Modeling and Computation in the Space of Language: Symbolic and LLM-Based Approaches. [pdf]
Finite Expression Method for High-Dimensional PDEs. [pdf] [video]
Discretization Invariant Operator Learning: Algorithms and Theory. [pdf] [video]
Error Analysis of Operator Learning. [vidoe]
A Few Thoughts on Deep Learning-Based Scientific Computing. [pdf]
A Few Thoughts on Deep Network Approximation. [pdf]
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.