"""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/: /results_table.csv /coefficient_error_boxplot.svg /field_error_table.csv /field_error_bars.svg /r2_table.csv /parity_grid.svg /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}" ) )