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

Tags

Fields of Study

  • Computer science

Readers

  • Distributed Systems and Data Platform Development
  • Theoretical Analysis.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms
  • AI & ML - Neural Networks
  • Space