1. PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs
- Author
-
Hao, Zhongkai, Yao, Jiachen, Su, Chang, Su, Hang, Wang, Ziao, Lu, Fanzhi, Xia, Zeyu, Zhang, Yichi, Liu, Songming, Lu, Lu, and Zhu, Jun
- Subjects
FOS: Computer and information sciences ,Computer Science - Machine Learning ,FOS: Mathematics ,FOS: Physical sciences ,Mathematics - Numerical Analysis ,Numerical Analysis (math.NA) ,Computational Physics (physics.comp-ph) ,Physics - Computational Physics ,Machine Learning (cs.LG) - 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. While PINNacle does not guarantee success in all real-world scenarios, it represents a significant contribution to the field by offering a robust, diverse, and comprehensive benchmark suite that will undoubtedly foster further research and development in PINNs.
- Published
- 2023
- Full Text
- View/download PDF