期刊文献+

A REDUCED ORDER SCHWARZ METHOD FOR NONLINEAR MULTISCALE ELLIPTIC EQUATIONS BASED ON TWO-LAYER NEURAL NETWORKS

原文传递
导出
摘要 Neural networks are powerful tools for approximating high dimensional data that have been used in many contexts,including solution of partial differential equations(PDEs).We describe a solver for multiscale fully nonlinear elliptic equations that makes use of domain decomposition,an accelerated Schwarz framework,and two-layer neural networks to approximate the boundary-to-boundarymap for the subdomains,which is the key step in the Schwarz procedure.Conventionally,the boundary-to-boundary map requires solution of boundary-value elliptic problems on each subdomain.By leveraging the compressibility of multiscale problems,our approach trains the neural network offline to serve as a surrogate for the usual implementation of the boundary-to-boundary map.Our method is applied to a multiscale semilinear elliptic equation and a multiscale p-Laplace equation.In both cases we demonstrate significant improvement in efficiency as well as good accuracy and generalization performance.
出处 《Journal of Computational Mathematics》 SCIE CSCD 2024年第2期570-596,共27页 计算数学(英文)
基金 supported in part by National Science Foundation via grant 1934612 a DOE Subcontract 8F-30039 from Argonne National Laboratory an AFOSR subcontract UTA20-001224 from UT-Austin.The work of SC supported in part by NSF-DMS-1750488 and ONR-N00014-21-1-2140.
  • 相关文献

参考文献3

二级参考文献1

共引文献74

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部