Ground-Wing / scripts /plotting /coefficient_error.py
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"""Benchmark results: every number and figure of the paper's benchmarking section.
Two metrics are calculated:
Integral coefficients: per-simulation absolute percentage error on $C_l$ and $C_d$ plus
two coefficients of determination, $R^2_\\mathrm{fit}$ (squared Pearson correlation, i.e. the
linearity of the predicted-versus-true scatter) and $R^2_{1:1}$ (taken about the $1{:}1$
line, so it also penalises bias and scale errors).
Surface fields: MSE, relative $L_1$ and relative $L_2$ on $C_p$ and $|\\bm{w_s}|$,
recomputed element by element from the prediction meshes by surface_metrics.py.
Outputs, under outputs/results/:
<split>/results_table.csv <split>/coefficient_error_boxplot.svg
<split>/field_error_table.csv <split>/field_error_bars.svg
<split>/r2_table.csv <split>/parity_grid.svg
<split>/delta_cl_{abupt,xmeshgraphnet}.svg
benchmark_summary.csv split_comparison.svg
directional_accuracy.csv abupt_training_targets.csv
The last section prints the LaTeX rows of tab:results, tab:field_errors,
tab:results_splits and tab:abupt_targets.
Run surface_metrics.py first: both the coefficients and the surface-field tables read its
output.
"""
from __future__ import annotations
import sys
from pathlib import Path
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from scipy import stats
sys.path.insert(0, str(Path(__file__).resolve().parent))
from inference_io import ( # noqa: E402
appendix_model_labels,
field_labels,
metrics_dir,
here,
model_labels,
output_dir,
split_labels,
splits,
load_coefficients,
relative_error,
reported_models,
test_run_ids,
)
# Text is typeset by LaTeX in the paper's fonts and every figure is drawn at the width at
# which it is included.
text_width_in = 6.5
plt.rcParams.update({
"text.usetex": True,
"text.latex.preamble": r"\usepackage{newtxtext,newtxmath}\usepackage{bm}",
"font.family": "serif",
"font.size": 9,
"axes.labelsize": 9,
"axes.titlesize": 9,
"legend.fontsize": 8,
"xtick.labelsize": 8,
"ytick.labelsize": 8,
"figure.dpi": 120,
})
def save(fig, path: Path) -> Path:
"""Write one SVG and close the figure."""
path.parent.mkdir(parents=True, exist_ok=True)
fig.savefig(path, format="svg", bbox_inches="tight")
plt.close(fig)
print(f" wrote {path.relative_to(here)}")
return path
# One colour per model, held fixed across every figure.
model_colors = dict(zip(model_labels, plt.get_cmap("tab10").colors))
split_colors = dict(zip(splits, ["tab:blue", "tab:orange", "tab:green"]))
coeffs = ("Cl", "Cd")
coeff_labels = {"Cl": "$C_l$", "Cd": "$C_d$"}
output_dir.mkdir(parents=True, exist_ok=True)
print(f"figure output: {output_dir}\n")
# ---------------------------------------------------------------------------
# Integral coefficient accuracy
# ---------------------------------------------------------------------------
def coefficient_stats(split: str, model: str) -> dict:
"""Every coefficient-level statistic for one split/model."""
df = load_coefficients(split, model)
row = {
"split": split,
"model_key": model,
"model": model_labels[model],
"samples": len(df),
}
for coeff in coeffs:
key = coeff.lower()
err = relative_error(df, coeff)
true = df[coeff].to_numpy(dtype=float)
pred = df[f"{coeff}Pred"].to_numpy(dtype=float)
fit = stats.linregress(true, pred)
row |= {
f"{key}_mean_pct": err.mean(),
f"{key}_std_pct": err.std(),
f"{key}_median_pct": err.median(),
f"{key}_p95_pct": float(np.percentile(err, 95)),
f"{key}_max_pct": err.max(),
f"{key}_r2_fit": fit.rvalue**2,
f"{key}_r2_1to1": 1.0
- np.sum((pred - true) ** 2) / np.sum((true - true.mean()) ** 2),
f"{key}_slope": fit.slope,
}
return row
coefficients = pd.DataFrame(
[coefficient_stats(split, model) for split in splits for model in reported_models()]
)
def ranked_models(split: str) -> list[str]:
"""Model keys of one split ordered by mean Cl error, best first."""
block = coefficients[coefficients["split"] == split].sort_values("cl_mean_pct")
return list(block["model_key"])
def boxplot_errors(split: str, output_path: Path) -> Path:
"""Per-simulation Cd (left) and Cl (right) relative-error distributions."""
models = ranked_models(split)
frames = {m: load_coefficients(split, m) for m in models}
labels = [model_labels[m] for m in models]
fig, axes = plt.subplots(1, 2, figsize=(text_width_in, 3.1), sharex=True)
for ax, coeff in zip(axes, ("Cd", "Cl")):
box = ax.boxplot(
[relative_error(frames[m], coeff) for m in models],
tick_labels=labels,
patch_artist=True,
widths=0.6,
flierprops=dict(marker=".", markersize=3, markeredgewidth=0.4),
medianprops=dict(color="black", linewidth=1.0),
)
for patch, model in zip(box["boxes"], models):
patch.set_facecolor(model_colors[model])
patch.set_alpha(0.55)
patch.set_linewidth(0.6)
ax.set_ylabel(rf"{coeff_labels[coeff]} relative error [\%]")
ax.set_yscale("log")
ax.grid(True, which="both", axis="y", alpha=0.3, linewidth=0.4)
ax.tick_params(axis="x", rotation=35)
for label in ax.get_xticklabels():
label.set_horizontalalignment("right")
fig.tight_layout()
return save(fig, output_path)
for split in splits:
block = coefficients[coefficients["split"] == split].sort_values("cl_mean_pct")
(output_dir / split).mkdir(parents=True, exist_ok=True)
block.drop(columns="model_key").to_csv(output_dir / split / "results_table.csv", index=False)
print("=" * 96)
print(f"{split_labels[split]} split -- test set: {len(test_run_ids(split))} simulations")
print("=" * 96)
print(
block[[
"model", "samples",
"cl_mean_pct", "cl_std_pct", "cl_r2_fit", "cl_r2_1to1",
"cd_mean_pct", "cd_std_pct", "cd_r2_fit", "cd_r2_1to1",
]].to_string(index=False, float_format=lambda v: f"{v:.3f}")
)
boxplot_errors(split, output_dir / split / "coefficient_error_boxplot.svg")
print()
# Ranking by mean Cl error on the stratified split: the order every table and figure uses.
paper_order = ranked_models("stratified")
print(f"figure/table order (stratified ranking): {[model_labels[m] for m in paper_order]}")
# ---------------------------------------------------------------------------
# Surface field accuracy
# ---------------------------------------------------------------------------
field_stat_columns = [
"mse_abs", "l1_abs", "l2_abs", "rmse_abs", "srmse", "mse_rel", "l1_rel", "l2_rel", "r2",
]
def load_field_metrics() -> pd.DataFrame:
"""Merged per-run field metrics for every split and model."""
path = metrics_dir / "field_metrics.csv"
if not path.exists():
raise FileNotFoundError(f"{path} is missing -- run `python3 surface_metrics.py` first")
merged = pd.read_csv(path, dtype={"run_id": str})
if merged[field_stat_columns].isna().any().any():
raise ValueError("field metrics contain NaNs")
return merged
field_metrics = load_field_metrics()
field_summary = (
field_metrics.groupby(["split", "model", "field"])
.agg(runs=("run_id", "nunique"), **{
f"{c}_{stat}": (c, stat)
for c in field_stat_columns
for stat in ("mean", "std", "median")
})
.reset_index()
)
field_summary["model_label"] = field_summary["model"].map(model_labels)
def field_error_bars(split: str, output_path: Path) -> Path:
"""Relative L2 per model, one panel per surface field, with the 1-sigma spread."""
models = ranked_models(split)
block = field_summary[field_summary["split"] == split].set_index(["field", "model"])
fields = list(field_labels)
means_all = {
field: np.array([block.loc[(field, m), "l2_rel_mean"] for m in models]) * 100
for field in fields
}
spreads = {
field: np.array([block.loc[(field, m), "l2_rel_std"] for m in models]) * 100
for field in fields
}
# The panels share their y-axis, so the limit has to leave room for the tallest bar of
# either of them plus its label.
top = 1.15 * max((means_all[f] + spreads[f]).max() for f in fields)
fig, axes = plt.subplots(1, len(fields), figsize=(text_width_in, 2.8), sharey=True)
x = np.arange(len(models))
for ax, field in zip(np.atleast_1d(axes), fields):
means, spread = means_all[field], spreads[field]
ax.bar(
x, means, yerr=spread, capsize=2,
color=[model_colors[m] for m in models], alpha=0.85,
error_kw=dict(elinewidth=0.6, capthick=0.6),
)
for xi, value, err in zip(x, means, spread):
ax.annotate(
f"{value:.1f}", (xi, value + err), textcoords="offset points",
xytext=(0, 3), ha="center", fontsize=6,
)
ax.set_ylim(0, top)
ax.set_title(field_labels[field])
ax.set_xticks(x, [model_labels[m] for m in models], rotation=35, ha="right")
ax.grid(True, axis="y", alpha=0.3, linewidth=0.4)
np.atleast_1d(axes)[0].set_ylabel(r"Relative $L_2$ error [\%]")
fig.tight_layout()
return save(fig, output_path)
paper_field_columns = ["mse_abs_mean", "l1_rel_mean", "l2_rel_mean"]
for split in splits:
block = field_summary[field_summary["split"] == split].copy()
block["rank"] = block["model"].map({m: i for i, m in enumerate(ranked_models(split))})
block = block.sort_values(["field", "rank"]).drop(columns="rank")
block.to_csv(output_dir / split / "field_error_table.csv", index=False)
print("=" * 96)
print(f"{split_labels[split]} split -- surface field errors")
print("=" * 96)
print(
block[["field", "model_label", "runs", *paper_field_columns]].to_string(
index=False, float_format=lambda v: f"{v:.4f}"
)
)
field_error_bars(split, output_dir / split / "field_error_bars.svg")
print()
# ---------------------------------------------------------------------------
# One row per split and model with every reported metric, plus the figure that puts the
# three splits side by side.
# ---------------------------------------------------------------------------
field_wide = field_summary.pivot_table(
index=["split", "model"],
columns="field",
values=["mse_abs_mean", "l1_rel_mean", "l2_rel_mean", "r2_mean", "srmse_mean"],
)
field_wide.columns = [f"{field}_{metric}" for metric, field in field_wide.columns]
field_wide = field_wide.reset_index()
benchmark_summary = coefficients.merge(
field_wide, left_on=["split", "model_key"], right_on=["split", "model"],
suffixes=("", "_field"),
).drop(columns="model_field")
benchmark_summary["rank"] = [
ranked_models(s).index(m)
for s, m in zip(benchmark_summary["split"], benchmark_summary["model_key"])
]
benchmark_summary["split_rank"] = benchmark_summary["split"].map(
{s: i for i, s in enumerate(splits)}
)
benchmark_summary = (
benchmark_summary.sort_values(["split_rank", "rank"])
.drop(columns=["rank", "split_rank"])
.reset_index(drop=True)
)
benchmark_summary.to_csv(output_dir / "benchmark_summary.csv", index=False)
print(f"wrote {(output_dir / 'benchmark_summary.csv').relative_to(here)}")
for split in splits:
block = benchmark_summary[benchmark_summary["split"] == split]
block.drop(columns="model_key").to_csv(output_dir / split / "r2_table.csv", index=False)
def split_comparison(output_path: Path) -> Path:
"""Mean Cl and Cd error per model, grouped by split, with 1-sigma error bars."""
models = paper_order
indexed = benchmark_summary.set_index(["split", "model_key"])
fig, axes = plt.subplots(1, 2, figsize=(text_width_in, 3.0), sharex=True)
x = np.arange(len(models))
width = 0.26
for ax, coeff in zip(axes, coeffs):
key = coeff.lower()
for i, split in enumerate(splits):
values = [indexed.loc[(split, m), f"{key}_mean_pct"] for m in models]
errs = [indexed.loc[(split, m), f"{key}_std_pct"] for m in models]
ax.bar(
x + (i - 1) * width, values, width, yerr=errs, capsize=2,
label=split_labels[split], color=split_colors[split], alpha=0.85,
error_kw=dict(elinewidth=0.6, capthick=0.6),
)
ax.set_ylabel(rf"Mean {coeff_labels[coeff]} error [\%]")
ax.set_yscale("log")
ax.set_xticks(x, [model_labels[m] for m in models], rotation=35, ha="right")
ax.grid(True, which="both", axis="y", alpha=0.3, linewidth=0.4)
axes[0].legend(loc="upper left", frameon=False)
fig.tight_layout()
return save(fig, output_path)
split_comparison(output_dir / "split_comparison.svg")
print("\n" + "=" * 96)
print("Mean coefficient error across the three splits [%]")
print("=" * 96)
print(
benchmark_summary.pivot_table(
index="model", columns="split", values=["cl_mean_pct", "cd_mean_pct"]
).to_string(float_format=lambda v: f"{v:.2f}")
)
# ---------------------------------------------------------------------------
# Predicted-versus-true parity grid: one column per model, Cd on the top row and Cl on the
# bottom, with both coefficients of determination annotated in each panel.
# ---------------------------------------------------------------------------
def parity_grid(split: str, output_path: Path) -> Path:
models = ranked_models(split)
indexed = coefficients.set_index(["split", "model_key"])
fig, axes = plt.subplots(
2, len(models), figsize=(text_width_in, 2.9), sharex="row", sharey="row"
)
for row, coeff in enumerate(("Cd", "Cl")):
frames = {m: load_coefficients(split, m) for m in models}
lo = min(min(df[coeff].min(), df[f"{coeff}Pred"].min()) for df in frames.values())
hi = max(max(df[coeff].max(), df[f"{coeff}Pred"].max()) for df in frames.values())
pad = 0.05 * (hi - lo)
lo, hi = lo - pad, hi + pad
for col, model in enumerate(models):
ax = axes[row, col]
df = frames[model]
ax.plot([lo, hi], [lo, hi], "k-", linewidth=0.6, zorder=1)
ax.scatter(
df[coeff], df[f"{coeff}Pred"], s=4, alpha=0.75, zorder=2,
color=model_colors[model], edgecolors="none",
)
row_stats = indexed.loc[(split, model)]
key = coeff.lower()
ax.annotate(
f"$R^2_{{\\mathrm{{fit}}}}={row_stats[f'{key}_r2_fit']:.3f}$\n"
f"$R^2_{{1{{:}}1}}={row_stats[f'{key}_r2_1to1']:.3f}$",
(0.05, 0.95), xycoords="axes fraction", va="top", fontsize=6,
)
ax.set_xlim(lo, hi)
ax.set_ylim(lo, hi)
ax.set_aspect("equal")
ax.tick_params(labelsize=6, length=2, pad=1)
ax.grid(True, alpha=0.25, linewidth=0.4)
if row == 0:
ax.set_title(model_labels[model], fontsize=7)
if col == 0:
ax.set_ylabel(rf"Predicted {coeff_labels[coeff]}", fontsize=8)
ax.set_xlabel(rf"True {coeff_labels[coeff]}", fontsize=7)
fig.tight_layout(h_pad=0.6, w_pad=0.3)
return save(fig, output_path)
for split in splits:
parity_grid(split, output_dir / split / "parity_grid.svg")
# ---------------------------------------------------------------------------
# Directional consistency. Every ordered pair of test simulations contributes a true and a
# predicted coefficient delta; a pair counts as a directional match when the two have the
# same sign. Only the half-plane of positive true deltas is evaluated -- the pair (a, b) and
# its mirror (b, a) carry the same information.
# ---------------------------------------------------------------------------
delta_threshold_pct = 0.10
def delta_pairs(split: str, model: str, coeff: str):
"""True and predicted pairwise deltas, plus the tolerance band of one split/model."""
df = load_coefficients(split, model)
true = df[coeff].to_numpy(dtype=float)
pred = df[f"{coeff}Pred"].to_numpy(dtype=float)
# element (r, i) of the outer difference is the delta of run i against reference r
delta_true = (true[None, :] - true[:, None]).ravel()
delta_pred = (pred[None, :] - pred[:, None]).ravel()
keep = delta_true > 0
threshold = delta_threshold_pct * abs(true.mean())
return delta_true[keep], delta_pred[keep], threshold
def delta_stats(split: str, model: str, coeff: str) -> dict:
"""Directional-consistency statistics for one split/model/coefficient."""
delta_true, delta_pred, threshold = delta_pairs(split, model, coeff)
matches = np.sign(delta_true) == np.sign(delta_pred)
within = np.abs(delta_pred - delta_true) <= threshold
fit = stats.linregress(delta_true, delta_pred)
return {
"split": split,
"model": model_labels[model],
"coefficient": coeff,
"pairs": 2 * len(delta_true),
"directional_accuracy_pct": 100 * matches.mean(),
"within_threshold_pct": 100 * within.mean(),
"slope": fit.slope,
"r2": fit.rvalue**2,
}
def plot_delta(split: str, model: str, coeff: str, output_path: Path) -> Path:
"""Predicted vs. true pairwise deltas, coloured by directional agreement."""
delta_true, delta_pred, threshold = delta_pairs(split, model, coeff)
matches = np.sign(delta_true) == np.sign(delta_pred)
row = delta_stats(split, model, coeff)
span = max(delta_true.max(), delta_pred.max()) * 1.05
floor = min(delta_pred.min(), 0.0) - 0.05 * span
fig, ax = plt.subplots(figsize=(text_width_in * 0.72, 2.9))
ax.fill_between([0, span], 0, span, color="tab:green", alpha=0.07, linewidth=0)
ax.fill_between([0, span], floor, 0, color="tab:red", alpha=0.07, linewidth=0)
ax.scatter(
delta_true[matches], delta_pred[matches], s=2, alpha=0.35,
color="tab:green", edgecolors="none", label="correct sign",
)
if (~matches).any():
ax.scatter(
delta_true[~matches], delta_pred[~matches], s=4, alpha=0.8,
color="tab:red", edgecolors="none", label="wrong sign",
)
line = np.array([0.0, span])
ax.plot(line, line, "k-", linewidth=0.8, label="perfect match")
ax.plot(line, line + threshold, "k--", linewidth=0.6, alpha=0.7,
label=rf"$\pm{delta_threshold_pct * 100:.0f}\%$ tolerance")
ax.plot(line, line - threshold, "k--", linewidth=0.6, alpha=0.7)
ax.axhline(0, color="black", linewidth=0.5, alpha=0.5)
ax.set_xlim(0, span)
ax.set_ylim(floor, span)
ax.set_xlabel(rf"True $\Delta {coeff_labels[coeff].strip('$')}$")
ax.set_ylabel(rf"Predicted $\Delta {coeff_labels[coeff].strip('$')}$")
ax.annotate(
rf"correct sign: {row['directional_accuracy_pct']:.1f}\%"
"\n"
rf"within tolerance: {row['within_threshold_pct']:.1f}\%",
(0.97, 0.06), xycoords="axes fraction", fontsize=7, ha="right",
)
ax.legend(loc="upper left", frameon=False, markerscale=2.5, handlelength=1.4)
ax.grid(True, alpha=0.25, linewidth=0.4)
fig.tight_layout()
return save(fig, output_path)
# Statistics for every model
delta_figure_models = {"abupt": "abupt", "xaeronet": "xmeshgraphnet"}
delta_summary = pd.DataFrame([
delta_stats(split, model, coeff)
for split in splits
for model in reported_models()
for coeff in coeffs
])
delta_summary.to_csv(output_dir / "directional_accuracy.csv", index=False)
for split in splits:
for model, file_name in delta_figure_models.items():
plot_delta(split, model, "Cl", output_dir / split / f"delta_cl_{file_name}.svg")
print("\n" + "=" * 96)
print("Directional consistency (all ordered pairs)")
print("=" * 96)
print(delta_summary.to_string(index=False, float_format=lambda v: f"{v:.1f}"))
# ---------------------------------------------------------------------------
# Appendix: AB-UPT trained on the surface fields alone (the benchmarked run, `abupt`)
# against the variant additionally trained on the volumetric targets (`abupt_volume`).
# ---------------------------------------------------------------------------
training_targets = {
"abupt": "Surface only",
"abupt_volume": "Surface + volume",
}
assert "abupt_volume" in appendix_model_labels, "abupt_volume must be an appendix model"
fields_by_variant = field_summary.set_index(["split", "model", "field"])
rows = []
for split in splits:
for variant, targets in training_targets.items():
df = load_coefficients(split, variant)
row = {
"split": split,
"split_label": split_labels[split],
"variant": variant,
"targets": targets,
"samples": len(df),
}
for coeff in coeffs:
err = relative_error(df, coeff)
row |= {
f"{coeff.lower()}_mean_pct": err.mean(),
f"{coeff.lower()}_std_pct": err.std(),
}
for field in field_labels:
stat = fields_by_variant.loc[(split, variant, field)]
if stat["runs"] != len(df):
raise ValueError(
f"{split}/{variant}/{field}: {stat['runs']} field rows for {len(df)} runs"
)
row[f"{field}_l2_rel_mean"] = stat["l2_rel_mean"]
row[f"{field}_mse_abs_mean"] = stat["mse_abs_mean"]
rows.append(row)
abupt_targets = pd.DataFrame(rows)
abupt_targets.to_csv(output_dir / "abupt_training_targets.csv", index=False)
print(f"\nwrote {(output_dir / 'abupt_training_targets.csv').relative_to(here)}\n")
print(
abupt_targets[[
"split_label", "targets", "samples",
"cl_mean_pct", "cl_std_pct", "cd_mean_pct", "cd_std_pct",
"Cp_l2_rel_mean", "ws_l2_rel_mean",
]].to_string(index=False, float_format=lambda v: f"{v:.4f}")
)
# ---------------------------------------------------------------------------
# Paper-ready LaTeX table rows. The paper reports the stratified split in full and the other
# two side by side.
# ---------------------------------------------------------------------------
paper_split = "stratified"
architectures = {
"abupt": "Transformer",
"geotransolver": "Transformer",
"aerojepa": "JEPA",
"gaot": "Transformer",
"xaeronet": "GNN",
"domino": "CNN",
}
indexed = benchmark_summary.set_index(["split", "model_key"])
fields_indexed = field_summary.set_index(["split", "model", "field"])
def rule(title: str) -> None:
print("\n" + "=" * 96)
print(title)
print("=" * 96)
rule(f"tab:results rows -- {paper_split} split")
for model in ranked_models(paper_split):
r = indexed.loc[(paper_split, model)]
print(
f"{model_labels[model]} & {architectures[model]} & "
f"{r['cl_mean_pct']:.2f}, {r['cl_std_pct']:.2f} & "
f"{r['cl_r2_fit']:.3f} & {r['cl_r2_1to1']:.3f} & "
f"{r['cd_mean_pct']:.2f}, {r['cd_std_pct']:.2f} & "
f"{r['cd_r2_fit']:.3f} & {r['cd_r2_1to1']:.3f} \\\\"
)
rule(f"tab:field_errors rows -- {paper_split} split")
for model in ranked_models(paper_split):
cells = []
for field in field_labels:
r = fields_indexed.loc[(paper_split, model, field)]
cells += [
f"{r['mse_abs_mean']:.4f}" if field == "Cp" else f"{r['mse_abs_mean']:.3f}",
f"{100 * r['l1_rel_mean']:.2f}",
f"{100 * r['l2_rel_mean']:.2f}",
]
print(f"{model_labels[model]} & " + " & ".join(cells) + " \\\\")
rule("tab:results_splits rows -- drag-outlier and interpolated")
for model in ranked_models(paper_split):
cells = []
for split in ("outliers", "interpolated"):
r = indexed.loc[(split, model)]
cells += [
f"{r['cl_mean_pct']:.2f}, {r['cl_std_pct']:.2f}",
f"{r['cd_mean_pct']:.2f}, {r['cd_std_pct']:.2f}",
f"{100 * r['Cp_l2_rel_mean']:.2f}",
f"{100 * r['ws_l2_rel_mean']:.2f}",
]
print(f"{model_labels[model]} & " + " & ".join(cells) + " \\\\")
rule("tab:abupt_targets rows")
for split in splits:
for i, variant in enumerate(training_targets):
r = abupt_targets[
(abupt_targets["split"] == split) & (abupt_targets["variant"] == variant)
].iloc[0]
# The split name sits on the first row of each pair; no multirow package needed.
label = split_labels[split] if i == 0 else ""
print(
f"{label} & {r['targets']} & "
f"{r['cl_mean_pct']:.2f}, {r['cl_std_pct']:.2f} & "
f"{r['cd_mean_pct']:.2f}, {r['cd_std_pct']:.2f} & "
f"{100 * r['Cp_l2_rel_mean']:.2f} & {100 * r['ws_l2_rel_mean']:.2f} \\\\"
)
print(r"\midrule" if split != splits[-1] else r"\bottomrule")
rule(f"Directional consistency quoted in the prose -- {paper_split} split")
print(
delta_summary[delta_summary["split"] == paper_split].to_string(
index=False, float_format=lambda v: f"{v:.1f}"
)
)