主持人：朱升峰

报告人简介：胡丹，理学博士，教授，博士生导师。北京大学数学学士（2002）和博士（2007），导师为张平文院士，美国纽约大学库朗研究所博士后。2010 年 1 月进入上海交通大学自然科学研究院和数学科学学院工作。主要从事血管与血流、生命科学中的稀有事件等问题的建模、模拟和分析和人工智能基础理论研究。代表性工作发表于Phys. Rev. Lett.、Nature Commun.和PLoS Biol.等顶级杂志，其中关于血管适应性生长方面的工作被Nature选为年度工作亮点。

报告摘要：Deep learning has achieved wide success in solving Partial Differential Equations (PDEs), with particular strength in handling high dimensional problems and problems with irregular geometries. In this work, we report a residual-informed neural network (RINN) for PDEs. Compared to Physics-informed neural networks, RINN avoids computation of high order derivatives of the network, thus can significantly accelerate the training process. Meanwhile, we propose a non-uniform random walk to generate adaptive samples (Nurvas) for solving PDEs with low-regularity solutions. In Nurvas, the adaptive samples are obtained without additional computational cost and without an explicit representation of the desired probability density function.