Problem
Research questions and friction points this paper is trying to address.
Energy-based models
system identification
stability guarantees
port-Hamiltonian dynamics
absorbing invariance
Hybrid Energy-Based Models for Physical AI: Provably Stable Identification of Port-Hamiltonian Dynamics
🤖 AI Summary
Existing energy-based models struggle to simultaneously achieve expressive power and global stability in system identification. This work proposes a hybrid energy-based architecture that combines dynamic visible units with static hidden units to jointly model system dynamics. By introducing absorption invariance, the framework broadens the class of stabilizable systems and establishes an energy dissipation theory under nonsmooth activations. Leveraging Clarke derivatives and radial unboundedness conditions, the approach formally unifies model expressivity with provable safety guarantees. Experiments on multi-well and ring-shaped dynamical systems demonstrate the model’s high representational capacity alongside its intrinsic stability properties.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Energy-Based Models
Absorbing Invariance
Port-Hamiltonian Systems
Hybrid Architecture
Clarke Derivatives
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