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

Excerpt

arXiv:2610.01356v1 Announce Type: new 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 on