mlsanityData to 7 Oct 2026

Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Prior

arXiv 2305.09017 ↗First posted 15 May 2023eess.SY cs.LG cs.SYcited by 15

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Abstract (arXiv)

Data-driven approaches achieve remarkable results for the modeling of complex dynamics based on collected data. However, these models often neglect basic physical principles which determine the behavior of any real-world system. This omission is unfavorable in two ways: The models are not as data-efficient as they could be by incorporating physical prior knowledge, and the model itself might not be physically correct. We propose Gaussian Process Port-Hamiltonian systems (GP-PHS) as a physics-informed Bayesian learning approach with uncertainty quantification. The Bayesian nature of GP-PHS uses collected data to form a distribution over all possible Hamiltonians instead of a single point estimate. Due to the underlying physics model, a GP-PHS generates passive systems with respect to designated inputs and outputs. Further, the proposed approach preserves the compositional nature of Port-Hamiltonian systems.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). Builds on 10 of its 28 references that are in the map. First posted on arXiv 15 May 2023.

Builds on

10 of 28 references.

References · 10

  1. 2019Hamiltonian Neural Networkscited by 702
  2. 2015Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)cited by 175
  3. 2020Efficiently Sampling Functions from Gaussian Process Posteriorscited by 125
  4. 2017Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equationscited by 72
  5. 2021Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systemscited by 66
  6. 2020Symplectic Gaussian Process Regression of Hamiltonian Flow Mapscited by 17
  7. 2021Gaussian processes meet NeuralODEs: A Bayesian framework for learning the dynamics of partially observed systems from scarce and noisy datacited by 13
  8. 2020Learning ODE Models with Qualitative Structure Using Gaussian Processescited by 9
  9. 2020Prediction with Approximated Gaussian Process Dynamical Modelscited by 8
  10. 2018Equilibrium Distributions and Stability Analysis of Gaussian Process State Space Modelscited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 3; 2025: 6; 2026: 4.

15 papers.

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  1. 2023Neural Autoencoder-Based Structure-Preserving Model Order Reduction and Control Design for High-Dimensional Physical Systemscited by 7
  2. 2023Gaussian process learning of nonlinear dynamicscited by 5
  3. 2024Data-driven identification of latent port-Hamiltonian systemscited by 3
  4. 2024Data-driven identification of port-Hamiltonian DAE systems by Gaussian processescited by 2
  5. 2024Combining Federated Learning and Control: A Surveycited by 2
  6. 2026PHDME: Physics-Informed Diffusion Models without Explicit Governing Equationscited by 2
  7. 2025Plug-and-Play Physics-informed Learning using Uncertainty Quantified Port-Hamiltonian Modelscited by 1
  8. 2025Bayesian Inference and Learning in Nonlinear Dynamical Systems: A Framework for Incorporating Explicit and Implicit Prior Knowledgecited by 1
  9. 2025Learning Generalized Hamiltonian Dynamics with Stability from Noisy Trajectory Datacited by 1
  10. 2025Physics-based deep kernel learning for parameter estimation in high dimensional PDEscited by 1
  11. 2025Learning Dynamics from Input-Output Data with Hamiltonian Gaussian Processescited by 1
  12. 2025Learning Passive Continuous-Time Dynamics with Multistep Port-Hamiltonian Gaussian Processescited by 0
3 more
  1. 2026Co-Learning Port-Hamiltonian Systems and Optimal Energy-Shaping Controlcited by 0
  2. 2026Structure-Preserving Gaussian Processes Via Discrete Euler-Lagrange Equationscited by 0
  3. 2026A unified perspective of Gaussian process approximation for differential equationscited by 0