{"ID":2861774,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.00384","arxiv_id":"2510.00384","title":"Learning Passive Continuous-Time Dynamics with Multistep Port-Hamiltonian Gaussian Processes","abstract":"We propose the multistep port-Hamiltonian Gaussian process (MS-PHS GP) to learn physically consistent continuous-time dynamics and a posterior over the Hamiltonian from noisy, irregularly-sampled trajectories. By placing a GP prior on the Hamiltonian surface $H$ and encoding variable-step multistep integrator constraints as finite linear functionals, MS-PHS GP enables closed-form conditioning of both the vector field and the Hamiltonian surface without latent states, while enforcing energy balance and passivity by design. We state a finite-sample vector-field bound that separates the estimation and variable-step discretization terms. Lastly, we demonstrate improved vector-field recovery and well-calibrated Hamiltonian uncertainty on mass-spring, Van der Pol, and Duffing benchmarks.","short_abstract":"We propose the multistep port-Hamiltonian Gaussian process (MS-PHS GP) to learn physically consistent continuous-time dynamics and a posterior over the Hamiltonian from noisy, irregularly-sampled trajectories. By placing a GP prior on the Hamiltonian surface $H$ and encoding variable-step multistep integrator constrain...","url_abs":"https://arxiv.org/abs/2510.00384","url_pdf":"https://arxiv.org/pdf/2510.00384v2","authors":"[\"Chi Ho Leung\",\"Philip E. Paré\"]","published":"2025-10-01T00:55:28Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"eess.SY\"]","methods":"[]","has_code":false}