Port-Hamiltonian Neural Networks for Systems with Multiple Asymptotically Stable Equilibria
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...
| Authors | Simon Heilig, Jens Püttschneider, Mohammad Itani et al. |
|---|---|
| Primary category | cs.LG |
| Published | 1 October 2026 |
| Last updated at source | 4 October 2026 |
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