Priori Error Estimate of Deep Mixed Residual Method for Elliptic PDEs

In this work, we derive a priori error estimate of the mixed residual method when solving some elliptic PDEs. Our work is the first theoretical study of this method. We prove that the neural network solutions will converge if we increase the training samples and network size without any constraint o...

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Bibliographic Details
Published inarXiv.org
Main Authors Li, Lingfeng, Xue-cheng, Tai, Jiang, Yang, Zhu, Quanhui
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 15.06.2022
Subjects
Neural networks
Ritz method
Training
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ISSN2331-8422

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Summary:In this work, we derive a priori error estimate of the mixed residual method when solving some elliptic PDEs. Our work is the first theoretical study of this method. We prove that the neural network solutions will converge if we increase the training samples and network size without any constraint on the ratio of training samples to the network size. Besides, our results suggest that the mixed residual method can recover high order derivatives better than the deep Ritz method, which has also been verified by our numerical experiments.
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SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
ISSN:2331-8422