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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 |
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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.
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Received: 28 December 2022
Revised: 28 February 2023
Accepted manuscript online: 07 March 2023
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PACS:
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07.05.Mh
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(Neural networks, fuzzy logic, artificial intelligence)
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02.30.Jr
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(Partial differential equations)
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84.35.+i
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(Neural networks)
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| Fund: 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). |
Corresponding Authors:
Qingzhi Hou
E-mail: qhou@tju.edu.cn
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Cite this article:
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 2023 Chin. Phys. B 32 070702
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