Machine learning memory kernels as closure for non-Markovian stochastic processes
File(s)TNNLS-2021-P-18548_Revised_Manuscript.pdf (4.67 MB)
Accepted version
Author(s)
Russo, Antonio
Duran-Olivencia, Miguel A
Kevrekidis, Ioannis G
Kalliadasis, Serafim
Type
Journal Article
Abstract
Finding the dynamical law of observable quantities lies at the core of physics. Within the particular field of statistical mechanics, the generalized Langevin equation (GLE) comprises a general model for the evolution of observables covering a great deal of physical systems with many degrees of freedom and an inherently stochastic nature. Although formally exact, GLE brings its own great challenges. It depends on the complete history of the observables under scrutiny, as well as the microscopic degrees of freedom, all of which are often inaccessible. We show that these drawbacks can be overcome by adopting elements of machine learning from empirical data, in particular coupling a multilayer perceptron (MLP) with the formal structure of GLE and calibrating the MLP with the data. This yields a powerful computational tool capable of describing noisy complex systems beyond the realms of statistical mechanics. It is exemplified with a number of representative examples from different fields: from a single colloidal particle and particle chains in a thermal bath to climatology and finance, showing in all cases excellent agreement with the actual observable dynamics. The new framework offers an alternative perspective for the study of nonequilibrium processes opening also a new route for stochastic modeling.
Editor(s)
Song, Yongduan
Date Issued
2024-05-01
Date Acceptance
2022-09-18
Citation
IEEE Transactions on Neural Networks and Learning Systems, 2024, 35 (5), pp.6531-6543
ISSN
1045-9227
Publisher
Institute of Electrical and Electronics Engineers
Start Page
6531
End Page
6543
Journal / Book Title
IEEE Transactions on Neural Networks and Learning Systems
Volume
35
Issue
5
Copyright Statement
Copyright © 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Identifier
https://ieeexplore.ieee.org/document/9947343
Subjects
Generalised Langevin equation (GLE)
Machine learning
Non-Markovian processes
Stochastic modeling
Publication Status
Published
Coverage Spatial
United States
Date Publish Online
2022-11-14