Deep adaptive sampling for numerical PDEs

Speaker: Tao Zhou (Academy of Mathematics and Systems Science, CAS)

Date:    2022.11.24

Time:    10:00 am

Venue:   BIMSA 1129B

Zoom:  537 192 5549    Passcode: BIMSA

Video

 

Abtract:

Adaptive computation is of great importance in numerical simulations. The ideas for adaptive computations can be dated back to adaptive finite element methods in 1970s. In this talk, we shall first review some recent development for adaptive method with applications. Then, we shall propose a deep adaptive sampling method for solving PDEs where deep neural networks are utilized to approximate the solutions. In particular, we propose the failure informed PINNs (FI-PINNs), which can adaptively refine the training set with the goal of reducing the failure probability. Compared to the neural network approximation obtained with uniformly distributed collocation points, the developed algorithms can significantly improve the accuracy, especially for low regularity and high-dimensional problems.

 

Speaker Intro.

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,近期的主要研究课题包括深度学习与科学计算,深度生成模型及其应用等。在国际权威期刊如SIAM ReviewSINUMJCP等发表论文70余篇。2018年获优秀青年科学基金资助,2022年获中组部高层次人才专项资助。现担任SIAM J Sci ComputJ Sci Comput等国际期刊编委,国际不确定性量化期刊(International Journal for UQ)副主编。