Physics informed neural networks for an inverse problem in peridynamic models

Author:

Difonzo Fabio V.,Lopez Luciano,Pellegrino Sabrina F.

Abstract

AbstractDeep learning is a powerful tool for solving data driven differential problems and has come out to have successful applications in solving direct and inverse problems described by PDEs, even in presence of integral terms. In this paper, we propose to apply radial basis functions (RBFs) as activation functions in suitably designed Physics Informed Neural Networks (PINNs) to solve the inverse problem of computing the perydinamic kernel in the nonlocal formulation of classical wave equation, resulting in what we call RBF-iPINN. We show that the selection of an RBF is necessary to achieve meaningful solutions, that agree with the physical expectations carried by the data. We support our results with numerical examples and experiments, comparing the solution obtained with the proposed RBF-iPINN to the exact solutions.

Funder

Regione Puglia

Gruppo Nazionale per il Calcolo Scientifico

Consiglio Nazionale Delle Ricerche

Publisher

Springer Science and Business Media LLC

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Boundary integrated neural networks for 2D elastostatic and piezoelectric problems;International Journal of Mechanical Sciences;2024-10

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