Structure-preserving neural networks

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.

Automated summary

The method developed uses feedforward neural networks to learn physical systems from data while ensuring compliance with the first and second principles of thermodynamics. By enforcing the metriplectic structure of dissipative Hamiltonian systems, it minimizes the amount of data required and naturally achieves conservation of energy and dissipation of entropy in its predictions. No prior knowledge of the system is necessary, and the method can handle both conservative and dissipative, discrete and continuous systems.