Learning Passive Continuous-Time Dynamics with Multistep Port-Hamiltonian Gaussian Processes

• URL: http://arxiv.org/abs/2510.00384v2
• Date: Sat, 04 Oct 2025 05:12:01 GMT
• Title: Learning Passive Continuous-Time Dynamics with Multistep Port-Hamiltonian Gaussian Processes
• Abstract summary: 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.<n>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.<n>We demonstrate improved vector-field recovery and well-calibrated Hamiltonian uncertainty on mass-spring, Van der Pol, and Duffing benchmarks.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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