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Learning non-Markovian physics from data

Article dans une revue avec comité de lecture
Author
GONZÁLEZ, David
95355 University of Zaragoza - Universidad de Zaragoza [Zaragoza]
CHINESTA, Francisco
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]
CUETO, Elías
95355 University of Zaragoza - Universidad de Zaragoza [Zaragoza]

URI
http://hdl.handle.net/10985/19926
DOI
10.1016/j.jcp.2020.109982
Date
2021
Journal
Journal of Computational Physics

Abstract

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.

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