Physically Consistent Neural ODEs for Learning Multi-Physics Systems

TL;DR

This paper introduces Physically Consistent Neural ODEs (PC-NODEs) that incorporate thermodynamic principles via the IPHS framework, enabling reliable, physics-aware modeling of multi-physics systems from data.

Contribution

It presents a novel neural ODE approach grounded in IPHS, ensuring physical consistency and allowing prior knowledge integration in learning system dynamics.

Findings

Successfully learned thermodynamics of a building from real data.

Accurately modeled gas-piston system dynamics in simulations.

Demonstrated extensibility to multi-physics distributed systems.

Abstract

Despite the immense success of neural networks in modeling system dynamics from data, they often remain physics-agnostic black boxes. In the particular case of physical systems, they might consequently make physically inconsistent predictions, which makes them unreliable in practice. In this paper, we leverage the framework of Irreversible port-Hamiltonian Systems (IPHS), which can describe most multi-physics systems, and rely on Neural Ordinary Differential Equations (NODEs) to learn their parameters from data. Since IPHS models are consistent with the first and second principles of thermodynamics by design, so are the proposed Physically Consistent NODEs (PC-NODEs). Furthermore, the NODE training procedure allows us to seamlessly incorporate prior knowledge of the system properties in the learned dynamics. We demonstrate the effectiveness of the proposed method by learning the thermodynamics of a building from the real-world measurements and the dynamics of a simulated gas-piston system. Thanks to the modularity and flexibility of the IPHS framework, PC-NODEs can be extended to learn physically consistent models of multi-physics distributed systems.