Learning Dynamics from Input-Output Data with Hamiltonian Gaussian Processes
This work addresses a practical limitation in model-based control by enabling physically consistent learning from more accessible input-output data, though it is incremental as it builds on existing Hamiltonian GP frameworks.
The paper tackles the problem of learning dynamics from input-output data without requiring velocity or momentum measurements, using Hamiltonian Gaussian Processes to ensure physical consistency, and demonstrates competitive performance in a nonlinear simulation case study compared to state-of-the-art methods that rely on such measurements.
Embedding non-restrictive prior knowledge, such as energy conservation laws, in learning-based approaches is a key motive to construct physically consistent models from limited data, relevant for, e.g., model-based control. Recent work incorporates Hamiltonian dynamics into Gaussian Process (GP) regression to obtain uncertainty-quantifying models that adhere to the underlying physical principles. However, these works rely on velocity or momentum data, which is rarely available in practice. In this paper, we consider dynamics learning with non-conservative Hamiltonian GPs, and address the more realistic problem setting of learning from input-output data. We provide a fully Bayesian scheme for estimating probability densities of unknown hidden states, of GP hyperparameters, as well as of structural hyperparameters, such as damping coefficients. Considering the computational complexity of GPs, we take advantage of a reduced-rank GP approximation and leverage its properties for computationally efficient prediction and training. 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.