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arXiv Machine Learning By Simon Heilig, Jens P\"uttschneider, Mohammad Itani, Asja Fischer, Timm Faulwasser

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

Read the original on arXiv Machine Learning →

The paper introduces a new class of port‑Hamiltonian neural networks that can model systems with multiple asymptotically stable equilibria. By parameterizing the Hamiltonian as a product of Bregman divergences generated by an input‑convex network, the authors overcome the limitation of previous models that could only represent a single attractor. They prove local Lyapunov stability, show that additional non‑asymptotically stable equilibria must exist, and demonstrate improved convergence on three benchmark systems.

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