Neural network-based machine learning is capable of approximating functions in very high dimension with unprecedented efficiency and accuracy. This has opened up many exciting new possibilities, one of which is to use machine learning algorithms to assist multi-scale modeling. In this review, we use three examples to illustrate the process involved in using machine learning in multi-scale modeling: ab initio molecular dynamics, ab initio meso-scale models, such as Landau models and generalized Langevin equation, and hydrodynamic models for non-Newtonian flows.
Machine learning-assisted multi-scale modeling
Note: Paper published as part of the Special Topic on Cascades of Scales: Applications and Mathematical Methodologies.
Weinan E, Huan Lei, Pinchen Xie, Linfeng Zhang; Machine learning-assisted multi-scale modeling. J. Math. Phys. 28 July 2023; 64 (7): 071101. https://doi.org/10.1063/5.0149861
Download citation file: