报告题目： Deep adaptive density approximation for Fokker-Plank type equations

报 告 人： 周涛 研究员，中科院数学与系统科学研究院

报告时间：2023年5月10日 上午10:00 -- 12:00

腾讯会议 ID：627-828-604

会议链接：https://meeting.tencent.com/dm/HFOSUdmQ6ZGJ

报告摘要：

We propose adaptive deep learning method based on normalizing flow for classic/nonlocal Fokker-Planck equations. The solution of such equation is a probability density function. Traditional mesh-based methods may across difficulties since the dimension of spatial variable can be very high. To this end, we represent the solution by a flow-based generative model (e.g. KRnet) which constructs a mapping from a simple distribution to the target distribution (i.e., the unknow solution). An adaptive procedure for choosing the training set is presented. Meanwhile, either Monte Carlo sampling or an auxiliary density model, Gaussian radial basis functions which have analytical fractional Laplacian, is applied to approximate the fractional Laplacian. Numerical examples are presented to show the effectiveness of the proposed approach. Finally, we design bounded KRNet and show applications to Keller-Segel equations and kinetic Fokker-Planck equations. ⋅

报告人简介：

周涛，中国科学院数学与系统科学研究院研究员。曾于瑞士洛桑联邦理工大学从事博士后研究。主要研究方向为不确定性量化、偏微分方程数值方法以及时间并行算法等。在国际权威期刊SIAM Review、SINUM、JCP等发表论文70余篇。2016年获CSIAM青年科技奖，2018年获优秀青年科学基金资助，2022年获中组部高层次基础人才专项资助。2022年获得第三届王选杰出青年学者奖。2018年曾担任某部门《核挑战专题》不确定性量化方向首席科学家，并在2021年被授予“挑战英才”称号。现担任SIAM J Sci Comput、J Sci Comput、Commun. Comput. Phys. 等多个国际权威期刊编委，国际不确定性量化期刊（International Journal for UQ）副主编。周涛研究员目前担任东亚工业与应用数学学会副主席，并担任学会期刊East Asian Journal on Applied Mathematics主编。