Hybrid Energy-Based Models for Physical AI: Provably Stable Identification of Port-Hamiltonian Dynamics
Summary: arXiv:2604.00277v1 Announce Type: cross
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.
Introduction
In recent years, the integration of energy-based models into the realm of physical AI has gained traction. These models are particularly valued for their ability to provide interpretable and structure-preserving alternatives to traditional neural ordinary differential equations (ODEs). However, the deployment of EBMs in system identification has been stymied by a lack of formal stability guarantees, which are essential for ensuring that the models do not exhibit unstable behavior.
Key Contributions
This article presents several key contributions aimed at enhancing the applicability and stability of EBMs:
- Introduction of Absorbing Invariance: We expand the classical notion of global Lyapunov stability to incorporate absorbing invariance, thereby broadening the scope of stability-preserving architectures. This flexibility allows for the development of more expressive EBMs.
- Nonsmooth Activations: Our work extends EBM theory to accommodate nonsmooth activations. By establishing negative energy dissipation via Clarke derivatives, we derive new conditions for radial unboundedness, which reveal a tradeoff between stability and expressivity in standard EBMs.
- Hybrid Architecture Design: We propose a novel hybrid architecture that features a dynamic visible layer coupled with static hidden layers. This architecture is proven to maintain absorbing invariance under mild assumptions and is shown to extend these guarantees to port-Hamiltonian EBMs.
Experimental Validation
To validate our theoretical developments, we conducted experiments on metric-deformed multi-well and ring systems. The results demonstrate that our hybrid EBM architecture successfully combines expressivity with robust safety guarantees. By design, these models not only exhibit the necessary flexibility to adapt to complex dynamics but also ensure that stability is preserved across various scenarios.
Conclusion
The introduction of hybrid energy-based models marks a significant advancement in the field of physical AI, particularly in the context of system identification. By addressing the limitations of previous architectures and providing formal stability guarantees, our work lays the groundwork for future research and applications in this domain. The framework we propose not only enhances the expressivity of EBMs but also ensures that they remain safe and stable, making them a valuable tool for real-world applications.
Future Work
Looking ahead, further exploration of the interplay between expressivity and stability in EBMs is essential. Additionally, we aim to expand the scope of our models to accommodate more complex dynamical systems and investigate their performance in real-world applications.