Distinguished Lecture Series in Mathematics 系列数学前沿学术讲座

报告题目：Selection dynamics for Deep Neural Networks

报告人：Prof. Peter Markowich     （King Abdullah University of Science  and Technology）

时间：2022年1月13日 16:00-17:30 PM (Beijing time), 9:00-10:30 AM (CET)

地点:  ZOOM URL: https://zoom.us/j/97412413730

          Meeting ID: 974 1241 3730
          Passcode: 321050

摘要：

We present a partial differential equation framework for deep residual neural networks and for the associated learning problem. This is done by carrying out the continuum limits of neural networks with respect to width and depth. We study the wellposedness, the large time solution behavior, and the characterization of the steady states of the forward problem. Several useful time-uniform estimates and stability/instability conditions are presented. We state and prove optimality conditions for the inverse deep learning problem, using standard variational calculus, the Hamilton-Jacobi-Bellmann equation and the Pontryagin maximum principle. This serves to establish a mathematical foundation for investigating the algorithmic and theoretical connections between neural networks, PDE theory, variational analysis, optimal control, and deep learning.

报告人简介:

Professor Markowich's primary research interests are in the mathematical and numerical analysis of partial differential equations (PDEs) and their application in physics, biology and engineering.

In particular, he is interested in:

• classical and quantum mechanical kinetic theory

• analytical and numerical problems occurring in highly      oscillatory PDEs (like semi classical asymptotics)

• Wigner transforms

• nonlinear PDEs describing dispersive and, resp., diffusive      phenomena

• singular perturbations and long-time asymptotics

• generalized Sobolev inequalities

• inverse problems in solid state physics

• image processing using PDEs

举办单位：威斯尼斯人5158cc、交叉科学研究院

                 北京国家应用数学中心、北京成像理论与技术高精尖创新中心

                 光场成像与数字几何北京市重点实验室

联系人：杨佳