108301 20230519145350.0 doi 10.1016/j.jcp.2020.109982 sideral 121210 ART-2021-121210 eng González, D. Universidad de Zaragoza (orcid)0000-0003-3003-5856 Learning non-Markovian physics from data 2021 Access copy available to the general public Unrestricted 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. info:eu-repo/grantAgreement/ES/DGA-FSE/T24-20R info:eu-repo/grantAgreement/ES/MINECO-CICYT/DPI2017-85139-C2-1-R info:eu-repo/grantAgreement/ES/UZ/ESI-ENSAM-Simulated Reality info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 4.645 2021 PHYSICS, MATHEMATICAL 3 / 56 = 0.054 2021 Q1 T1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS 40 / 112 = 0.357 2021 Q2 T2 2.069 2021 Applied Mathematics 2021 Q1 Computational Mathematics 2021 Q1 Physics and Astronomy (miscellaneous) 2021 Q1 Numerical Analysis 2021 Q1 Modeling and Simulation 2021 Q1 7.1 2021 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Chinesta, F. Cueto, E. Universidad de Zaragoza (orcid)0000-0003-1017-4381 5004 605 Universidad de Zaragoza Dpto. Ingeniería Mecánica Área Mec.Med.Cont. y Teor.Est. 428, 109982 (2021), [14 pp] J. comput. phys. Journal of Computational Physics 0021-9991 1301409 http://zaguan.unizar.es/record/108301/files/texto_completo.pdf Postprint 2057930 http://zaguan.unizar.es/record/108301/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:108301 articulos driver 2023-05-18-13:25:53 ARTICLE