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【几何与代数基础科学研究中心】DNN for PDEs: Residual-informed neural networks and non-uniform random walk for adaptive sampling
胡丹(上海交通大学)
11月14日周四下午2: 00-3:00  闵行校区数学楼401

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hbs红宝石平台工作。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.