Uniformly accurate machine learning-based hydrodynamic models for kinetic equations
Abstract
This paper addresses 2 very important issues of current interest: multiscale modeling in the absence of scale separation and building interpretable and truly reliable physical models using machine learning. We demonstrate that machine learning can indeed help us to build reliable multiscale models for problems with which classical multiscale methods have had trouble. To this end, one has to develop the appropriate models or algorithms for each of the 3 major components in the machine-learning procedure: labeling the data, learning from the data, and exploring the state space. We use the kinetic equation as an example and demonstrate that uniformly accurate moment systems can be constructed this way.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Oct 16, 2019
- Source ID
- 10.1073/pnas.1909854116
Entities
People
- Chao Ma
- Jiequn Han
- Weinan E
- Zheng Ma
Organizations
- Beijing Institute of Big Data Research
- Office of Naval Research
- Princeton University
- Purdue University