--- 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. ## What is in this repository This Hugging Face dataset hosts the **benchmark protocol artifacts** + **logged results** of 1,539 controlled 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 # 33/52 PDE × probe-window pairs │ └── 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 ├── 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, 27 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 ``` ## 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 runs | union | 1,510 enumerable + 29 probes | 1,539 | | 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 bound | `regret_bound_validation.json` | 33/52 overall, 33/39 if k∈{10,50,100} | 33/52, 33/39 | | Accuracy–regret dissociation | `routing_evaluation/results.json` folds + `results/paper_a/*` runs | 0.0850 vs 0.0011 (77.6× unrounded) | 77× | | Family-macro accuracy (LOPO-F) | `routing_evaluation/results.json` | 81.2% physics-loss-final (6/8) | 81.2% | | 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 1.1.0) carries 13 `rai:` fields. `mlcroissant validate --jsonld croissant.json` (mlcroissant 1.1.0) reports 0 errors and 1 warning: the `@context` includes `examples`, `equivalentProperty` and `samplingRate`, which are Croissant 1.1 keys absent from the 1.0 reference context. ## 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: .