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Structure-preserving neural networks

Authors :
Quercus Hernandez
Elías Cueto
David González
Alberto Badías
Francisco Chinesta
Aragón Institute of Engineering Research [Zaragoza] (I3A)
University of Zaragoza - Universidad de Zaragoza [Zaragoza]
Laboratoire Procédés et Ingénierie en Mécanique et Matériaux (PIMM)
Conservatoire National des Arts et Métiers [CNAM] (CNAM)-Arts et Métiers Sciences et Technologies
HESAM Université (HESAM)-HESAM Université (HESAM)
Source :
Journal of Computational Physics, Journal of Computational Physics, Elsevier, 2020, pp.1-16. ⟨10.1016/j.jcp.2020.109950⟩, Zaguán. Repositorio Digital de la Universidad de Zaragoza, instname
Publication Year :
2021
Publisher :
Elsevier BV, 2021.

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 [M. Grmela and H.C Oettinger (1997). Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Phys. Rev. E. 56 (6): 6620-6632]. 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 include conservative as well as dissipative systems, discrete as well as continuous ones.<br />Comment: 19 pages, 11 figures

Details

ISSN :
00219991 and 10902716
Volume :
426
Database :
OpenAIRE
Journal :
Journal of Computational Physics
Accession number :
edsair.doi.dedup.....dec0c99cd9560831c8321dc6e19d50b9
Full Text :
https://doi.org/10.1016/j.jcp.2020.109950