Port-Hamiltonian Neural Networks for Systems with Multiple Asymptotically Stable Equilibria
Port-Hamiltonian networks are extended to multiple stable equilibria using Bregman divergences.
Stable port-Hamiltonian neural networks use a Hamiltonian that is a global Lyapunov function with a single minimum, so they cannot represent multi-attractor systems such as a double well. The authors parametrize the Hamiltonian as a product of Bregman divergences generated by one input-convex network. They prove local Lyapunov stability, the existence of additional non-asymptotically stable equilibria, bounded equilibria, and almost-everywhere stability under a hyperbolicity assumption. On three systems the model recovers energy-surface characteristics and improves convergence speed by 1.8× to 8.5×.
- Standard stable port-Hamiltonian networks represent only one attractor.
- The Hamiltonian is a product of Bregman divergences.
- Proofs cover local Lyapunov stability and bounded equilibria.
- Convergence improves 1.8x to 8.5x on three systems.
From the original article
1 min read at arxiv.orgStable 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.
By Simon Heilig · arxiv.org
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