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11 — Pearson correlation between POD coefficients and (raw inputs,
derived inputs, output metrics).
Fits PCA on the first TRAIN_SIZE samples, projects all 2000 onto the
basis, computes Pearson R between each PC coefficient and a curated
set of raw / derived / output quantities, then renders a single table-
style heatmap.
"""
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.gridspec import GridSpec
from matplotlib.transforms import blended_transform_factory
from sklearn.decomposition import PCA
from scipy import stats
from _utils import (
load_data, compute_rth, CHIP_AREA, PARAM_IDX,
TRAIN_SIZE, N_MODES, PLOTS_DIR,
)
FS = 20
LATEX = {
# Raw
"Q1": r"$Q_1$", "Q2": r"$Q_2$",
"m1": r"$\dot{m}_1$", "m2": r"$\dot{m}_2$",
"T_in1": r"$T_{\mathrm{in},1}$", "T_in2": r"$T_{\mathrm{in},2}$",
# Derived
"Q_total": r"$Q_1 + Q_2$",
"m_total": r"$\dot{m}_1 + \dot{m}_2$",
"T_in_avg": r"$\bar{T}_{\mathrm{in}}$",
"Q1 - Q2": r"$Q_1 - Q_2$",
"m1 - m2": r"$\dot{m}_1 - \dot{m}_2$",
"T_in1 - T_in2": r"$T_{\mathrm{in},1} - T_{\mathrm{in},2}$",
"Q1 / m1": r"$Q_1 / \dot{m}_1$",
"Q2 / m2": r"$Q_2 / \dot{m}_2$",
"Q1/m1 - Q2/m2": r"$Q_1/\dot{m}_1 - Q_2/\dot{m}_2$",
# Outputs
"Tmax_chip1": r"$T_{\max,\mathrm{chip1}}$",
"Tmax_chip2": r"$T_{\max,\mathrm{chip2}}$",
"Rth1": r"$R_{\mathrm{th},1}$",
"Rth2": r"$R_{\mathrm{th},2}$",
}
DESC = {
"Q1": "Chip 1 heat load",
"Q2": "Chip 2 heat load",
"m1": "Inlet 1 mass flow rate",
"m2": "Inlet 2 mass flow rate",
"T_in1": "Inlet 1 temperature",
"T_in2": "Inlet 2 temperature",
"Q_total": "Total heat load",
"m_total": "Total mass flow rate",
"T_in_avg": "Mean inlet temperature",
"Q1 - Q2": "Heat load difference",
"m1 - m2": "Flow rate difference",
"T_in1 - T_in2": "Inlet temp. difference",
"Q1 / m1": "Side 1 thermal load",
"Q2 / m2": "Side 2 thermal load",
"Q1/m1 - Q2/m2": "Thermal load difference",
"Tmax_chip1": "Chip 1 peak temperature",
"Tmax_chip2": "Chip 2 peak temperature",
"Rth1": "Chip 1 thermal resistance",
"Rth2": "Chip 2 thermal resistance",
}
def build_features(parameters, fields, coords):
Q1 = parameters[:, PARAM_IDX["Q1"]] * CHIP_AREA
Q2 = parameters[:, PARAM_IDX["Q2"]] * CHIP_AREA
m1 = parameters[:, PARAM_IDX["m1"]]
m2 = parameters[:, PARAM_IDX["m2"]]
T1 = parameters[:, PARAM_IDX["T_in1"]]
T2 = parameters[:, PARAM_IDX["T_in2"]]
rth1, rth2, tmax1, tmax2 = compute_rth(fields, coords, parameters)
return {
# Raw
"Q1": Q1, "Q2": Q2, "m1": m1, "m2": m2, "T_in1": T1, "T_in2": T2,
# Derived
"Q_total": Q1 + Q2,
"m_total": m1 + m2,
"T_in_avg": (T1 + T2) / 2,
"Q1 - Q2": Q1 - Q2,
"m1 - m2": m1 - m2,
"T_in1 - T_in2": T1 - T2,
"Q1 / m1": Q1 / m1,
"Q2 / m2": Q2 / m2,
"Q1/m1 - Q2/m2": Q1 / m1 - Q2 / m2,
# Outputs
"Tmax_chip1": tmax1, "Tmax_chip2": tmax2,
"Rth1": rth1, "Rth2": rth2,
}
def main():
parameters, fields, coords, _ = load_data()
pca = PCA(n_components=N_MODES).fit(fields[:TRAIN_SIZE])
coeffs = pca.transform(fields)
var = pca.explained_variance_ratio_
feats = build_features(parameters, fields, coords)
n_raw, n_derived, n_out = 6, 9, 4
names = list(feats.keys())
sep1, sep2 = n_raw - 0.5, n_raw + n_derived - 0.5
cat_labels = [
("Raw Inputs", n_raw / 2 - 0.5),
("Derived Inputs", n_raw + n_derived / 2 - 0.5),
("Outputs", n_raw + n_derived + n_out / 2 - 0.5),
]
n_p = len(names)
R = np.zeros((n_p, N_MODES))
for j, n in enumerate(names):
for i in range(N_MODES):
R[j, i], _ = stats.pearsonr(feats[n], coeffs[:, i])
fig = plt.figure(figsize=(16, 14))
gs = GridSpec(1, 3, width_ratios=[5.0, 2.75, 0.15], wspace=0.0)
ax_table = fig.add_subplot(gs[0, 0])
ax_heat = fig.add_subplot(gs[0, 1])
ax_cbar = fig.add_subplot(gs[0, 2])
im = ax_heat.imshow(R, cmap="RdBu_r", vmin=-1, vmax=1, aspect="auto")
ax_heat.set_xticks(range(N_MODES))
ax_heat.set_xticklabels([f"PC{i+1}\n({var[i]*100:.1f}%)" for i in range(N_MODES)],
fontsize=FS - 4)
ax_heat.xaxis.set_ticks_position("top")
ax_heat.xaxis.set_label_position("top")
ax_heat.set_yticks([])
for j in range(n_p):
for i in range(N_MODES):
r = R[j, i]
color = "white" if abs(r) > 0.55 else "black"
ax_heat.text(i, j, f"{r:+.2f}", ha="center", va="center",
fontsize=FS - 2, color=color)
for s in [sep1, sep2]:
ax_heat.axhline(y=s, color="black", linewidth=2.5)
cbar = fig.colorbar(im, cax=ax_cbar)
cbar.set_label("Pearson $R$", fontsize=FS - 2)
cbar.ax.tick_params(labelsize=FS - 4)
ax_table.set_xlim(0, 1)
ax_table.set_ylim(n_p - 0.5, -0.5)
ax_table.axis("off")
trans_top = blended_transform_factory(ax_table.transData, ax_table.transAxes)
for x, h in [(0.05, "Type"), (0.34, "Description"), (0.79, "Symbol")]:
ax_table.text(x, 1.03, h, fontsize=FS - 2, ha="center", va="bottom",
fontweight="bold", transform=trans_top)
for s in [sep1, sep2]:
ax_table.plot([0.0, 1.0], [s, s], color="black", linewidth=2.5,
transform=ax_table.transData, clip_on=False)
ax_table.plot([0.10, 0.10], [-0.5, n_p - 0.5], color="gray",
linewidth=0.5, alpha=0.5)
ax_table.plot([0.58, 0.58], [-0.5, n_p - 0.5], color="gray",
linewidth=0.5, alpha=0.5)
for label, y_pos in cat_labels:
ax_table.text(0.05, y_pos, label, fontsize=FS - 2, ha="center",
va="center", rotation=90, fontweight="bold")
for j, n in enumerate(names):
ax_table.text(0.12, j, DESC.get(n, n), fontsize=FS - 2,
ha="left", va="center")
ax_table.text(0.60, j, LATEX.get(n, n), fontsize=FS - 2,
ha="left", va="center")
PLOTS_DIR.mkdir(parents=True, exist_ok=True)
out = PLOTS_DIR / "pearson_correlation.png"
plt.savefig(out, dpi=300, bbox_inches="tight")
print(f"Saved {out}")
plt.close()
if __name__ == "__main__":
main()
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