Solving PDEs using deep neural networks with error control
数学专题报告
报告题目(Title)：Solving PDEs using deep neural networks with error control
报告人(Speaker)：毛志平 教授 （宁波东方理工大学）
地点(Place)：#腾讯会议：636-971-314
时间(Time)：2025年10月15日 （周三）14:00-15:00
邀请人(Inviter)：段玉萍
报告摘要
Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and computational efficiency. To address these challenges, we propose both Galerkin and collocation adaptive methods that uses neural networks to construct basis functions guided by the equation residual. The approximate solution is computed within the space spanned by these basis functions. Additionally, we introduce adaptive strategies for collocation point selection and parameter initialization to enhance robustness and improve the expressiveness of the neural networks. We also derive the approximation error estimate and validate the proposed method with several numerical experiments on various challenging PDEs, demonstrating both high accuracy and robustness of the proposed methods.
主讲人简介
毛志平教授2009年本科毕业于重庆大学，2015年博士毕业于厦门大学计算数学专业，国家高层次青年人才，2015年10 月至 2020 年 9 月在美国布朗大学应用数学系从事博士后研究，国家级青年人才计划入选者。毛志平教授主要从事深度学习与偏微分方程数值解，特别是谱方法研究以及深度学习求解复杂系统方面的研究，其目前在SIREV, JCP， SISC， SINUM、 CMAME等国际高水平杂志上发表论文 40 余篇。
