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Deep learning of thermodynamics-aware reduced-order models from data

Article dans une revue avec comité de lecture
Author
HERNANDEZ, Quercus
161327 Aragón Institute of Engineering Research [Zaragoza] [I3A]
BADIAS, Alberto
161327 Aragón Institute of Engineering Research [Zaragoza] [I3A]
GONZALEZ, David
161327 Aragón Institute of Engineering Research [Zaragoza] [I3A]
ccCHINESTA SORIA, Francisco
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]
ccCUETO, Elias
161327 Aragón Institute of Engineering Research [Zaragoza] [I3A]

URI
http://hdl.handle.net/10985/20176
DOI
10.1016/j.cma.2021.113763
Date
2021
Journal
Computer Methods in Applied Mechanics and Engineering

Abstract

We 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.

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