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Title: Inverse Weak Adversarial Networks (iWAN) : A Computational Method for High-dimensional Inverse Problems

Abstract: In this talk, I will present a weak adversarial network approach to solve a class of inverse problems. Using the weak formulation of PDE, we rewrite the inverse problem as a minimax problem. Leveraged with deep neural networks, the solution of inverse problem, including the solution of PDE and the unknown media, can be solved simultaneously by finding the network parameters for the saddle point. While the parameters are updated, the networks gradually approximate the solution of the inverse problem. Theoretical justifications are provided on the convergence of the proposed algorithm. The proposed method is mesh-free without any spatial discretization, and is suitable for problems with high dimensionality and low regularity on solutions. Numerical experiments on a variety of test problems demonstrate the promising accuracy and efficiency of this approach. This presentation is based on the joint work with Gang Bao (Zhejiang), Xiaojing Ye (Georgia State Univ.) and Yaohua Zang (Zhejiang).

Bio: Haomin Zhou is a professor in the School of Mathematics at Georgia Institute of Technology. He received his B.S. in pure mathematics from Peking University, M.Phil in applied mathematics from the Chinese University of Hong Kong, and Ph.D. in applied mathematics from University of California, Los Angeles in 1991, 1996 and 2000 respectively. He spent 3 years in California Institute of Technology as a postdoctoral scholar and von Karman instructor, before joining Georgia Institute of Technology as an
assistant professor in 2003. His research interests include numerical analysis and scientific computing, specialized in PDE and wavelet techniques in image processing, numerical methods for stochastic differential equations, and discrete optimal transport. He is a recipient of the NSF CAREER AWARD in applied and computational mathematics in 2007, and Feng Kang prize in scientific computing in 2019.