Datasets:
Tasks:
Tabular Regression
Languages:
English
Size:
1K<n<10K
ArXiv:
Tags:
computational-fluid-dynamics
surrogate-modeling
proper-orthogonal-decomposition
electronics-cooling
thermal-management
reduced-order-model
License:
| """ | |
| 09 — Dataset size sensitivity study + error decomposition. | |
| Trains a fresh POD-NN at each of several training sizes against a | |
| fixed 400-sample held-out test set. For each model, total Test MSE | |
| is decomposed into MSE_POD (truncation error: Y_test vs POD-projected | |
| Y_test) and MSE_NN (regression error: NN-predicted vs POD-projected). | |
| Outputs: | |
| - dataset_size_sensitivity.png — Test MSE & Max AE vs N (paper Fig 3a) | |
| - error_decomposition.png — MSE_POD vs MSE_NN per N (paper Fig 5) | |
| - dataset_size_sensitivity.csv — raw numbers | |
| """ | |
| import csv | |
| import numpy as np | |
| import matplotlib.pyplot as plt | |
| from sklearn.metrics import mean_squared_error | |
| from _utils import ( | |
| load_data, train_pod_nn, predict_field, seed_all, | |
| TEST_SIZE, N_MODES, EPOCHS, ANALYZED_DIR, PLOTS_DIR, | |
| ) | |
| SIZES = [10, 25, 50, 75, 100, 150, 200, 500, 1000, 1600] | |
| def main(): | |
| parameters, fields, _, _ = load_data() | |
| X_test = parameters[-TEST_SIZE:] | |
| Y_test = fields[-TEST_SIZE:] | |
| n_pool = len(parameters) - TEST_SIZE | |
| results = [] | |
| for size in SIZES: | |
| if size > n_pool: | |
| print(f"Skipping size={size} (exceeds train pool {n_pool})") | |
| continue | |
| seed_all() | |
| print(f"\n=== Training N={size} ===") | |
| trained = train_pod_nn(parameters[:size], fields[:size], | |
| n_modes=N_MODES, epochs=EPOCHS, verbose=0) | |
| Y_pred = predict_field(trained, X_test) | |
| mse = mean_squared_error(Y_test.flatten(), Y_pred.flatten()) | |
| max_ae = float(np.max(np.abs(Y_test - Y_pred))) | |
| # Error decomposition | |
| pca = trained["pca"] | |
| Y_pod = pca.inverse_transform(pca.transform(Y_test)) | |
| mse_pod = float(np.mean((Y_pod - Y_test) ** 2)) | |
| mse_nn = float(np.mean((Y_pred - Y_pod) ** 2)) | |
| results.append({ | |
| "dataset_size": size, "mse": mse, "max_ae": max_ae, | |
| "mse_pod": mse_pod, "mse_nn": mse_nn, | |
| }) | |
| print(f" MSE={mse:.4f} MaxAE={max_ae:.4f} " | |
| f"MSE_POD={mse_pod:.4f} MSE_NN={mse_nn:.4f}") | |
| # Save raw numbers | |
| csv_path = ANALYZED_DIR / "dataset_size_sensitivity.csv" | |
| csv_path.parent.mkdir(parents=True, exist_ok=True) | |
| with open(csv_path, "w", newline="") as f: | |
| w = csv.DictWriter(f, fieldnames=["dataset_size", "mse", "max_ae", | |
| "mse_pod", "mse_nn"]) | |
| w.writeheader(); w.writerows(results) | |
| print(f"\nSaved {csv_path}") | |
| sizes = [r["dataset_size"] for r in results] | |
| mses = [r["mse"] for r in results] | |
| max_aes = [r["max_ae"] for r in results] | |
| FS = 24 | |
| fig, ax1 = plt.subplots(figsize=(10, 6)) | |
| ax2 = ax1.twinx() | |
| ax1.plot(sizes, mses, "o-", color="tab:blue", linewidth=2, | |
| markersize=8, label=r"Test MSE (K$^2$)") | |
| ax2.plot(sizes, max_aes, "D-", color="tab:red", linewidth=2, | |
| markersize=8, label="Test Max AE (K)") | |
| ax1.set_xlabel("Training Dataset Size", fontsize=FS) | |
| ax1.set_ylabel(r"Test MSE (K$^2$)", fontsize=FS, color="tab:blue") | |
| ax2.set_ylabel("Test Max AE (K)", fontsize=FS, color="tab:red") | |
| ax1.tick_params(labelsize=FS - 4, axis="both") | |
| ax2.tick_params(labelsize=FS - 4, axis="y", labelcolor="tab:red") | |
| ax1.tick_params(axis="y", labelcolor="tab:blue") | |
| ax1.grid(True, alpha=0.3) | |
| plt.tight_layout() | |
| PLOTS_DIR.mkdir(parents=True, exist_ok=True) | |
| out = PLOTS_DIR / "dataset_size_sensitivity.png" | |
| plt.savefig(out, dpi=300, bbox_inches="tight") | |
| print(f"Saved {out}") | |
| plt.close() | |
| # --- Error decomposition bar plot (paper Fig 5) --- | |
| mse_pods = [r["mse_pod"] for r in results] | |
| mse_nns = [r["mse_nn"] for r in results] | |
| FS2 = 20 | |
| x = np.arange(len(sizes)) | |
| width = 0.35 | |
| fig, ax = plt.subplots(figsize=(14, 6)) | |
| bars_pod = ax.bar(x - width / 2, mse_pods, width, | |
| label=r"$\mathrm{MSE_{POD}}$", color="tab:orange", | |
| edgecolor="black", linewidth=0.5) | |
| bars_nn = ax.bar(x + width / 2, mse_nns, width, | |
| label=r"$\mathrm{MSE_{NN}}$", color="tab:purple", | |
| edgecolor="black", linewidth=0.5) | |
| for bar in list(bars_pod) + list(bars_nn): | |
| ax.text(bar.get_x() + bar.get_width() / 2, bar.get_height(), | |
| f"{bar.get_height():.1f}", ha="center", va="bottom", | |
| fontsize=FS2 - 4) | |
| ax.set_xlabel("Training Dataset Size (N)", fontsize=FS2) | |
| ax.set_ylabel(r"MSE (K$^2$)", fontsize=FS2) | |
| ax.set_xticks(x) | |
| ax.set_xticklabels([str(s) for s in sizes]) | |
| ax.tick_params(labelsize=FS2 - 4) | |
| ax.legend(fontsize=FS2 - 4) | |
| ax.grid(True, alpha=0.3, axis="y") | |
| plt.tight_layout() | |
| out_decomp = PLOTS_DIR / "error_decomposition.png" | |
| plt.savefig(out_decomp, dpi=300, bbox_inches="tight") | |
| print(f"Saved {out_decomp}") | |
| plt.close() | |
| if __name__ == "__main__": | |
| main() | |