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arXiv · 2306.08827

PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs

Zhongkai Hao·Jiachen Yao·Chang Su·Hang Su·Ziao Wang·Fanzhi Lu·Zeyu Xia·Yichi Zhang·Songming Liu·Lu Lu·Jun Zhu
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Abstract

While significant progress has been made on Physics-Informed Neural Networks (PINNs), a comprehensive comparison of these methods across a wide range of Partial Differential Equations (PDEs) is still lacking. This study introduces PINNacle, a benchmarking tool designed to fill this gap. PINNacle provides a diverse dataset, comprising over 20 distinct PDEs from various domains, including heat conduction, fluid dynamics, biology, and electromagnetics. These PDEs encapsulate key challenges inherent to real-world problems, such as complex geometry, multi-scale phenomena, nonlinearity, and high dimensionality. PINNacle also offers a user-friendly toolbox, incorporating about 10 state-of-the-art PINN methods for systematic evaluation and comparison. We have conducted extensive experiments with these methods, offering insights into their strengths and weaknesses. In addition to providing a standardized means of assessing performance, PINNacle also offers an in-depth analysis to guide future research, particularly in areas such as domain decomposition methods and loss reweighting for handling multi-scale problems and complex geometry. To the best of our knowledge, it is the largest benchmark with a diverse and comprehensive evaluation that will undoubtedly foster further research in PINNs.

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Zhongkai Hao, Jiachen Yao, Chang Su, Hang Su, Ziao Wang, Fanzhi Lu, Zeyu Xia, Yichi Zhang, Songming Liu, Lu Lu, Jun Zhu. 2023-10-05. PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs. https://arxiv.org/abs/2306.08827

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