Artificial neural network approximations of Cauchy inverse problem for linear PDEs

作者：

Highlights：

• Neural network approximation is proposed to deal with ill-posedness of Cauchy inverse problem.

• The proposed method is suitable for both time-dependent and time-independent cases.

• It is straightforward to apply in high dimensional cases or problems with singular domain.

• Deeper and wider neural networks yield better accuracy for the approximation in this paper.

摘要

•Neural network approximation is proposed to deal with ill-posedness of Cauchy inverse problem.•The proposed method is suitable for both time-dependent and time-independent cases.•It is straightforward to apply in high dimensional cases or problems with singular domain.•Deeper and wider neural networks yield better accuracy for the approximation in this paper.

论文关键词：Cauchy inverse problem,Artificial neural network,Well-posedness,High dimension,Irregular domain

论文评审过程：Received 29 October 2020, Revised 18 July 2021, Accepted 20 September 2021, Available online 9 October 2021, Version of Record 9 October 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126678