Learning non-Markovian physics from data

González, D. (Universidad de Zaragoza) ; Chinesta, F. ; Cueto, E. (Universidad de Zaragoza)

Resumen: We present a method for the data-driven learning of physical phenomena whose evolution in time depends on history terms. It is well known that a Mori-Zwanzig-type projection produces a description of the physical phenomena that depends on history, and also incorporates noise. If the data stream is sampled from the projected Mori-Zwanzig manifold, the description of the phenomenon will always depend on one or more unresolved variables, a priori unknown, and will also incorporate noise. The present work introduces a novel technique able to unveil the presence of such internal variables—although without giving it a precise physical meaning—and to minimize the inherent noise. The method is based upon a refinement of the scale at which the phenomenon is described by means of kernel-PCA techniques. By learning the metriplectic form of the evolution of the physics, the resulting approximation satisfies basic thermodynamic principles such as energy conservation and positive entropy production. Examples are provided that show the potential of the method in both discrete and continuum mechanics.

Idioma: Inglés

DOI: 10.1016/j.jcp.2020.109982

Año: 2021

Publicado en: Journal of Computational Physics 428, 109982 (2021), [14 pp]
ISSN: 0021-9991

Factor impacto JCR: 4.645 (2021)

Categ. JCR: PHYSICS, MATHEMATICAL rank: 3 / 56 = 0.054 (2021) - Q1 - T1
Categ. JCR: COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS rank: 40 / 112 = 0.357 (2021) - Q2 - T2

Factor impacto CITESCORE: 7.1 - Physics and Astronomy (Q1) - Mathematics (Q1) - Computer Science (Q1)

Factor impacto SCIMAGO: 2.069 - Applied Mathematics (Q1) - Computational Mathematics (Q1) - Physics and Astronomy (miscellaneous) (Q1) - Numerical Analysis (Q1) - Modeling and Simulation (Q1)

Financiación: info:eu-repo/grantAgreement/ES/DGA-FSE/T24-20R
Financiación: info:eu-repo/grantAgreement/ES/MINECO-CICYT/DPI2017-85139-C2-1-R
Financiación: info:eu-repo/grantAgreement/ES/UZ/ESI-ENSAM-Simulated Reality

Tipo y forma: Article (PostPrint)

Área (Departamento): Área Mec.Med.Cont. y Teor.Est. (Dpto. Ingeniería Mecánica)