Artificial neural network approximations of Cauchy inverse problem for linear PDEs

Yixin Li and Xianliang Hu

Applied Mathematics and Computation, 2022, vol. 414, issue C

Abstract: A novel artificial neural network method is proposed for solving Cauchy inverse problems. Using multiple-layers network as an approximation we present a non-mesh discretization to solve the problems. The existence and convergence are shown to establish the well-posedness of neural network approximations for the Cauchy inverse problems. Numerical results on 2D to 8D cases show that compared to finite element method, the neural network approach easier extends to high dimensional case. The stability and accuracy of the proposed network approach are investigated by the experiments with noisy boundary and irregular computational domain. Our studies conclude that the neural network method alleviates the influence of noise and it is observed that networks with wider and deeper hidden layers could lead to better approximation.

Keywords: Cauchy inverse problem; Artificial neural network; Well-posedness; High dimension; Irregular domain (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:414:y:2022:i:c:s0096300321007621

DOI: 10.1016/j.amc.2021.126678

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