提出可证明稳定的混合能量模型，用于物理系统识别。
Hybrid Energy-Based Models for Physical AI: Provably Stable Identification of Port-Hamiltonian Dynamics
- 设计含动态可见层的混合能量模型架构
- 在多阱和环状系统上验证了稳定性和表达性兼顾
- 适合需要安全保证的物理系统建模任务
能量基模型（EBM）通过在学习到的李雅普诺夫函数上进行梯度下降实现推理，提供可解释、结构保持的替代方案，与物理人工智能天然契合。然而其在系统识别中的应用受限，现有架构缺乏全局稳定性的形式化保证，无法排除不稳定模式。本文提出一种具有稳定、耗散、吸收不变动力学的EBM框架。不同于经典全局李雅普诺夫稳定性，吸收不变性扩展了稳定性保持架构的类别，使EBM更具灵活性和表达力。通过引入克拉克导数，将EBM理论推广至非光滑激活函数，并推导出径向无界性新条件，揭示标准EBM中稳定性与表达力之间的权衡。为此，我们提出包含动态可见层和静态隐藏层的混合架构，在温和假设下证明其吸收不变性，并展示该保证可扩展至端口-哈密顿EBM。在度量变形的多阱与环状系统上的实验验证了方法的有效性，表明该混合EBM架构从设计上兼具表达力与可证明的安全性。
原文摘要 · Abstract (English)
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.
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