000127555 001__ 127555 000127555 005__ 20230911114509.0 000127555 0247_ $$2doi$$a10.1016/j.cma.2021.113763 000127555 0248_ $$2sideral$$a123957 000127555 037__ $$aART-2021-123957 000127555 041__ $$aeng 000127555 100__ $$aHernandez, Quercus$$uUniversidad de Zaragoza 000127555 245__ $$aDeep learning of thermodynamics-aware reduced-order models from data 000127555 260__ $$c2021 000127555 5060_ $$aAccess copy available to the general public$$fUnrestricted 000127555 5203_ $$aWe present an algorithm to learn the relevant latent variables of a large-scale discretized physical system and predict its time evolution using thermodynamically-consistent deep neural networks. Our method relies on sparse autoencoders, which reduce the dimensionality of the full order model to a set of sparse latent variables with no prior knowledge of the coded space dimensionality. Then, a second neural network is trained to learn the metriplectic structure of those reduced physical variables and predict its time evolution with a so-called structure-preserving neural network. This data-based integrator is guaranteed to conserve the total energy of the system and the entropy inequality, and can be applied to both conservative and dissipative systems. The integrated paths can then be decoded to the original full-dimensional manifold and be compared to the ground truth solution. This method is tested with two examples applied to fluid and solid mechanics. 000127555 536__ $$9info:eu-repo/grantAgreement/ES/MINECO-CICYT/DPI2017-85139-C2-1-R 000127555 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/ 000127555 590__ $$a6.588$$b2021 000127555 591__ $$aMECHANICS$$b9 / 138 = 0.065$$c2021$$dQ1$$eT1 000127555 591__ $$aMATHEMATICS, INTERDISCIPLINARY APPLICATIONS$$b4 / 108 = 0.037$$c2021$$dQ1$$eT1 000127555 591__ $$aENGINEERING, MULTIDISCIPLINARY$$b8 / 92 = 0.087$$c2021$$dQ1$$eT1 000127555 592__ $$a2.179$$b2021 000127555 593__ $$aComputational Mechanics$$c2021$$dQ1 000127555 593__ $$aPhysics and Astronomy (miscellaneous)$$c2021$$dQ1 000127555 593__ $$aMechanics of Materials$$c2021$$dQ1 000127555 593__ $$aComputer Science Applications$$c2021$$dQ1 000127555 594__ $$a10.3$$b2021 000127555 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000127555 700__ $$0(orcid)0000-0001-7639-6767$$aBadías, Alberto$$uUniversidad de Zaragoza 000127555 700__ $$0(orcid)0000-0003-3003-5856$$aGonzález, David$$uUniversidad de Zaragoza 000127555 700__ $$aChinesta, Francisco 000127555 700__ $$0(orcid)0000-0003-1017-4381$$aCueto, Elías$$uUniversidad de Zaragoza 000127555 7102_ $$15004$$2605$$aUniversidad de Zaragoza$$bDpto. Ingeniería Mecánica$$cÁrea Mec.Med.Cont. y Teor.Est. 000127555 773__ $$g379 (2021), 113763 [18 pp]$$pComput. methods appl. mech. eng.$$tComputer Methods in Applied Mechanics and Engineering$$x0045-7825 000127555 8564_ $$s1315073$$uhttps://zaguan.unizar.es/record/127555/files/texto_completo.pdf$$yVersión publicada 000127555 8564_ $$s1823554$$uhttps://zaguan.unizar.es/record/127555/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000127555 909CO $$ooai:zaguan.unizar.es:127555$$particulos$$pdriver 000127555 951__ $$a2023-09-11-10:59:30 000127555 980__ $$aARTICLE