analiza aiqbench
This research introduces a novel architecture for Port-Hamiltonian neural networks capable of modeling dynamic systems with multiple stable equilibria, overcoming the single-attractor limitation of previous global Lyapunov functions. By parametrizing the Hamiltonian as a product of Bregman divergences, the method successfully recovers complex energy landscapes and significantly accelerates convergence speeds on benchmark systems. The work advances theoretical guarantees for stability in control-oriented machine learning models while maintaining rigorous mathematical proofs essential for safety-critical applications.
Port-Hamiltonian Neural Networks for Systems with Multiple Asymptotically Stable Equilibria
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 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$\times$.
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$\times$.
Machine Learning (cs.LG); Systems and Control (eess.SY)
arXiv:2610.01356 [cs.LG]
(or arXiv:2610.01356v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.01356 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 224 cuvinte
Subiecte conexe
Learning Deterministic and Stochastic Forced Hamiltonian Systems
arXiv · 21 aug. 2026
Quantum Port-Hamiltonian Neural Networks: Learning Conservative and Dissipative Dynamics via Measurement-Induced Nonlinearity
arXiv · 22 iul. 2026
AUP Learning Cloud: Streamlining AI Education on AMD
AMD · 6 aug. 2026
Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation
arXiv · 20 iul. 2026