PDEBench: An Extensive Benchmark for Scientific Machine Learning

Makoto Takamoto, Timothy Praditia, Raphael Leiteritz, Dan MacKinlay, Francesco Alesiani, Dirk Pflüger, Mathias Niepert

Keywords: Scientific Machine Learning, Benchmark, Partial Differential Equations, PINN, FNO, U-Net, Inverse problem

Abstract: Machine learning-based modeling of physical systems has experienced increased interest in recent years. Despite some impressive progress, there is still a lack of benchmarks for Scientific ML that are easy to use but still challenging and repre- sentative of a wide range of problems. We introduce PDEBENCH, a benchmark suite of time-dependent simulation tasks based on Partial Differential Equations (PDEs). PDEBENCH comprises both code and data to benchmark the performance of novel machine learning models against both classical numerical simulations and machine learning baselines. Our proposed set of benchmark problems con- tribute the following unique features: (1) A much wider range of PDEs compared to existing benchmarks, ranging from relatively common examples to more real- istic and difficult problems; (2) much larger ready-to-use datasets compared to prior work, comprising multiple simulation runs across a larger number of ini- tial and boundary conditions and PDE parameters; (3) more extensible source codes with user-friendly APIs for data generation and baseline results with popular machine learning models (FNO, U-Net, PINN, Gradient-Based Inverse Method). PDEBENCH allows researchers to extend the benchmark freely for their own pur- poses using a standardized API and to compare the performance of new models to existing baseline methods. We also propose new evaluation metrics with the aim to provide a more holistic understanding of learning methods in the context of Scientific ML. With those metrics we identify tasks which are challenging for recent ML methods and propose these tasks as future challenges for the community. The code is available at https://github.com/pdebench/PDEBench.

URL: https://github.com/pdebench/PDEBench

Author Statement: Yes

TL;DR: We provide a benckmark for Scientific Machine Learning

Dataset Url:

Baselines url
https://github.com/pdebench/PDEBench

Dataset permanent url
https://darus.uni-stuttgart.de/dataverse/sciml_benchmark

Temporary url
PDEBench Dataset https://darus.uni-stuttgart.de/privateurl.xhtml?token=1be27526-348a-40ed-9fd0-c62f588efc01
PDEBench Pre-Trained Models https://darus.uni-stuttgart.de/privateurl.xhtml?token=cd862f8c-8e1b-49d2-b4da-b35f8df5ac85

Permanent url
PDEBench Dataset https://darus.uni-stuttgart.de/dataset.xhtml?persistentId=doi:10.18419/darus-2986
PDEBench Pre-Trained Models https://darus.uni-stuttgart.de/dataset.xhtml?persistentId=doi:10.18419/darus-2987

Dataset DOI
doi:10.18419/darus-2986
doi:10.18419/darus-2987

DOI url
http://dx.doi.org/10.18419/darus-2986
http://dx.doi.org/10.18419/darus-2987

License:

MIT for solver code and baseline code
NLE Academic License (Academic or non-profit organization noncommercial research use only) for selected code (one solver and baseline)
Dataset license CC BY

Contribution Process Agreement: Yes

In Person Attendance: Yes

Community Implementations: [ 2 code implementations](https://www.catalyzex.com/paper/arxiv:2210.07182/code)