---
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"* (anonymous submission, NeurIPS 2026 Evaluations and Datasets Track).

## 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
```

## 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(
    "PINNBench/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` | 77.27× (0.0850 / 0.0011) | 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 mitigation (AdvDiff1D) | `adaptive_epsilon/results.json` | 0.78 → 0.98 | 0.78 → 0.97 |

## 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

A validated Croissant 1.0 metadata file is included as `croissant.json` (RAI fields complete: data collection, preprocessing, annotation protocol, personal/sensitive information, safety, deidentification, fairness, biases, release/maintenance). Validate with:

```
https://huggingface.co/spaces/JoaquinVanschoren/croissant-checker
```

## Citation

The paper is currently in submission to NeurIPS 2026 Evaluations and Datasets Track (double-blind). A BibTeX entry will be added to this dataset card after the review period.

## 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

During the anonymous review period, all communication is routed through the OpenReview discussion thread of the submission. After camera-ready, the maintainer details will be added here.