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
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File size: 3,925 Bytes
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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()
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