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. We will also discuss the challengings, both theoretical and practical that we still face.
Weinan E is a professor in the Department of Mathematics and Program in Applied and Computational Mathematics at Princeton University. He is also the director of the Center for Data Science at Peking University, and the director of the newly established Beijing Institute of Big Data Research.
He was elected as a member of the Chinese Academy of Sciences in 2011. He became an inaugural fellow of the Society of Industrial and Applied Mathematics in 2009 and an inaugural fellow of American Mathematical Society in 2012. He was also elected a member of the Institute of Physics in 2005.