Year: 2022
Type: 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.
Authors: Antonio Russo, Miguel A. Durán-Olivencia, Ioannis G. Kevrekidis, Serafim Kalliadasis
Institutions: Imperial College London, Johns Hopkins University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G1045913000, G1669642419, G2354669367, Complex Interfacial Flows: From the Nano- to the Macro-Scale, G4401462600, Statistical mechanics of soft matter: Derivation, analysis and implementation of dynamic density functional theories, G5348725440, Multiscale Analysis of Complex Interfacial Phenomena (MACIPh): Coarse graining, Molecular modelling, stochasticity, and experimentation, G8730730436
OpenAlex ID: W3204042378