mlsanityData to 7 Oct 2026

Ensemble forecasts in reproducing kernel Hilbert space family

arXiv 2207.14653 ↗First posted 29 Jul 2022math-ph cs.LG math.DScited by 1

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Abstract (arXiv)

A methodological framework for ensemble-based estimation and simulation of high dimensional dynamical systems such as the oceanic or atmospheric flows is proposed. To that end, the dynamical system is embedded in a family of reproducing kernel Hilbert spaces (RKHS) with kernel functions driven by the dynamics. In the RKHS family, the Koopman and Perron-Frobenius operators are unitary and uniformly continuous. This property warrants they can be expressed in exponential series of diagonalizable bounded evolution operators defined from their infinitesimal generators. Access to Lyapunov exponents and to exact ensemble based expressions of the tangent linear dynamics are directly available as well. The RKHS family enables us the devise of strikingly simple ensemble data assimilation methods for trajectory reconstructions in terms of constant-in-time linear combinations of trajectory samples. Such an embarrassingly simple strategy is made possible through a fully justified superposition principle ensuing from several fundamental theorems.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 22 of its 99 references that are in the map. First posted on arXiv 29 Jul 2022.

Builds on

22 of 99 references.

References · 22

  1. 2021Modern Koopman Theory for Dynamical Systemscited by 269
  2. 2019Data-driven approximation of the Koopman generator: Model reduction, system identification, and controlcited by 85
  3. 2022Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spacescited by 66
  4. 2018Kernel Flows: from learning kernels from data into the abysscited by 49
  5. 2017Eigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spacescited by 48
  6. 2021Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systemscited by 44
  7. 2021Koopman Operator Dynamical Models: Learning, Analysis and Controlcited by 42
  8. 2016Kernel Distribution Embeddings: Universal Kernels, Characteristic Kernels and Kernel Metrics on Distributionscited by 39
  9. 2020Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximizationcited by 37
  10. 2020Learning Variational Data Assimilation Models and Solverscited by 36
  11. 2020Kernel-based approximation of the Koopman generator and Schr"odinger operatorcited by 31
  12. 2020Supervised learning from noisy observations: Combining machine-learning techniques with data assimilationcited by 27
10 more
  1. 2020Learning dynamical systems from data: a simple cross-validation perspectivecited by 23
  2. 2021Kernel Learning for Robust Dynamic Mode Decomposition: Linear and Nonlinear Disambiguation Optimization (LANDO)cited by 22
  3. 2019Learning Latent Dynamics for Partially-Observed Chaotic Systemscited by 18
  4. 2021Data-driven geophysical forecasting: Simple, low-cost, and accurate baselines with kernel methodscited by 15
  5. 2021Learning dynamical systems from data: A simple cross-validation perspective, part III: Irregularly-Sampled Time Seriescited by 14
  6. 2020Kernel Analog Forecasting: Multiscale Test Problemscited by 11
  7. 2020Sparsity-promoting algorithms for the discovery of informative Koopman invariant subspacescited by 10
  8. 2020Kernel-based Prediction of Non-Markovian Time Seriescited by 9
  9. 2021Eigenvalues of Autocovariance Matrix: A Practical Method to Identify the Koopman Eigenfrequenciescited by 1
  10. 2022Bridging Koopman Operator and time-series auto-correlation based Hilbert-Schmidt operatorcited by 1

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Citing papers per year: 2025: 1.

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  1. 2025Koopman-Equivariant Gaussian Processescited by 6