ESR-PINNs: Physics-informed neural networks with expansion-shrinkage resampling selection strategies

doi:10.1088/1674-1056/acc1d5

中国物理B ›› 2023, Vol. 32 ›› Issue (7): 70702-070702.doi: 10.1088/1674-1056/acc1d5

ESR-PINNs: Physics-informed neural networks with expansion-shrinkage resampling selection strategies

Jianan Liu(刘佳楠)¹, Qingzhi Hou(侯庆志)^2,†, Jianguo Wei(魏建国)¹, and Zewei Sun(孙泽玮)¹

1 College of Intelligence and Computing, Tianjin University, Tianjin 300350, China;
2 State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300350, China

收稿日期:2022-12-28 修回日期:2023-02-28 接受日期:2023-03-07 出版日期:2023-06-15 发布日期:2023-06-29
通讯作者: Qingzhi Hou E-mail:qhou@tju.edu.cn
基金资助:
Project supported by the National Key Research and Development Program of China (Grant No. 2020YFC1807905), the National Natural Science Foundation of China (Grant Nos. 52079090 and U20A20316), and the Basic Research Program of Qinghai Province (Grant No. 2022-ZJ-704).

ESR-PINNs: Physics-informed neural networks with expansion-shrinkage resampling selection strategies

Jianan Liu(刘佳楠)¹, Qingzhi Hou(侯庆志)^2,†, Jianguo Wei(魏建国)¹, and Zewei Sun(孙泽玮)¹

1 College of Intelligence and Computing, Tianjin University, Tianjin 300350, China;
2 State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300350, China

Received:2022-12-28 Revised:2023-02-28 Accepted:2023-03-07 Online:2023-06-15 Published:2023-06-29
Contact: Qingzhi Hou E-mail:qhou@tju.edu.cn
Supported by:
Project supported by the National Key Research and Development Program of China (Grant No. 2020YFC1807905), the National Natural Science Foundation of China (Grant Nos. 52079090 and U20A20316), and the Basic Research Program of Qinghai Province (Grant No. 2022-ZJ-704).

摘要/Abstract

摘要： Neural network methods have been widely used in many fields of scientific research with the rapid increase of computing power. The physics-informed neural networks (PINNs) have received much attention as a major breakthrough in solving partial differential equations using neural networks. In this paper, a resampling technique based on the expansion-shrinkage point (ESP) selection strategy is developed to dynamically modify the distribution of training points in accordance with the performance of the neural networks. In this new approach both training sites with slight changes in residual values and training points with large residuals are taken into account. In order to make the distribution of training points more uniform, the concept of continuity is further introduced and incorporated. This method successfully addresses the issue that the neural network becomes ill or even crashes due to the extensive alteration of training point distribution. The effectiveness of the improved physics-informed neural networks with expansion-shrinkage resampling is demonstrated through a series of numerical experiments.

关键词: physical informed neural networks, resampling, partial differential equation

Abstract: Neural network methods have been widely used in many fields of scientific research with the rapid increase of computing power. The physics-informed neural networks (PINNs) have received much attention as a major breakthrough in solving partial differential equations using neural networks. In this paper, a resampling technique based on the expansion-shrinkage point (ESP) selection strategy is developed to dynamically modify the distribution of training points in accordance with the performance of the neural networks. In this new approach both training sites with slight changes in residual values and training points with large residuals are taken into account. In order to make the distribution of training points more uniform, the concept of continuity is further introduced and incorporated. This method successfully addresses the issue that the neural network becomes ill or even crashes due to the extensive alteration of training point distribution. The effectiveness of the improved physics-informed neural networks with expansion-shrinkage resampling is demonstrated through a series of numerical experiments.

Key words: physical informed neural networks, resampling, partial differential equation

中图分类号: (Neural networks, fuzzy logic, artificial intelligence)

07.05.Mh

02.30.Jr (Partial differential equations) 84.35.+i (Neural networks)

Jianan Liu(刘佳楠), Qingzhi Hou(侯庆志), Jianguo Wei(魏建国), and Zewei Sun(孙泽玮). ESR-PINNs: Physics-informed neural networks with expansion-shrinkage resampling selection strategies[J]. 中国物理B, 2023, 32(7): 70702-070702.

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ESR-PINNs: Physics-informed neural networks with expansion-shrinkage resampling selection strategies

ESR-PINNs: Physics-informed neural networks with expansion-shrinkage resampling selection strategies

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