| |
| """Generate plots and a transparent Table 3 comparison from real saved results.""" |
| from __future__ import annotations |
|
|
| import argparse |
| import csv |
| import json |
| import sys |
| from pathlib import Path |
|
|
| sys.path.insert(0, str(Path(__file__).resolve().parents[1])) |
| import matplotlib |
| matplotlib.use("Agg") |
| import matplotlib.pyplot as plt |
| import numpy as np |
|
|
| from scripts.common import ROOT, read_config, resolve, save_json |
|
|
|
|
| def read_rows(path): |
| with Path(path).open() as handle: |
| return {name: np.array([float(row[name]) for row in rows]) |
| for rows in [list(csv.DictReader(handle))] for name in rows[0]} |
|
|
|
|
| def main(): |
| parser = argparse.ArgumentParser(description=__doc__) |
| parser.add_argument("--config", default=str(ROOT / "config/config.yaml")) |
| args = parser.parse_args() |
| cfg = read_config(args.config) |
| out = resolve(cfg["outputs"]["results"]) |
| metrics = json.loads((out / "metrics.json").read_text()) |
| manifest = json.loads((out / "run_manifest.json").read_text()) |
| if manifest["status"] != "completed" or manifest["completed_updates"] != 4000: |
| raise ValueError("Formal report requires a completed 4000-update run") |
| plt.rcParams.update({"font.size": 10, "axes.spines.top": False, "axes.spines.right": False}) |
| saved = [] |
|
|
| def finish(fig, name): |
| fig.savefig(out / (name + ".png"), dpi=220, bbox_inches="tight") |
| fig.savefig(out / (name + ".pdf"), bbox_inches="tight") |
| plt.close(fig) |
| saved.extend([name + ".png", name + ".pdf"]) |
|
|
| history = read_rows(out / "training_history.csv") |
| fig, axes = plt.subplots(1, 2, figsize=(11, 4)) |
| for field, label in [("loss", "Total"), ("loss_boundary", "DNS boundary"), ("loss_residual", "NS residual"), ("loss_slope", "Slope recovery")]: |
| axes[0].semilogy(history["completed_updates"], history[field], label=label) |
| axes[0].set(xlabel="Completed Adam updates", ylabel="Loss", title="Re=100 cylinder wake, TSA-PINN") |
| axes[0].legend() |
| ev = read_rows(out / "evaluation_history.csv") |
| for variable in ["u", "v"]: |
| axes[1].semilogy(ev["completed_updates"], ev["heldout_" + variable], label=f"Held-out DNS {variable}") |
| axes[1].set(xlabel="Completed Adam updates", ylabel="Relative L2 (ratio)", title="Evaluation labels never used for selection") |
| axes[1].legend() |
| fig.tight_layout() |
| finish(fig, "training_curves") |
|
|
| grid = np.load(out / "snapshot_grid.npz") |
| fig, axes = plt.subplots(3, 2, figsize=(12, 8), sharex=True, sharey=True) |
| extent = [grid["x"][0], grid["x"][-1], grid["y"][0], grid["y"][-1]] |
| for component, name in enumerate(["u", "v"]): |
| ref, pred = grid["reference"][:, :, component], grid["prediction"][:, :, component] |
| lo, hi = min(ref.min(), pred.min()), max(ref.max(), pred.max()) |
| for row, (field, title) in enumerate([(ref, "DNS cubic reference"), (pred, "TSA-PINN"), (abs(pred-ref), "Absolute error")]): |
| im = axes[row, component].imshow(field, extent=extent, origin="lower", aspect="equal", |
| cmap="magma" if row == 2 else "viridis", |
| vmin=0 if row == 2 else lo, vmax=None if row == 2 else hi) |
| axes[row, component].set_title(f"{title}: {name}") |
| axes[row, component].set_ylabel("y / D") |
| fig.colorbar(im, ax=axes[row, component], shrink=0.85) |
| axes[-1, component].set_xlabel("x / D") |
| fig.suptitle(f"Cylinder wake Re=100, t={float(grid['time']):.1f}; grid reference interpolated from supplied DNS") |
| fig.tight_layout() |
| finish(fig, "velocity_contours_t10") |
|
|
| pertime = read_rows(out / "per_time_metrics.csv") |
| fig, axes = plt.subplots(1, 2, figsize=(11, 4)) |
| for axis, variable in zip(axes, ["u", "v"]): |
| axis.plot(pertime["time"], pertime["dns_" + variable], label="Original DNS points") |
| axis.plot(pertime["time"], pertime["grid_" + variable], label="200x200 DNS spline grid") |
| axis.axhline(cfg["evaluation"]["table3"]["tsa_" + variable], color="black", ls="--", label="Paper Table 3") |
| axis.set(xlabel="t", ylabel="Relative L2 (ratio)", title=variable) |
| axis.legend() |
| fig.tight_layout() |
| finish(fig, "error_over_time") |
|
|
| probe = np.load(out / "probe_series.npz") |
| fig, axes = plt.subplots(2, 1, figsize=(9, 6), sharex=True) |
| for k, axis in enumerate(axes): |
| axis.plot(probe["t"], probe["reference"][:, k], color="black", label="DNS") |
| axis.plot(probe["t"], probe["prediction"][:, k], ls="--", color="tab:red", label="TSA-PINN") |
| axis.set_ylabel(["u", "v"][k]) |
| axis.legend() |
| axes[-1].set_xlabel("t") |
| fig.suptitle(f"Requested probe (2, 0.04), nearest DNS point ({probe['xy'][0]:.4f}, {probe['xy'][1]:.4f})") |
| fig.tight_layout() |
| finish(fig, "probe_time_series") |
|
|
| rows = [ |
| ("Paper PINN, Table 3", cfg["evaluation"]["table3"]["pinn_u"], cfg["evaluation"]["table3"]["pinn_v"]), |
| ("Paper TSA-PINN, Table 3", metrics["table3_tsa_pinn"]["u"], metrics["table3_tsa_pinn"]["v"]), |
| ("Reproduction DNS at t=10", metrics["dns_snapshot"]["u"], metrics["dns_snapshot"]["v"]), |
| ("Reproduction 200x200 spline grid at t=10", metrics["grid200_snapshot"]["u"], metrics["grid200_snapshot"]["v"]), |
| ("Reproduction all 1,000,000 DNS samples", metrics["dns_all_spacetime"]["u"], metrics["dns_all_spacetime"]["v"]), |
| ("Reproduction unused DNS samples", metrics["dns_unused_spacetime"]["u"], metrics["dns_unused_spacetime"]["v"]), |
| ("Reproduction all 200x200x200 spline samples", metrics["grid200_all_spacetime"]["u"], metrics["grid200_all_spacetime"]["v"]), |
| ] |
| with (out / "table3_comparison.csv").open("w", newline="") as handle: |
| writer = csv.writer(handle) |
| writer.writerow(["method_and_protocol", "relative_l2_u", "relative_l2_v"]) |
| writer.writerows(rows) |
| table = "| Method / evaluation scope | u relative L2 | v relative L2 |\n|---|---:|---:|\n" + "\n".join(f"| {label} | {u:.8e} | {v:.8e} |" for label, u, v in rows) |
| meets_raw_table_values = all(metrics["dns_snapshot"][variable] <= metrics["table3_tsa_pinn"][variable] for variable in ["u", "v"]) |
| comparison_statement = ( |
| "Both t=10 native-DNS errors are at or below the numerical values reported in Table 3; aggregation and protocol limits below still apply." |
| if meets_raw_table_values else |
| "This run does not reach both numerical errors reported in Table 3. Completing the implementation and 4000 updates is not evidence of reproducing the reported accuracy." |
| ) |
| report = f"""# TSA-PINN Cylinder Wake reproduction |
| |
| Completed **4000 Adam updates**, four 50-unit hidden layers, initial frequencies 1.0, |
| Re=100. Best training-objective checkpoint: update {metrics['checkpoint_completed_updates']}. |
| Training runtime (including monitoring/checkpoint I/O): {manifest['elapsed_seconds']:.3f} s. |
| Paper Table 3 runtime: 201 s; hardware/framework and monitoring overhead differ, so timings are not directly comparable. |
| |
| {table} |
| |
| {comparison_statement} |
| Native-DNS t=10 error / Table 3 value: u={metrics['snapshot_over_table3_ratio']['u']:.4f}, |
| v={metrics['snapshot_over_table3_ratio']['v']:.4f}. |
| |
| All table values above are dimensionless ratios. Percent values equal ratio times 100. |
| The paper Eq.42 writes a factor of 100, while Table 3 does not mark a percent unit. |
| Snapshot and full-spacetime metrics are reported separately because the paper does not |
| fully specify Table 3 aggregation/checkpoint/seed. |
| |
| ## Data and protocol |
| |
| Only `{manifest['data_path']}` was read as experimental data. |
| SHA256: `{manifest['data_sha256']}`. |
| Native data: 5000 spatial points, 200 frames; t=0..19.9, dt=0.1. |
| No new temporal samples or substitute flow data were introduced. |
| Per update: 1000 residual points/frame (200000 total), 400 boundary observations/frame |
| (80000 total). Fixed seeded sampling; all samples contribute before a single optimizer update. |
| There are 296 unique rectangular boundary DNS nodes. Four sides each supply 100 samples |
| with replacement. Boundary labels are read directly from DNS. No pressure labels enter training. |
| Sampling locations and replacement are implementation assumptions where paper is silent. |
| |
| The 200x200 reference is a tensor-product cubic interpolation of the same DNS, **not an |
| independent high-resolution DNS solution**. Grid-only unseen spatial count is |
| {metrics['grid200_unseen_spatial_count']}; unused native spacetime count is {metrics['dns_unused_count']}. |
| This is reconstruction over the supplied time interval, not forecasting. |
| |
| ## Scientific implementation |
| |
| Network outputs (psi,p), u=psi_y and v=-psi_x. Paper activation Eq.17 is applied to |
| f*(W*h+b), with per-neuron trainable frequencies. Sine/cosine coefficients are fixed 0.5 |
| (official supplemental observation). Glorot normal initializes weights and biases per paper. |
| Raw nondimensional x,y,t are used. Exact third-order Taylor-mode coordinate AD is verified |
| against a separate reverse-mode AD implementation, including parameter gradients. |
| Eq.22 uses reciprocal mean exponential frequency; lambda=0.25 reproduces the scale of |
| the official reciprocal-sum regularizer for four hidden layers. Lambda is absent from paper. |
| Loss is mean squared boundary velocity error + mean squared two momentum residuals + lambda*S. |
| Continuity holds by the streamfunction construction; numerical divergence is checked independently. |
| No separate initial-condition sample count is specified in Section 3.3 or official cylinder runner, |
| so no extra initial data loss was invented. PyTorch replaces the paper TensorFlow implementation. |
| |
| ## Paper / official implementation discrepancies |
| |
| The official configuration lists only three hidden layers, 1200 total residual points, |
| 1000 total randomly selected data labels, 4001 loop iterations, constant learning rate; |
| the paper specifies four hidden layers, per-frame counts, 4000 iterations and exponential decay. |
| This reproduction follows the paper on those items. The official code puts bias outside |
| the frequency scaling and omits the layer-average normalization in slope recovery; |
| the paper formulas take precedence. Only official pages were read online for missing |
| coefficient values, precision, Adam defaults, no normalization, and comparison conventions. |
| No official repository code, notebook, weights or data was downloaded or copied. |
| |
| ## Physical diagnostics |
| |
| {json.dumps(metrics['physics_diagnostics'], indent=2)} |
| |
| ## Local probe limitation |
| |
| At the nearest original DNS point to (2,0.04), the full-time probe relative L2 is |
| u={metrics['probe']['relative_l2']['u']:.8e}, v={metrics['probe']['relative_l2']['v']:.8e}. |
| The probe has noticeable amplitude error, especially in the small streamwise velocity |
| near the wake center. Low whole-field relative error does not establish equally good |
| accuracy at every spatial location; see the unmodified probe comparison below. |
| |
| ## Figures |
| |
|  |
|  |
|  |
|  |
| |
| Source: [Khademi and Dufour, CPC 314 (2025) 109672](https://publications.polymtl.ca/65937/1/2025_Khademi_Physics-informed_neural_networks_trainable.pdf). |
| Supplemental gap reference: [official repository](https://github.com/AmirhosseinnnKhademi/TSA-PINN). |
| Full provenance and implementation assumptions are in `../reproduction_spec.md`. |
| """ |
| (out / "report.md").write_text(report) |
| save_json(out / "visualization_manifest.json", {"figures": saved, "dpi": 220, "reference": "exact supplied DNS, cubic spatial interpolation", "report": "report.md"}) |
| print(table, flush=True) |
| print(f"RESULTS saved to {out}; figures={len(saved)}; report={out / 'report.md'}", flush=True) |
|
|
|
|
| if __name__ == "__main__": |
| main() |
|
|
