1. PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs
- Author
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Hao, Zhongkai, Yao, Jiachen, Su, Chang, Su, Hang, Wang, Ziao, Lu, Fanzhi, Xia, Zeyu, Zhang, Yichi, Liu, Songming, Lu, Lu, and Zhu, Jun
- Subjects
Computer Science - Machine Learning ,Mathematics - Numerical Analysis ,Physics - Computational Physics - 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.
- Published
- 2023