发表机构
Ruhr University Bochum; Hamburg University of Technology（波鸿鲁尔大学; 汉堡工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对端口-哈密顿神经网络只能表示单一吸引子系统的局限，提出将哈密顿函数参数化为Bregman散度乘积，实现多稳定平衡点建模，并提升收敛速度1.8-8.5倍。
AI 中文摘要
稳定的端口-哈密顿神经网络通过构造保证渐近稳定性。然而，其哈密顿函数是一个具有单一全局最小值的全局李雅普诺夫函数，因此它们只能表示具有一个吸引子的动态系统。我们证明，这甚至排除了具有形成双阱能量景观的简单系统，并通过将哈密顿函数参数化为由一个输入凸网络生成的Bregman散度的乘积来克服这一限制。我们证明了所得模型是局部李雅普诺夫稳定的，稳定平衡点的共存迫使存在额外的非渐近稳定平衡点，所有平衡点位于有界区域内，并且在双曲性假设下，几乎处处稳定性成立。在三个系统上，我们的方法能够恢复能量表面特征，并将收敛速度提高1.8倍至8.5倍。
英文摘要
Stable port-Hamiltonian neural networks certify asymptotic stability by construction. Yet, their Hamiltonian is a global Lyapunov function with a single global minimum, so they can represent only dynamic systems with one attractor. We demonstrate that this excludes even simple systems with energy landscapes forming a double well, and we overcome the restriction by parametrising the Hamiltonian as a product of Bregman divergences generated by one input-convex network. We prove that the resulting model is locally Lyapunov stable, that the coexistence of stable equilibria forces additional non-asymptotically-stable equilibria to exist, that all equilibria lie in a bounded region, and under a hyperbolicity assumption that almost-everywhere stability holds. On three systems our approach is able to recover the energy surface characteristics and improve the convergence speed by 1.8$\times$-8.5$\times$.
CommentsAccepted at NeurIPS 2026 Workshop: AXIOM - Foundations of Efficient Deep Learning
