Presentation

Slides

• Finite Expression Method for Discovering Physical Laws. [pdf] 

• Finite Expression Method for High-Dimensional PDEs. [pdf] [video]

• Discretization Invariant Operator Learning: Algorithms and Theory. [pdf] 

• A Few Thoughts on Deep Learning-Based Scientific Computing. [pdf] 

• A Few Thoughts on Deep Network Approximation. [pdf] 

Summer School

• Mathematical Theory and Applications of Deep Learning, 15 Lectures, Tianyuan Mathematical Center in Central China, Wuhan University, August 15-30, 2022.

       Lecture [slides] 

Lecture 1:    Basic machine learning and deep feedforward neural networks. 

Lecture 2:    Recurrent neural networks.

Lecture 3:    Tabular methods in reinforcement learning. 

Lecture 4:    Approximate methods in reinforcement learning.

Lecture 5:    Data-driven recovery of equations and prediction.

Lecture 6:    Solving PDEs via DNN parametrization.

Lecture 7:    Solving PDEs via finite expressions.

Lecture 8:    Solving PDEs via operator learning.

Lecture 9:    Deep learning for inverse problems.

Lecture 10: DNN approximation - preliminary and Barron space.

Lecture 11: DNN approximation - bit extraction.

Lecture 12: DNN approximation - KST.

Lecture 13: DNN optimization theory.

Lecture 14: DNN generalization theory.

Lecture 15: Operator learning theorey.