mlsanityData to 7 Oct 2026

Learning dynamical systems from data: a simple cross-validation perspective

arXiv 2007.05074 ↗First posted 9 Jul 2020cs.LG math.DS nlin.CDcited by 23

Not on the map. Why?

Abstract (arXiv)

Regressing the vector field of a dynamical system from a finite number of observed states is a natural way to learn surrogate models for such systems. We present variants of cross-validation (Kernel Flows citeOwhadi19 and its variants based on Maximum Mean Discrepancy and Lyapunov exponents) as simple approaches for learning the kernel used in these emulators.

Key facts. Cited by 23 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Jul 2020.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 6; 2022: 5; 2023: 3; 2024: 2; 2025: 5; 2026: 2.

23 papers.

Sort:

  1. 2023Kernel Methods are Competitive for Operator Learningcited by 50
  2. 2021Computational Graph Completioncited by 28
  3. 2021Learning to Forecast Dynamical Systems from Streaming Datacited by 17
  4. 2022One-Shot Learning of Stochastic Differential Equations with Data Adapted Kernelscited by 15
  5. 2023Learning Dynamical Systems from Data: A Simple Cross-Validation Perspective, Part V: Sparse Kernel Flows for 132 Chaotic Dynamical Systemscited by 15
  6. 2021Learning dynamical systems from data: A simple cross-validation perspective, part III: Irregularly-Sampled Time Seriescited by 14
  7. 2022Nonparametric learning of kernels in nonlocal operatorscited by 10
  8. 2022Learning "best" kernels from data in Gaussian process regression. With application to aerodynamicscited by 9
  9. 2025Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysiscited by 6
  10. 2024Kernel Methods for the Approximation of the Eigenfunctions of the Koopman Operatorcited by 5
  11. 2021Fast calculation of Gaussian Process multiple-fold cross-validation residuals and their covariancescited by 4
  12. 2022Gaussian Process Hydrodynamicscited by 4
11 more
  1. 2023Some of the variables, some of the parameters, some of the times, with some physics known: Identification with partial informationcited by 4
  2. 2024Self-test loss functions for learning weak-form operators and gradient flowscited by 4
  3. 2025Structured Kolmogorov-Arnold Neural ODEs for Interpretable Learning and Symbolic Discovery of Nonlinear Dynamicscited by 4
  4. 2021Analysis of Structured Deep Kernel Networkscited by 2
  5. 2021Data-driven modelling of nonlinear dynamics by barycentric coordinates and memorycited by 1
  6. 2022Ensemble forecasts in reproducing kernel Hilbert space familycited by 1
  7. 2025Discovery of Probabilistic Dirichlet-to-Neumann Maps on Graphscited by 1
  8. 2026Kernel Methods for Stochastic Dynamical Systems with Application to Koopman Eigenfunctions: Feynman-Kac Representations and RKHS Approximationcited by 1
  9. 2026Kernel Methods for Some Transport Equations with Application to Learning Kernels for the Approximation of Koopman Eigenfunctions: A Unified Approach via Variational Methods, Green's Functions and the Method of Characteristicscited by 1
  10. 2025Gaussian process policy iteration with additive Schwarz acceleration for forward and inverse HJB and mean field game problemscited by 0
  11. 2025A joint optimization approach to identifying sparse dynamics using least squares kernel collocationcited by 0