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Structure-preserving neural networks

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

URI
http://hdl.handle.net/10985/19561
DOI
10.1016/j.jcp.2020.109950
Date
2020
Journal
Journal of Computational Physics

Abstract

We develop a method to learn physical systems from data that employs feedforward neural networks and whose predictions comply with the first and second principles of thermodynamics. The method employs a minimum amount of data by enforcing the metriplectic structure of dissipative Hamiltonian systems in the form of the so-called General Equation for the Non-Equilibrium Reversible-Irreversible Coupling, GENERIC (Öttinger and Grmela (1997) [36]). The method does not need to enforce any kind of balance equation, and thus no previous knowledge on the nature of the system is needed. Conservation of energy and dissipation of entropy in the prediction of previously unseen situations arise as a natural by-product of the structure of the method. Examples of the performance of the method are shown that comprise conservative as well as dissipative systems, discrete as well as continuous ones.

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