报告题目：Generative model for importance sampling and PDE adaptivity
报告人：Xiang Zhou（香港城市大学）
时间：2019年6月25日（星期二）4:00—5:00
地点：苏州大学本部精正楼（数学楼）307
摘要：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 and its power manifests in high dim.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.
欢迎参加！