Deep learning and partial differential equations
October 14 to October 18, 2019
American Institute of Mathematics,
San Jose, California
and Lexing Ying
This workshop will be devoted to the interplay
between deep learning and partial differential equations.
The main topics for the workshop are:
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.
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.
- 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.