Port-metriplectic neural networks: thermodynamics-informed machine learning of complex physical systems

TL;DR

This paper introduces port-metriplectic neural networks that incorporate thermodynamics principles into machine learning models to better understand and predict complex physical systems, ensuring energy conservation and entropy production.

Contribution

It extends port-Hamiltonian formalism to port-metriplectic formalism, embedding thermodynamic laws into neural networks for modeling complex physical systems.

Findings

Networks can learn system physics by parts, reducing experimental characterization effort.

Predictions are accurate at the system scale, demonstrating practical applicability.

The approach effectively enforces thermodynamic principles in learned models.

Abstract

We develop inductive biases for the machine learning of complex physical systems based on the port-Hamiltonian formalism. To satisfy by construction the principles of thermodynamics in the learned physics (conservation of energy, non-negative entropy production), we modify accordingly the port-Hamiltonian formalism so as to achieve a port-metriplectic one. We show that the constructed networks are able to learn the physics of complex systems by parts, thus alleviating the burden associated to the experimental characterization and posterior learning process of this kind of systems. Predictions can be done, however, at the scale of the complete system. Examples are shown on the performance of the proposed technique.