讲座题目: Deep learning for solving forward and inverse PDE problems: Algorithms and Applications

报告人：孟旭辉 教授， 华中科技大学数学与应用学科交叉创新研究院

时 间：2025年3月21日 10:00-12:00

地 点：西安交通大学兴庆校区北二楼大厅会议室（203A）

邀请人：刘海湖 教授，王宁宁 副研究员

报告摘要：

Deep learning algorithms have emerged recently for solving partial differential equations (PDEs), especially in conjunction with sparse data. In particular, the recently developed physics-informed neural networks (PINNs) have shown their effectiveness in solving both forward and inverse PDE problems. Different from the classical numerical methods in which the differential operators are approximated by the data on certain discrete lattices (meshes), PINNs compute all the differential operators of a PDE using the automatic differentiation technique involved in the backward propagation. Consequently, no mesh (structured mesh or unstructured mesh used in the classical numerical methods) is required for the PINN to solve PDEs, which saves a lot of effort in grid generation. Another attractive feature is that PINNs are capable of solving the inverse PDE problems effectively and with the same code that is used for forward problems. In this talk, I will introduce several newly developed PINNs for solving forward and inverse PDE problems as well as their applications: (1) Monte Carlo PINNs for solving the phonon Boltzmann transport equation; (2) multi-fidelity PINNs for inverse PDE problems with multi-fidelity data; (3) Bayesian physics-informed neural networks for quantifying uncertainties in predictions; and (4) applications of the proposed deep learning algorithms in various scientific and engineering disciplines.

专家简介：孟旭辉，华中科技大学数学与应用学科交叉创新研究院教授，国家级青年人才项目获得者，小米青年学者，华中卓越学者特聘教授。2017年博士毕业于华中科技大学能源与动力工程学院；2018年-2022年美国布朗大学应用数学系博士后。截至目前已在SIAM Review、JCP、CMAME等期刊发表SCI论文30余篇，谷歌学术总引用6500余次，8篇论文入选ESI高被引论文，入选2024年Stanford/Elsevier联合发布的全球前2%顶尖科学家榜单；担任JCP、SISC、CMAME及多个Nature子刊审稿人。