000108301 001__ 108301 000108301 005__ 20230519145350.0 000108301 0247_ $$2doi$$a10.1016/j.jcp.2020.109982 000108301 0248_ $$2sideral$$a121210 000108301 037__ $$aART-2021-121210 000108301 041__ $$aeng 000108301 100__ $$0(orcid)0000-0003-3003-5856$$aGonzález, D.$$uUniversidad de Zaragoza 000108301 245__ $$aLearning non-Markovian physics from data 000108301 260__ $$c2021 000108301 5060_ $$aAccess copy available to the general public$$fUnrestricted 000108301 5203_ $$aWe 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. 000108301 536__ $$9info:eu-repo/grantAgreement/ES/DGA-FSE/T24-20R$$9info:eu-repo/grantAgreement/ES/MINECO-CICYT/DPI2017-85139-C2-1-R$$9info:eu-repo/grantAgreement/ES/UZ/ESI-ENSAM-Simulated Reality 000108301 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/ 000108301 590__ $$a4.645$$b2021 000108301 591__ $$aPHYSICS, MATHEMATICAL$$b3 / 56 = 0.054$$c2021$$dQ1$$eT1 000108301 591__ $$aCOMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS$$b40 / 112 = 0.357$$c2021$$dQ2$$eT2 000108301 594__ $$a7.1$$b2021 000108301 592__ $$a2.069$$b2021 000108301 593__ $$aApplied Mathematics$$c2021$$dQ1 000108301 593__ $$aComputational Mathematics$$c2021$$dQ1 000108301 593__ $$aPhysics and Astronomy (miscellaneous)$$c2021$$dQ1 000108301 593__ $$aNumerical Analysis$$c2021$$dQ1 000108301 593__ $$aModeling and Simulation$$c2021$$dQ1 000108301 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000108301 700__ $$aChinesta, F. 000108301 700__ $$0(orcid)0000-0003-1017-4381$$aCueto, E.$$uUniversidad de Zaragoza 000108301 7102_ $$15004$$2605$$aUniversidad de Zaragoza$$bDpto. Ingeniería Mecánica$$cÁrea Mec.Med.Cont. y Teor.Est. 000108301 773__ $$g428, 109982 (2021), [14 pp]$$pJ. comput. phys.$$tJournal of Computational Physics$$x0021-9991 000108301 8564_ $$s1301409$$uhttps://zaguan.unizar.es/record/108301/files/texto_completo.pdf$$yPostprint 000108301 8564_ $$s2057930$$uhttps://zaguan.unizar.es/record/108301/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000108301 909CO $$ooai:zaguan.unizar.es:108301$$particulos$$pdriver 000108301 951__ $$a2023-05-18-13:25:53 000108301 980__ $$aARTICLE