摘要：

In this talk, we explore two deep learning methods for solving high-dimensional PDEs. First, we introduce EPR-Net, a novel deep learning approach for constructing potential landscapes of high-dimensional non-equilibrium steady-state (NESS) systems. The coincidence between the minimum loss of EPR-Net and the entropy production rate in NESS theory allows simultaneous potential landscape construction and clear physical interpretation. EPR-Net can be combined with dimensionality reduction and extended to systems with state-dependent diffusion coefficients. Next, we propose Deep Picard Iteration (DPI) for solving high-dimensional nonlinear parabolic PDEs. DPI combines Picard iteration with neural networks, avoiding the computational difficulties of directly optimizing PDE objective functions. It uses the Feynman-Kac formula for function evaluation, the Bismut-Elworthy-Li formula for gradient estimation. Numerical experiments demonstrate DPI’s faster convergence, lower computational cost, and higher solution accuracy compared to existing methods.

报告人信息： 

赵悦，北京大学大数据科学中心博士生，主要研究方向为深度学习与科学计算。

欢迎大家参与3月12号的午餐会。报告时间是12:30-13:30，午餐于12:15开始提供。请有意参与的老师和同学在3月11日15:00前填写以下问卷：https://www.wjx.cn/vm/OcU6L5b.aspx# 。