报 告 人：周翔 [香港城市大学 副教授]
报告时间：2019年6月24日 (周一) 10:00 - 11:00
邀 请 人：李晓强
The generative model with the aid of deep neural network now significantly advances the possibility of efficiently sampling the high dimensional complex probability distribution. The well-known GAN is based on the observed data from the unknown target distribution in which the learning and generating are coupled together. The importance sampling such as the rare event simulation does not have data or only has very scarce data, but its target distribution has the known expression (up to a multiplicative constant). Somewhat, the importance sampling is a stochastic version of mesh adaptivity for numerical PDE(partial differential equation). I will start with the traditional moving mesh method based on the harmonic map, but from a perspective of generative model for sampling complex random variables. The techniques developed here have the following contributions: (1) a formulation to enable sampling by solving elliptic variational problems, which is intrinsically suitable for the existing machine learning methods； (2) a rational mechanism to find the correct monitor function to generate the target distribution； (3) an old and new idea for the adaptivity in high dim PDE by constructing optimal collocation points.
Simple toy examples will be illustrated but the implementation of large scale problems is still ongoing.
Dr Xiang Zhou is the associate professor at School of Data Science and Department of Mathematics, City University of Hong Kong. He received his BSc from Peking University and PhD from Princeton University. Before joining City University in 2012, he worked as a research associate at Princeton University and Brown University. His major research area is the study of rare event. His research interests include the development and analysis of algorithms for transitions in nonlinear stochastic dynamical systems, the efficient Monte Carlo simulation of rare events, the numerical methods for saddle point and the exploration of high dimensional non-convex energy landscapes in physical models and machine learning models. His research results have turned into peer-reviewed papers in SIAM journals, Journal of Computational Physics, Journal of Chemical Physics, Nonlinearity and Annals of Applied Probability, etc.