PDEBench

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Date: 2022-10-13

Name: PDEBench

Domain: Computational Science & AI, Climate & Earth Science, Mathematics

Focus: Benchmark suite for ML-based surrogates solving time-dependent PDEs

Task Types: Supervised Learning

Metrics: RMSE, boundary RMSE, Fourier RMSE

Models: FNO, U-Net, PINN, Gradient-Based inverse methods

AI/ML Motif: Regression

Resources

Benchmark: Visit

Results: Gemini LLM Deep Research

Keywords

PDEs CFD scientific ML surrogate modeling NeurIPS

Citation

Makoto Takamoto, Timothy Praditia, Raphael Leiteritz, Dan MacKinlay, Francesco Alesiani, Dirk Pflüger, and Mathias Niepert. Pdebench: an extensive benchmark for scientific machine learning. 2024. URL: https://arxiv.org/abs/2210.07182, arXiv:2210.07182.

@misc{takamoto2024pdebenchextensivebenchmarkscientific,
  archiveprefix = {arXiv},
  author        = {Makoto Takamoto and Timothy Praditia and Raphael Leiteritz and Dan MacKinlay and Francesco Alesiani and Dirk Pflüger and Mathias Niepert},
  eprint        = {2210.07182},
  primaryclass  = {cs.LG},
  title         = {PDEBENCH: An Extensive Benchmark for Scientific Machine Learning},
  url           = {https://arxiv.org/abs/2210.07182},
  year          = {2024}
}

Ratings

CategoryRating

Software

5.00

GitHub repository (https://github.com/pdebench/PDEBench) is actively maintained and includes training pipelines, data loaders, and evaluation scripts. Installation and usage are well-documented.

Specification

5.00

Clearly defined tasks for forward and inverse PDE problems, with structured input/output formats, system constraints, and task specifications.

Dataset

5.00

Diverse PDE datasets (synthetic and real-world) hosted on DaRUS with DOIs. Datasets are well-documented, structured, and follow FAIR practices.

Metrics

4.00

Includes RMSE, boundary RMSE, and Fourier-domain RMSE. These are well-suited to PDE problems, though rationale behind metric choices could be expanded in some cases.

Reference Solution

4.00

Baselines (FNO, U-Net, PINN, etc.) are available and documented, but not every model includes full training and evaluation reproducibility out-of-the-box.

Documentation

4.00

Strong documentation on GitHub including examples, configs, and usage instructions. Some model-specific details and tutorials could be further expanded.

Average rating: 4.50/5

Radar plot

$PDEBench radar$

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