Article
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Surrogate-Based Physics-Informed Neural Networks for Elliptic Partial Differential Equations
Version 1
: Received: 20 May 2023 / Approved: 22 May 2023 / Online: 22 May 2023 (09:48:22 CEST)
A peer-reviewed article of this Preprint also exists.
Zhi, P.; Wu, Y.; Qi, C.; Zhu, T.; Wu, X.; Wu, H. Surrogate-Based Physics-Informed Neural Networks for Elliptic Partial Differential Equations. Mathematics 2023, 11, 2723. Zhi, P.; Wu, Y.; Qi, C.; Zhu, T.; Wu, X.; Wu, H. Surrogate-Based Physics-Informed Neural Networks for Elliptic Partial Differential Equations. Mathematics 2023, 11, 2723.
Abstract
This study aimed at exploring what role artificial intelligence techniques could play in the futural numerical analysis. In this paper, a convolutional neural network techniques based on modified loss function is proposed as a surrogate of finite element method(FEM). Several surrogate-based physics-informed neural networks(PINNs) are developed to solve representative boundary value problems based on elliptic partial differential equations (PDEs). Results from the proposed surrogate-based approach are in good agreement with ones from conventional FEM. It is found that modification of the loss function could improve the prediction accuracy of the neural network. It is indicated that to some extent the artificial intelligence technique could replace conventional numerical analysis as a great surrogate model.
Keywords
Surrogate Model; Convolutional Neural Network; Physics-Informed Neural Networks; Elliptic PDE; FEM
Subject
Engineering, Civil Engineering
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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