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│   ├── regret_bound_validation.json   # submission-era check (k=20 empty, k=50 regret reused); superseded by regret_bound_v13/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.

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

@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.