Hybrid Energy-Based Models for Physical AI: Provably Stable Identification of Port-Hamiltonian Dynamics

TL;DR

This paper introduces a hybrid energy-based model framework for physical AI that guarantees stability and physical interpretability in system identification, extending to port-Hamiltonian dynamics with provable safety.

Contribution

It develops a novel hybrid EBM architecture with stability guarantees, extending theory to nonsmooth activations, and demonstrates its effectiveness on complex physical systems.

Findings

Hybrid EBM achieves stable system identification with physical interpretability.

Theoretical extension to nonsmooth activations with stability guarantees.

Experimental validation on multi-well and ring systems confirms effectiveness.

Abstract

Energy-based models (EBMs) implement inference as gradient descent on a learned Lyapunov function, yielding interpretable, structure-preserving alternatives to black-box neural ODEs and aligning naturally with physical AI. Yet their use in system identification remains limited, and existing architectures lack formal stability guarantees that globally preclude unstable modes. We address this gap by introducing an EBM framework for system identification with stable, dissipative, absorbing invariant dynamics. Unlike classical global Lyapunov stability, absorbing invariance expands the class of stability-preserving architectures, enabling more flexible and expressive EBMs. We extend EBM theory to nonsmooth activations by establishing negative energy dissipation via Clarke derivatives and deriving new conditions for radial unboundedness, exposing a stability-expressivity tradeoff in standard EBMs. To overcome this, we introduce a hybrid architecture with a dynamical visible layer and static hidden layers, prove absorbing invariance under mild assumptions, and show that these guarantees extend to port-Hamiltonian EBMs. Experiments on metric-deformed multi-well and ring systems validate the approach, showcasing how our hybrid EBM architecture combines expressivity with sound and provable safety guarantees by design.