README.md

---
license: apache-2.0
language:
- en
tags:
- physics-informed-neural-networks
- pinn
- pde
- benchmark
- evaluation
- routing
- causal-loss
- fourier-neural-operator
- deeponet
- scientific-machine-learning
pretty_name: PINNBench
size_categories:
- 1K<n<10K
task_categories:
- other
configs:
- config_name: routing_evaluation
  data_files: results_paper_combined/routing_evaluation/*.json
- config_name: stage_ablation
  data_files: results_paper_combined/stage_ablation/*.json
- config_name: meta_router
  data_files: results_paper_combined/meta_router/*.json
- config_name: regret_bound_validation
  data_files: results_paper_combined/routing_evaluation/regret_bound_validation.json
- config_name: adaptive_epsilon
  data_files: results_paper_combined/adaptive_epsilon/*.json
- config_name: external_probes
  data_files: results_paper_combined/{hypino,pinnacle,wang}*/*.json
---

# PINNBench

A controlled benchmark for evaluating training-policy selection in hybrid Physics-Informed Neural Network (PINN) and neural-operator solvers. PINNBench accompanies the paper *"PINNBench: A Benchmark and Evaluation Study of Training Policy Selection in Hybrid PINN-Operator Solvers"* (NeurIPS 2026, Evaluations and Datasets Track). Code: <https://github.com/suanlab/PINNBench>.

## What is in this repository

This Hugging Face dataset hosts the **benchmark protocol artifacts** + **logged results** of 3,545 recorded training runs on 13 PDE configurations spanning 8 equation families. The dataset is **not raw simulation data** (PDE reference solutions are analytical and regenerated at runtime); it is the **decision-relevant evaluation record** that supports the paper's headline claims.

```
results_paper_combined/
├── routing_evaluation/
│   ├── results.json              # 13-PDE leave-one-out CV (450 routing decisions × 4 selectors)
│   ├── holdout.json              # 3-PDE held-out generalization
│   ├── regret_bound_validation.json   # submission-era check (k=20 empty, k=50 regret reused); superseded by regret_bound_v13/
│   └── scaling_ablation.json     # routing accuracy vs. PDE count
├── meta_router/
│   └── results.json              # PDE-aware router (84.6% with 5+7 features)
├── stage_ablation/
│   └── *_ablation.json           # 9 PDEs × 2×2 (Stage1, Stage3) factorial × 10 seeds
│   # statistics over all 27 tests (BH-FDR step-up, corrected in v1.2.0): results/paper_c/ablation_statistics/
├── adaptive_epsilon/
│   └── results.json              # 4 PDEs × 4 conditions × 5 seeds (causal-weight collapse)
├── wang_comparison/
│   └── *_results.json            # Wang-style single-stage causal probe (4 PDEs)
├── hypino_*/                     # HyPINO native, adapter, target-PINN adaptation probes
├── pinnacle_subset_5task/
│   └── results.json              # PINNacle 5-task executable subset
├── statistical_tests.json        # BH-FDR corrected, 13 core tests
│   # --- added in v1.1.0 (camera-ready) ---
├── noise_sparsity_sweep*/        # 6 PDEs x 3 noise x 4 data sizes x 2 conditions x 5 seeds (720 runs)
├── heat3d_probe/                 # d=3 pretraining contrast, 10 seeds
├── multiscale2d_probe/           # MultiscaleHeat2D contrast + per-mode projection, 10 seeds
├── multiscale2d_policy_suite/    # full 5-policy library on MultiscaleHeat2D, 50 runs
├── dissociation_transfer/        # accuracy-regret dissociation on tabular classifier selection
├── k20_gap_check.json            # regret-bound check at probe window k=20
│   # --- added in v1.3.0 ---
├── ../paper_c/controls/          # 9 PDEs × 4 epoch-matched control arms × 10 seeds (360 runs)
├── ../paper_c/control_statistics/ # 54 BH-FDR tests for the controls
├── regret_bound_v13/             # regret check with observed regret recomputed per window (k=20 included)
├── ../rq6_ood_seeds2/            # Wave2D OOD, 5 more seeds (10 in total)
│   # --- added in v1.2.0 ---
├── routing_family_holdout/       # leave-one-family-out routing, base routers (whole family removed from training)
├── meta_router_family_holdout/   # leave-one-family-out routing, PDE-aware routers
├── hypino_matched_budget*/       # HyPINO vs hybrid at matched wall-clock budget (paper-cited, missing from 1.1.0)
├── pretrain_budget_sweep/        # Stage-1 budget sweep, 240 runs (paper-cited, missing from 1.1.0)
├── clamping_ablation/            # causal-weight clamping null result (paper-cited, missing from 1.1.0)
├── noisy_data_probe*/            # rebuttal-period Heat1D noise probes
└── rd_speed_D*/                  # reaction-diffusion front-speed sweeps
```

## How to load

The recommended access pattern is direct JSON read; result schemas are documented in `MANIFEST.md`.

```python
from huggingface_hub import hf_hub_download
import json

routing_path = hf_hub_download(
    "suanlab/PINNBench",
    "results_paper_combined/routing_evaluation/results.json",
    repo_type="dataset",
)
with open(routing_path) as f:
    routing = json.load(f)
```

`datasets`-library config aliases (`routing_evaluation`, `stage_ablation`, `meta_router`, `regret_bound_validation`, `adaptive_epsilon`, `external_probes`) are declared in the YAML header above for convenience.

## Verification

Every headline claim in the paper is recomputed from these JSONs by the script `scripts/verify_claims.py` in the source repository. Reproduced PASS results:

| Claim | Source artifact | Computed | Paper |
|---|---|---|---|
| Total recorded runs | all JSONs, one count per (training_time, seed) | 450 routing + 360 ablation + 459 single-PDE + 1,066 diagnostic (incl. 360 epoch-matched controls) + 1,210 robustness | 3,545 |
| Nested PDE-aware routing accuracy | `meta_router/results.json` | 84.62% (11/13) | 84.6% |
| Full RF+PDE routing | `meta_router/results.json` | 61.54% (8/13) | 61.5% |
| Stage-2 compute savings | analytical | 60.0% (K=3, Eₚ=50, E₂=500) | 60% |
| Diagnostic regret check | `regret_bound_v13/regret_bound_validation.json` | 44/52; 11/13 at every k∈{10,20,50,100}; violations: two Burgers configs | same |
| Accuracy–regret dissociation | `routing_evaluation/results.json` folds + `results/paper_a/*` runs | 0.0850 vs 0.0011 (77.6× unrounded) | 77× |
| Leave-one-family-out routing | `routing_family_holdout/`, `meta_router_family_holdout/` | PDE-aware GBR+PDE 84.6% → 69.2%, RF+PDE 84.6% → 61.5%; physics-loss heuristic 69.2% (family macro 81.2%) | same |
| Causal loss × pretraining | `paper_c/ablation_statistics/results.json` (27 BH-FDR tests) | +5.9% with (9/9 positive, 6 significant); −2.4% without (5/9 negative, 3 significant) | same |
| Epoch-matched controls | `paper_c/control_statistics/results.json` (54 tests) | causal vs uniform-weight Stage 3: −0.2% with pretraining, −3.9% without (9/9 worse); uniform Stage 3 +6.0%; pretraining at equal epochs +125–694% | same |
| KdV1D causal effect (PDE residual) | `rq1e_kdv_10seed_causal/results.json` | 0.0096 / 0.0105 | 0.010 / 0.011 |
| Adaptive-ε min causal weight (AdvDiff1D) | `adaptive_epsilon/results.json` | 0.78 (fixed, pretrained) → 0.98 (adaptive, no pretraining) | same |

## Reproducibility caveats

- All training results were computed at the **final epoch** of each stage (no best-checkpoint selection, no validation set).
- Evaluation points were regenerated per seed via `torch.rand` rather than loaded from a fixed grid; per-seed metric variance therefore includes evaluation-point sampling variance.
- The `rq1e_kdv_10seed_causal/results.json` summary aggregate has a `nan-mean` bug for some fields; per-seed means are recomputed by the verification script.

## Croissant metadata

`croissant.json` (Croissant 1.1, version 1.3.0) carries 13 `rai:` fields. `mlcroissant validate --jsonld croissant.json` (mlcroissant 1.1.0) reports 0 errors and 1 warning: our `@context` lacks three keys of the reference context (`examples`, `equivalentProperty`, `samplingRate`), none of which the file uses.

## Citation

```bibtex
@inproceedings{lee2026pinnbench,
  title     = {{PINNBench}: A Benchmark and Evaluation Study of Training Policy Selection in Hybrid {PINN}-Operator Solvers},
  author    = {Lee, Suan and Kim, Namhyeon and Jin, Dongmin},
  booktitle = {Advances in Neural Information Processing Systems (NeurIPS), Evaluations and Datasets Track},
  year      = {2026}
}
```

## License

Apache-2.0 for code and benchmark artifacts. PDE reference solutions are analytical and original to this work; no third-party data is redistributed.

## Contact

Issues and questions: <https://github.com/suanlab/PINNBench/issues>.