{"title":"Machine learning-assisted multi-scale modeling","authors":"W. E, H. Lei, Pinchen Xie, Linfeng Zhang","doi":"10.1063/5.0149861","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"73 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Physics Analysis Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1063/5.0149861","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
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.
期刊介绍:
Journal of Mathematical Physics, Analysis, Geometry (JMPAG) publishes original papers and reviews on the main subjects:
mathematical problems of modern physics;
complex analysis and its applications;
asymptotic problems of differential equations;
spectral theory including inverse problems and their applications;
geometry in large and differential geometry;
functional analysis, theory of representations, and operator algebras including ergodic theory.
The Journal aims at a broad readership of actively involved in scientific research and/or teaching at all levels scientists.