{"ID":2844980,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.05330","arxiv_id":"2511.05330","title":"Learning Dynamics from Input-Output Data with Hamiltonian Gaussian Processes","abstract":"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.","short_abstract":"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 uncertai...","url_abs":"https://arxiv.org/abs/2511.05330","url_pdf":"https://arxiv.org/pdf/2511.05330v2","authors":"[\"Jan-Hendrik Ewering\",\"Robin E. Herrmann\",\"Niklas Wahlström\",\"Thomas B. Schön\",\"Thomas Seel\"]","published":"2025-11-07T15:28:08Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"eess.SY\"]","methods":"[]","has_code":false}