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arXiv · 2610.01356

Port-Hamiltonian Neural Networks for Systems with Multiple Asymptotically Stable Equilibria

Simon Heilig·Jens Püttschneider·Mohammad Itani·Asja Fischer·Timm Faulwasser
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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$\times$.

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Simon Heilig, Jens Püttschneider, Mohammad Itani, Asja Fischer, Timm Faulwasser. 2026-10-01. Port-Hamiltonian Neural Networks for Systems with Multiple Asymptotically Stable Equilibria. https://arxiv.org/abs/2610.01356

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