Deep learning and partial differential equations

Original Announcement

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

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Papers arising from the workshop: