走向现代数学学术报告 - 周翔副教授（No. 752)

题目：Weak Generative Sampler

报告人：周翔 副教授（香港城市大学）

时间：2024年12月5日 10:00

腾讯会议ID：204113495

报告摘要：许多典型的高维偏微分方程（例如 Fokker-Planck 方程和 McKean-Vlasov 方程）的解代表着随机过程的概率密度分布函数。对无穷长时间达到的不变分布进行采样是很多计算物理、化学、统计等领域的核心问题。通过深度学习技术求解此类偏微分方程通常是直接找到一个满足一定正性和归一化条件的概率密度函数的神经网络。然而，应用中需要的不变测度的样本则需要对学习到的高维分布函数再次进行随机采样，而这是极具挑战性的任务。我们从静态Fokker-Planck 方程出发，引入了一个弱生成采样器（Weak Generative Sampler, WGS）(arxiv 2405.19256)，能够更高效地求解偏微分方程并直接通过传输网络从简单分布直接生成不变分布样本。我们提出的损失函数基于弱形式和随机化的测试函数。本次报告的详细内容将解释为什么在求解高维偏微分方程时，WGS 的高效性和自适应性如此容易实现。

报告人简介：Xiang ZHOU is the associate professor at Department of Mathematics and Department of Data Science in City University of Hong Kong. Xiang ZHOU received the BSc from Peking University (School of Mathematical Sciences) and PhD from Princeton University (PACM). Before joining the Department of Mathematics City University of Hong Kong in 2012, he worked as a research associate at Princeton University and Brown University. His research focuses on the numerical and mathematical aspects of computational algorithms for scientific computing problems in complex dynamical systems arising in natural science and engineering. His work integrates tools from probability theory, stochastic processes, dynamical systems, numerical analysis, optimization, optimal control, and machine learning to design efficient methods for better understanding complex phenomena such as rare events.