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:
| """ | |
| 06 — CFD vs POD-NN time analysis. | |
| Two figures (paper Fig 4): | |
| a) Cumulative wall-clock time crossover (CFD vs POD-NN). | |
| b) Per-component time bar chart (log scale): dataset generation, | |
| NN training, POD fit, and single inference. | |
| Both are analytical plots driven by measured timing constants. | |
| """ | |
| import numpy as np | |
| import matplotlib.pyplot as plt | |
| from _utils import PLOTS_DIR | |
| CFD_PER_ITER = 99.0 # s / CFD simulation | |
| PODNN_DATASET = 99.0 * 100 # 100 CFD sims for training | |
| PODNN_POD_TRAINING = 0.0318 # mean POD fit time, s | |
| PODNN_NN_TRAINING = 46.7705 # mean NN training time, s | |
| PODNN_TRAINING = PODNN_POD_TRAINING + PODNN_NN_TRAINING | |
| PODNN_UPFRONT = PODNN_DATASET + PODNN_TRAINING | |
| PODNN_PER_ITER = 0.24e-3 # 0.24 ms per inference | |
| def main(): | |
| n_cross = PODNN_UPFRONT / (CFD_PER_ITER - PODNN_PER_ITER) | |
| t_cross = CFD_PER_ITER * n_cross | |
| print(f"Crossover: {n_cross:.1f} iters ({t_cross/3600:.2f} hrs)") | |
| n_max = int(n_cross * 2.5) | |
| n = np.arange(0, n_max + 1) | |
| t_cfd = CFD_PER_ITER * n | |
| t_pod = PODNN_UPFRONT + PODNN_PER_ITER * n | |
| FS = 26 | |
| fig, ax = plt.subplots(figsize=(10, 6)) | |
| ax.plot(n, t_cfd / 3600, linewidth=2.5, color="tab:red", label="CFD") | |
| ax.plot(n, t_pod / 3600, linewidth=2.5, color="tab:blue", label="POD-NN") | |
| ax.axvline(n_cross, color="gray", linestyle="--", linewidth=1, alpha=0.7) | |
| ax.plot(n_cross, t_cross / 3600, "ko", markersize=10, zorder=5) | |
| ax.annotate(f"Crossover: {n_cross:.0f} iterations\n({t_cross/3600:.1f} hrs)", | |
| xy=(n_cross, t_cross / 3600), | |
| xytext=(n_cross + n_max * 0.08, t_cross / 3600 * 0.6), | |
| fontsize=FS - 8, ha="left", | |
| arrowprops=dict(arrowstyle="->", color="black", lw=1.5)) | |
| ax.set_xlabel("Number of Design Iterations", fontsize=FS) | |
| ax.set_ylabel("Cumulative Wall-Clock Time (hrs)", fontsize=FS) | |
| ax.tick_params(labelsize=FS - 4) | |
| ax.legend(fontsize=FS - 4) | |
| ax.grid(True, alpha=0.3) | |
| ax.set_xlim(0, n_max); ax.set_ylim(0, None) | |
| plt.tight_layout() | |
| PLOTS_DIR.mkdir(parents=True, exist_ok=True) | |
| out = PLOTS_DIR / "time_crossover.png" | |
| plt.savefig(out, dpi=300, bbox_inches="tight") | |
| print(f"Saved {out}") | |
| plt.close() | |
| # --- Per-component bar chart (paper Fig 4b) --- | |
| components = [ | |
| ("Dataset\nGeneration", PODNN_DATASET, "tab:orange"), | |
| ("NN\nTraining", PODNN_NN_TRAINING, "tab:blue"), | |
| ("POD\nFit", PODNN_POD_TRAINING, "tab:green"), | |
| ("Single\nInference", PODNN_PER_ITER, "tab:purple"), | |
| ] | |
| labels = [c[0] for c in components] | |
| values = [c[1] for c in components] | |
| colors = [c[2] for c in components] | |
| def fmt_time(s): | |
| if s >= 3600: return f"{s/3600:.1f} hr" | |
| if s >= 1: return f"{s:.1f} s" | |
| if s >= 1e-3: return f"{s*1e3:.1f} ms" | |
| return f"{s*1e6:.1f} µs" | |
| fig, ax = plt.subplots(figsize=(10, 6)) | |
| bars = ax.barh(labels, values, color=colors, edgecolor="white", height=0.5) | |
| ax.set_xscale("log") | |
| ax.set_xlabel("Wall-Clock Time (s)", fontsize=FS) | |
| ax.tick_params(labelsize=FS - 2) | |
| ax.grid(True, which="both", axis="x", alpha=0.3) | |
| ax.invert_yaxis() | |
| max_val = max(values) | |
| for bar, val in zip(bars, values): | |
| if val == max_val: | |
| ax.text(val * 0.6, bar.get_y() + bar.get_height() / 2, | |
| fmt_time(val), va="center", ha="right", fontsize=FS - 4, | |
| color="white", fontweight="bold") | |
| else: | |
| ax.text(val * 1.5, bar.get_y() + bar.get_height() / 2, | |
| fmt_time(val), va="center", ha="left", fontsize=FS - 4) | |
| plt.tight_layout() | |
| out_bar = PLOTS_DIR / "time_components_bar.png" | |
| plt.savefig(out_bar, dpi=300, bbox_inches="tight") | |
| print(f"Saved {out_bar}") | |
| plt.close() | |
| if __name__ == "__main__": | |
| main() | |