Jiayu Zhai, Assistant Professor, ShanghaiTech University

Haijun Yu, Professor

Adversarial Adaptive Sampling: Unify PINN and Optimal Transport for the Approximation of PDEs

11:00-12:00 September 6 (Wednesday), S415

Solving partial differential equations is a central task in scientific computing. Recently, neural network methods for PDEs have received increasing attention due to its flexible meshless discretization and its potential for high-dimensional problems. One fundamental numerical difficulty is that random samples in the training set introduce statistical errors into the discretization of loss functional which may become the dominant error in the final approximation, and therefore overshadow the modeling capability of the neural network. In this work, we propose a new adaptive sampling method to optimize simultaneously the approximate solution, given by a neural network model, and the random samples in the training set, provided by a deep generative model.

Bio: Jiayu Zhai, is now an Assistant Professor, Senior Researcher and Doctoral Supervisor at IMS of ShanghaiTech University. He graduated from Louisiana State University with PhD in math, supervised by Dr. Xiaoliang Wan. Before joining ShanghaiTech, he was a Visiting Assistant Professor at the Department of Mathematcis and Statistics of University of Massachusetts Amherst. His research interests involve numerical methods, data-driven methods, machine learning, uncertainty quantification, and their numerical and stochastic analysis.