …[truncated]

All robustness checks pass: tensors are float32/finite with positive stds, BatchNorm running stats are populated (6 tensors for 3 BN layers), and predictions are both **deterministic** and **batch-size invariant** (so however the grader batches the scored cases, each prediction is identical). Let me clean up background processes and do a final confirmation of the deliverable.

bash

cd /app && pkill -f 'exp/run' 2>/dev/null; pkill -f final_train 2>/dev/null; sleep 1
echo "=== Deliverable ===" && ls -la /app/outputs/model.pt
python -c "
import torch
ck=torch.load('/app/outputs/model.pt', weights_only=True)
print('keys:', sorted(ck))
print('feat_mean', ck['feat_mean'].tolist())
print('feat_std ', ck['feat_std'].tolist())
print('targ_mean', ck['targ_mean'].tolist())
print('targ_std ', ck['targ_std'].tolist())
print('state_dict entries:', len(ck['state_dict']))
"
echo "=== no stray training procs ===" && (ps aux | grep -E 'run[0-9]|final_train' | grep -v grep | wc -l)

output

=== Deliverable ===
-rw-r--r-- 1 h2tagent h2tagent 346611 Jun 19 23:23 /app/outputs/model.pt
keys: ['feat_mean', 'feat_std', 'state_dict', 'targ_mean', 'targ_std']
feat_mean [0.3835304379463196, 0.007914070971310139, 52.973655700683594, 0.0763944685459137]
feat_std  [0.3955599069595337, 0.03345881402492523, 12.785883903503418, 0.09557002782821655]
targ_mean [0.012763436883687973, 0.6596193313598633]
targ_std  [0.0051038553938269615, 0.5761952996253967]
state_dict entries: 27
=== no stray training procs ===
0

The deliverable is complete and verified. Here's a summary of what I did and why. ## Outcome I trained the pinned PointNet and wrote `/app/outputs/model.pt` containing `state_dict` plus all four normalization tensors (`feat_mean`, `feat_std`, `targ_mean`, `targ_std`). It loads into the exact architecture with `strict=True` and runs through the grader's intended path , `model((points − feat_mean)/feat_std) · targ_std + targ_mean` , producing deterministic, batch-size-invariant `[C_D, C_L]`. ## The core problem and my diagnosis The scored cases sit at **higher inlet velocity than any training case** (train/val v∈[31,75], but public_test v∈[75,82]). I confirmed this is the crux: a normally-trained model learns the correct *decreasing* C_D trend inside the training range but then **reverses it** in extrapolation (C_D curving back up, C_L spuriously inflating) , a classic nonlinear extrapolation failure. Since the checkpoint's input transform is affine-only, I couldn't fix this with feature engineering at inference; it had to be fixed in training. ## What actually drives the solution From the data I extracted the physics: - **C_D ∝ v^p with p ≈ −0.21** (fit controlling for geometry/AoA) , a striking match to the turbulent skin-friction law C_f ∝ Re^−0.2. - **C_L is velocity-independent** (residual correlation with v ≈ 0.05). This motivated **physics-based velocity augmentation**: for a fraction of each batch, resample the velocity channel across a range that brackets the test regime, rescale C_D by `(v_new/v_orig)^p`, and leave C_L unchanged. This teaches the fixed network the correct high-velocity behavior and, as a bonus, calibrates the BatchNorm running stats on high-velocity activations. ## Evidence it works I built velocity-gap holdouts (train on low v, test on held-out high v) because the provided val set is in-distribution and can't measure extrapolation. Mean NRMSE on the extrapolation holdout dropped from **≈0.37 (no augmentation) to ≈0.08–0.10**, with the result holding across a bigger gap and a deliberately noisier exponent (−0.157). A control confirmed that long training *without* augmentation stays catastrophic (0.37), so the augmentation , not the schedule , is the essential ingredient. The final model's velocity sweep shows C_D now monotonically decreasing through v=92 with flat C_L, exactly the correct physics. A couple of things worth flagging honestly: my headline extrapolation numbers come from the self-constructed velocity holdouts, since the real scored labels aren't available , the recipe was chosen to be robust (low seed variance, insensitive to the exact exponent/augmentation strength) rather than tuned to one number. And secondary choices like loss weighting and SWA were within noise, so I kept a simple, defensible configuration (mild [1.5,1] weighting, no SWA).

Final diff , what the agent changed

No file changes, the agent left the workspace untouched.

Verifier output , the proof behind the reward

tests/test.sh

# SyncVals normalized verifier summary
# task: airfrans-high-reynolds-drag-extrapolation
# attempt: 10  status: completed  raw_score: 0.49
# reward rule: continuous: score 0.49 < 0.5
# => reward = 0.0  (FAIL)
#
# Note: these tasks score via an external hidden grader; no pytest/verifier
# block is embedded in the agent transcript. The block below is the last
# sizable tool-output captured in the run (supporting evidence).
----------------------------------------------------------------------
=== Deliverable ===
-rw-r--r-- 1 h2tagent h2tagent 346611 Jun 19 23:23 /app/outputs/model.pt
keys: ['feat_mean', 'feat_std', 'state_dict', 'targ_mean', 'targ_std']
feat_mean [0.3835304379463196, 0.007914070971310139, 52.973655700683594, 0.0763944685459137]
feat_std  [0.3955599069595337, 0.03345881402492523, 12.785883903503418, 0.09557002782821655]
targ_mean [0.012763436883687973, 0.6596193313598633]
targ_std  [0.0051038553938269615, 0.5761952996253967]
state_dict entries: 27
=== no stray training procs ===
0

Reproduce this trial: git checkout 2f94510 && PYTHONPATH=src python3 scripts/build_site.py , then open trial/trial_a2944c69b75046ab. Re-running the agent live requires EVAL_PLATFORM_ENABLE_OAUTH_SMOKE=1 and is non-deterministic.

Trial trial_a2944c69b75046ab · verifier authoritative; classifier explanatory.