Deep learning and partial differential equations

October 14 to October 18, 2019

at the

American Institute of Mathematics, San Jose, California

organized by

Lin Lin, Jianfeng Lu, and Lexing Ying

Original Announcement

This workshop will be devoted to the interplay between deep learning and partial differential equations.

The main topics for the workshop are:

  1. Deep learning for high dimensional PDE problems. Many challenging problems from physical and data sciences (e.g. control theory, molecular dynamics, quantum mechanics) are modeled by PDEs, either of high dimensional functions or with high dimensional parameter fields. Deep neural networks potentially offer a novel and efficient tool for solving these PDE problems.
  2. PDE and stochastic analysis for deep learning. Though deep learning has brought remarkable empirical successes on many ML/AI problems, traditional statistical learning theories have not been able to explain them. Examples include the effectiveness of the stochastic gradient methods, the generalization power of deep learning, etc. Recently, methods from PDEs and stochastic analysis have provided new perspectives for answering these deep questions.
  3. PDE and analysis for new architectures. Many successful deep neural network architectures have deep connections with mathematical analysis: CNN with harmonic analysis, RNN and ResNet with ordinary differential equations, etc. The workshop will explore connections between PDE models with new neural network architectures.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Papers arising from the workshop:

Universal approximation of symmetric and anti-symmetric functions
by  Jiequn Han, Yingzhou Li, Lin Lin, Jianfeng Lu, Jiefu Zhang, Linfeng Zhang
A Mean-field analysis of Deep ResNet and Beyond: Towards provable optimization via overparameterization from depth
by  Yiping Lu, Chao Ma, Yulong Lu, Jianfeng Lu, Lexing Ying