arXiv：cs.LG（机器学习，全量分类）· Simon Heilig, Jens P\"uttschneider, Mohammad Itani, Asja Fischer, Timm Faulwasser·· 14 小时前AI 评分36
Port-Hamiltonian 神经网络突破单吸引子限制，可建模多渐近稳定平衡点系统
Port-Hamiltonian Neural Networks for Systems with Multiple Asymptotically Stable Equilibria
AI 导读
研究者提出将 Hamiltonian 参数化为一个输入凸网络生成的 Bregman 散度乘积，使 Port-Hamiltonian 神经网络能表示具有多个渐近稳定平衡点的系统，突破了原有全局 Lyapunov 函数仅支持单一吸引子的限制。
正文
Abstract: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$\times$.
| Comments: | Accepted at NeurIPS 2026 Workshop: AXIOM - Foundations of Efficient Deep Learning |
| Subjects: | Machine Learning (cs.LG); Systems and Control (eess.SY) |
| Cite as: | arXiv:2610.01356 [cs.LG] |
| (or arXiv:2610.01356v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.01356 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Simon Heilig [view email]
[v1]
Thu, 1 Oct 2026 09:25:51 UTC (505 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org