Structure-preserving neural networks

JOURNAL OF COMPUTATIONAL PHYSICS

卷:426

Article

Hernandez, Quercus¹  Badias, Alberto¹  Gonzalez, David¹  Chinesta, Francisco^2,3  Cueto, Elias¹ 

[1] Univ Zaragoza, Aragon Inst Engn Res I3A, Maria de Luna 3, E-50018 Zaragoza, Spain

[2] ENSAM ParisTech, ESI Chair, 155 Blvd Hop, F-75013 Paris, France

[3] ENSAM ParisTech, PIMM Lab, 155 Blvd Hop, F-75013 Paris, France

关键词: Scientific machine learning;    Neural networks;    Structure preservation;    GENERIC;   

DOI  :  10.1016/j.jcp.2020.109950

来源: Elsevier

【 摘 要 】

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 socalled General Equation for the Non-Equilibrium Reversible-Irreversible Coupling, GENERIC (Ottinger 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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free