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:
| """ | |
| 04 — Cumulative POD variance explained vs number of modes. | |
| Fits PCA up to min(n_samples, n_points) modes on the full dataset and | |
| plots the cumulative explained variance curve. | |
| """ | |
| import numpy as np | |
| import matplotlib.pyplot as plt | |
| from sklearn.decomposition import PCA | |
| from _utils import load_data, PLOTS_DIR | |
| def main(): | |
| _, fields, _, _ = load_data() | |
| max_modes = min(fields.shape[0], fields.shape[1]) | |
| pca = PCA(n_components=max_modes).fit(fields) | |
| cumulative = np.cumsum(pca.explained_variance_ratio_) | |
| print(f"{'Modes':>6} {'Cum Var (%)':>12}") | |
| for i in range(min(20, len(cumulative))): | |
| print(f"{i+1:>6} {cumulative[i]*100:>12.4f}") | |
| modes = np.arange(1, len(cumulative) + 1) | |
| FS = 20 | |
| fig, ax = plt.subplots(figsize=(9, 9)) | |
| ax.plot(modes, cumulative * 100, "o-", color="tab:green", | |
| linewidth=2, markersize=6) | |
| ax.set_xlabel(r"Number of POD Modes, $r$", fontsize=FS) | |
| ax.set_ylabel(r"Cumulative Variance Explained, $\eta_r$ (%)", fontsize=FS) | |
| ax.tick_params(labelsize=FS - 4) | |
| ax.set_ylim(None, 101) | |
| ax.grid(True, alpha=0.3) | |
| idx_9999 = np.searchsorted(cumulative, 0.9999) + 1 | |
| ax.set_xlim(0, min(idx_9999 + 5, len(cumulative))) | |
| plt.tight_layout() | |
| PLOTS_DIR.mkdir(parents=True, exist_ok=True) | |
| out = PLOTS_DIR / "pod_mode_variance.png" | |
| plt.savefig(out, dpi=300, bbox_inches="tight") | |
| print(f"Saved {out}") | |
| plt.close() | |
| if __name__ == "__main__": | |
| main() | |