Learning Passive Continuous-Time Dynamics with Multistep Port-Hamiltonian Gaussian Processes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914075050508288 |
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| author | Leung, Chi Ho Paré, Philip E. |
| author_facet | Leung, Chi Ho Paré, Philip E. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_00384 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning Passive Continuous-Time Dynamics with Multistep Port-Hamiltonian Gaussian Processes Leung, Chi Ho Paré, Philip E. Machine Learning Systems and Control 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. |
| title | Learning Passive Continuous-Time Dynamics with Multistep Port-Hamiltonian Gaussian Processes |
| topic | Machine Learning Systems and Control |
| url | https://arxiv.org/abs/2510.00384 |