mlsanityData to 14 Oct 2026

Koopman-Equivariant Gaussian Processes

arXiv 2502.06645 ↗First posted 10 Feb 2025cs.LG cs.SY eess.SYcited by 6

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Abstract (arXiv)

Credible forecasting and representation learning of dynamical systems are of ever-increasing importance for reliable decision-making. To that end, we propose a family of Gaussian processes (GP) for dynamical systems with linear time-invariant responses, which are nonlinear only in initial conditions. This linearity allows us to tractably quantify forecasting and representational uncertainty, simultaneously alleviating the challenge of computing the distribution of trajectories from a GP-based dynamical system and enabling a new probabilistic treatment of learning Koopman operator representations. Using a trajectory-based equivariance -- which we refer to as textitKoopman equivariance -- we obtain a GP model with enhanced generalization capabilities. To allow for large-scale regression, we equip our framework with variational inference based on suitable inducing points. Experiments demonstrate on-par and often better forecasting performance compared to kernel-based methods for learning dynamical systems.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 59 of its 131 references that are in the map. First posted on arXiv 10 Feb 2025.

Builds on

59 of 131 references.

References · 59

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38 more
  1. 2021Provably Strict Generalisation Benefit for Equivariant Modelscited by 91
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 4; 2026: 2.

6 papers.

  1. 2025MTIL: Encoding Full History with Mamba for Temporal Imitation Learningcited by 10
  2. 2025Information Shapes Koopman Representationcited by 4
  3. 2025kooplearn: A Scikit-Learn Compatible Library of Algorithms for Evolution Operator Learningcited by 1
  4. 2026Koopman operator theory: fundamentals, control, and applicationscited by 1
  5. 2025Bayesian Transfer Operators in Reproducing Kernel Hilbert Spacescited by 0
  6. 2026Equivariant Covariance Tensors: Guaranteed SPD Uncertainty for Tensor-Valued Geometric Learningcited by 0