发布时间：2025-10-19
Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations
主讲人：刘红良
摘要：In this talk, we propose a domain decomposition subspace neural network method for efficiently solving linear and nonlinear partial differential equations. By combining the principles of domain decomposition and subspace neural networks, the method constructs basis functions using neural networks to approximate PDE solutions. It imposes C^k continuity conditions at the interface of subdomains, ensuring smoothness across the global solution. Nonlinear PDEs are solved using Picard and Newton iterations, analogous to classical methods. Numerical experiments demonstrate that our method achieves exceptionally high accuracy, with errors reaching up to 10E-13, while significantly reducing computational costs. The results highlight superior accuracy and training efficiency of the method.
主讲人简介：刘红良，教授，博导，副院长。从事微分方程数值方法和数据科学的研究。获中国仿真学会优秀科技工作者、全国大学生数学建模竞赛优秀指导老师、湖南省教学成果奖和湘潭大学优秀教师等荣誉。主持国家自然科学基金面上项目、青年基金项目、数学天元青年基金项目等多个项目。相关成果发表在Journal of Scienti?c Computing、IEEE Transactions on Artificial Intelligence等期刊。出版教材《数学模型与建模算法》，主持《数学建模》国家一流线上课程。担任中国仿真学会仿真算法专业委员会副主任委员和仿真算法建模与仿真标准化技术专业委员会委员。
邀请人：黄乘明
时间：2025年10月21日19:00-21:00
地点： 腾讯会议室：788855763