Machine Learning and Multi-scale Modeling

Multi-scale modeling is an ambitious program that aims at unifying the different physical models at different scales for the practical purpose of developing accurate models and simulation protocals for properties of interest. Although the concept of multi-scale modeling is very powerful and very appealing, practical success on really challenging problems has been limited. One key difficulty has been our limited ability to represent complex models and complex functions.
In recent years,  machine learning has emerged as a promising tool to overcome the difficulty of representing complex functions and complex models.  In this talk, we will review some of the successes in applying machine learning to multi-scale modeling. These include molecular dynamics and model reduction for PDEs.
Another important issue is the mathematical foundation of modern machine learning, particularly in the over-parametrized regime where most of the deep learning models lie. I will also discuss our current understanding on this important issue.