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.
Abstract (translated)
基于能量的模型（EBMs）通过在学习得到的李雅普诺夫函数上执行梯度下降来实现推断，为黑箱神经常微分方程提供了可解释、结构保持的替代方案，并与物理人工智能自然契合。然而，其在系统辨识中的应用仍较为有限，且现有架构缺乏全局排除不稳定模式的正式稳定性保证。本文通过引入一个具备稳定、耗散、吸收不变动力学的EBM框架来弥补这一空白。与经典的全局李雅普诺夫稳定性不同，吸收不变性扩展了稳定性保持架构的范畴，从而支持更灵活、更具表达力的EBMs。我们通过克拉克导数建立负能量耗散，并推导径向无界性的新条件，将EBM理论扩展至非光滑激活函数，揭示了标准EBMs中存在的稳定性-表达性权衡。为克服此局限，我们提出一种混合架构：动态可见层与静态隐藏层，在温和假设下证明其吸收不变性，并表明此类保证可延伸至端口哈密顿EBMs。在度量变形多阱与环系统上的实验验证了该方法，展示了我们的混合EBM架构如何通过设计将表达力与可靠且可证明的安全性保证相结合。
URL
https://arxiv.org/abs/2604.00277
