Learning Dynamics from Input-Output Data with Hamiltonian Gaussian Processes
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915938362720256 |
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| author | Ewering, Jan-Hendrik Herrmann, Robin E. Wahlström, Niklas Schön, Thomas B. Seel, Thomas |
| author_facet | Ewering, Jan-Hendrik Herrmann, Robin E. Wahlström, Niklas Schön, Thomas B. Seel, Thomas |
| contents | Embedding non-restrictive prior knowledge, such as energy conservation laws, into learning methods is a key motive to construct physically consistent dynamics models from limited data, relevant for, e.g., model-based control. Recent work incorporates Hamiltonian dynamics into Gaussian Processes (GPs) to obtain uncertainty-quantifying, energy-consistent models, but these methods rely on -- rarely available -- velocity or momentum data. In this paper, we study dynamics learning using Hamiltonian GPs and focus on learning solely from input-output data, without relying on velocity or momentum measurements. Adopting a non-conservative formulation, energy exchange with the environment, e.g., through external forces or dissipation, can be captured. We provide a fully Bayesian scheme for estimating probability densities of unknown hidden states, GP hyperparameters, as well as structural hyperparameters, such as damping coefficients. The proposed method is evaluated in a nonlinear simulation case study and compared to a state-of-the-art approach that relies on momentum measurements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05330 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning Dynamics from Input-Output Data with Hamiltonian Gaussian Processes Ewering, Jan-Hendrik Herrmann, Robin E. Wahlström, Niklas Schön, Thomas B. Seel, Thomas Machine Learning Systems and Control Embedding non-restrictive prior knowledge, such as energy conservation laws, into learning methods is a key motive to construct physically consistent dynamics models from limited data, relevant for, e.g., model-based control. Recent work incorporates Hamiltonian dynamics into Gaussian Processes (GPs) to obtain uncertainty-quantifying, energy-consistent models, but these methods rely on -- rarely available -- velocity or momentum data. In this paper, we study dynamics learning using Hamiltonian GPs and focus on learning solely from input-output data, without relying on velocity or momentum measurements. Adopting a non-conservative formulation, energy exchange with the environment, e.g., through external forces or dissipation, can be captured. We provide a fully Bayesian scheme for estimating probability densities of unknown hidden states, GP hyperparameters, as well as structural hyperparameters, such as damping coefficients. The proposed method is evaluated in a nonlinear simulation case study and compared to a state-of-the-art approach that relies on momentum measurements. |
| title | Learning Dynamics from Input-Output Data with Hamiltonian Gaussian Processes |
| topic | Machine Learning Systems and Control |
| url | https://arxiv.org/abs/2511.05330 |