An Importance Sampling Method for Generating Optimal Interpolation Points in Training Physics-Informed Neural Networks

Hui Li (), Yichi Zhang, Zhaoxiong Wu, Zhe Wang and Tong Wu
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Hui Li: Department of Computer Science and Technology, Beijing University of Chemical Technology, Beijing 100029, China
Yichi Zhang: Department of Computer Science and Technology, Beijing University of Chemical Technology, Beijing 100029, China
Zhaoxiong Wu: Beijing Institute of Computer Technology and Applications, Beijing 100854, China
Zhe Wang: Beijing Institute of Computer Technology and Applications, Beijing 100854, China
Tong Wu: Beijing Institute of Computer Technology and Applications, Beijing 100854, China

Mathematics, 2025, vol. 13, issue 1, 1-20

Abstract: The application of machine learning and artificial intelligence to solve scientific challenges has significantly increased in recent years. A remarkable development is the use of Physics-Informed Neural Networks (PINNs) to solve Partial Differential Equations (PDEs) numerically. However, current PINN techniques often face problems with accuracy and slow convergence. To address these problems, we propose an importance sampling method to generate optimal interpolation points during training. Experimental results demonstrate that our method achieves a 43% reduction in root mean square error compared to state-of-the-art methods when applied to the one-dimensional Korteweg–De Vries equation.

Keywords: physics-informed neural networks; importance sampling; partial differential equations; discrete wavelet transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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