四川大学学报（自然科学版）2026，Vol.63Issue(1)：58-64,7.DOI:10.19907/j.0490-6756.240113
一种求解Stokes问题的深度学习混合方法
A deep-learning-based mixed method for Stokes systems
摘要
Abstract
Deep learning Galerkin Method(DGM)can approximate partial differential equations efficiently.In this paper,inspired by the mixed finite element method,a mixed method combing the deep learning method with the reducing order method of partial differential equation is proposed and used to solve the Stokes system.The velocity gradient is introduced to avoid the use of second-order automatic differentiation.A trained deep learning model is specifically applied to solve the mixed model.Convergence of the loss func-tion and optimality of the deep learning solution are analyzed.Numerical examples verify the effectiveness of the method.关键词
Stokes系统/深度学习/Galerkin法/收敛性分析Key words
Stokes system/deep learning/Galerkin method/convergence analysis分类
数理科学引用本文复制引用
杨楠,刘文艺,周言信,宋恩彬..一种求解Stokes问题的深度学习混合方法[J].四川大学学报（自然科学版）,2026,63(1):58-64,7.基金项目
国家自然科学基金(U2066203) （U2066203）
