Zhongqiang Zhang: Addressing multiscale issues in physics-informed neural networks

Abstract: Training in physics-informed machine learning usually lead to better resolutions of solutions with low frequencies and small gradients than multiscale solutions. In this talk we will discuss two approaches from our recent work on low-dimensional partial differential equations with small parameters and high-dimensional Fokker-Plank equations. Specifically, we  design the architecture of neural networks and straining strategies for these two classes of problems to address the scales arising in these problems

Short bio: Zhongqiang Zhang is an Associate Professor of Mathematics at Worcester Polytechnic Institute.  His research interests include numerical methods for stochastic and integral differential equations, computational probability, and mathematics for machine learning.  Before he joined in Worcester Polytechnic Institute in 2014, he received Ph.D. degrees in mathematics at Shanghai University in 2011 and in applied mathematics at Brown University in 2014.  He has published a book titled numerical methods for stochastic partial differential equations with white noise.

Homepage: https://users.wpi.edu/~zzhang7/