mlsanityData to 7 Oct 2026

Structure-preserving Gaussian Process Dynamics

arXiv 2102.01606 ↗First posted 2 Feb 2021cs.LGcited by 9

Not on the map. Why?

Abstract (arXiv)

Most physical processes posses structural properties such as constant energies, volumes, and other invariants over time. When learning models of such dynamical systems, it is critical to respect these invariants to ensure accurate predictions and physically meaningful behavior. Strikingly, state-of-the-art methods in Gaussian process (GP) dynamics model learning are not addressing this issue. On the other hand, classical numerical integrators are specifically designed to preserve these crucial properties through time. We propose to combine the advantages of GPs as function approximators with structure preserving numerical integrators for dynamical systems, such as Runge-Kutta methods. These integrators assume access to the ground truth dynamics and require evaluations of intermediate and future time steps that are unknown in a learning-based scenario. This makes direct inference of the GP dynamics, with embedded numerical scheme, intractable. Our key technical contribution is the evaluation of the implicitly defined Runge-Kutta transition probability. In a nutshell, we introduce an implicit layer for GP regression, which is embedded into a variational inference-based model learning scheme.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 22 of its 56 references that are in the map. First posted on arXiv 2 Feb 2021.

Builds on

22 of 56 references.

References · 22

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10 more
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 3; 2023: 1; 2024: 0; 2025: 2; 2026: 1.

9 papers.

  1. 2021Variational multiple shooting for Bayesian ODEs with Gaussian processescited by 15
  2. 2022Recognition Models to Learn Dynamics from Partial Observations with Neural ODEscited by 8
  3. 2023Learning Energy Conserving Dynamics Efficiently with Hamiltonian Gaussian Processescited by 6
  4. 2022Learning Interacting Dynamical Systems with Latent Gaussian Process ODEscited by 5
  5. 2021Structure-Preserving Learning Using Gaussian Processes and Variational Integratorscited by 3
  6. 2022The Past Does Matter: Correlation of Subsequent States in Trajectory Predictions of Gaussian Process Modelscited by 2
  7. 2025Data-efficient Kernel Methods for Learning Hamiltonian Systemscited by 2
  8. 2025Learning Dynamics from Input-Output Data with Hamiltonian Gaussian Processescited by 1
  9. 2026Structure-Preserving Gaussian Processes Via Discrete Euler-Lagrange Equationscited by 0