mlsanityData to 7 Oct 2026

Learning to Forecast Dynamical Systems from Streaming Data

arXiv 2109.09703 ↗First posted 20 Sep 2021math.DS cs.LG cs.NAcited by 17

Not on the map. Why?

Abstract (arXiv)

Kernel analog forecasting (KAF) is a powerful methodology for data-driven, non-parametric forecasting of dynamically generated time series data. This approach has a rigorous foundation in Koopman operator theory and it produces good forecasts in practice, but it suffers from the heavy computational costs common to kernel methods. This paper proposes a streaming algorithm for KAF that only requires a single pass over the training data. This algorithm dramatically reduces the costs of training and prediction without sacrificing forecasting skill. Computational experiments demonstrate that the streaming KAF method can successfully forecast several classes of dynamical systems (periodic, quasi-periodic, and chaotic) in both data-scarce and data-rich regimes. The overall methodology may have wider interest as a new template for streaming kernel regression.

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). Builds on 19 of its 92 references that are in the map. First posted on arXiv 20 Sep 2021.

Builds on

19 of 92 references.

References · 19

  1. 2016Generalization Properties of Learning with Random Featurescited by 163
  2. 2019Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systemscited by 96
  3. 2014Fastfood: Approximate Kernel Expansions in Loglinear Timecited by 72
  4. 2018Random Fourier Features for Kernel Ridge Regression: Approximation Bounds and Statistical Guaranteescited by 71
  5. 2018Kernel Flows: from learning kernels from data into the abysscited by 49
  6. 2020Data-driven reduced-order models via regularized operator inference for a single-injector combustion processcited by 42
  7. 2015Frequent Directions : Simple and Deterministic Matrix Sketchingcited by 39
  8. 2015Optimal Rates for Random Fourier Featurescited by 38
  9. 2018Approximation beats concentration? An approximation view on inference with smooth radial kernelscited by 33
  10. 2020Kernel-based approximation of the Koopman generator and Schr"odinger operatorcited by 31
  11. 2020Supervised learning from noisy observations: Combining machine-learning techniques with data assimilationcited by 27
  12. 2020Learning dynamical systems from data: a simple cross-validation perspectivecited by 23
7 more
  1. 2017Fixed-Rank Approximation of a Positive-Semidefinite Matrix from Streaming Datacited by 22
  2. 2018Streaming Kernel PCA with tildeO(√n) Random Featurescited by 11
  3. 2020Kernel Analog Forecasting: Multiscale Test Problemscited by 11
  4. 2019AdaOja: Adaptive Learning Rates for Streaming PCAcited by 10
  5. 2020Kernel-based Prediction of Non-Markovian Time Seriescited by 9
  6. 2015Streaming Kernel Principal Component Analysiscited by 8
  7. 2018On Kernel Derivative Approximation with Random Fourier Featurescited by 6

Built on by

Cited by year (2026 to 7 Oct)

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

17 papers.

Sort:

  1. 2022Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spacescited by 66
  2. 2024Probabilistic Forecasting with Stochastic Interpolants and F"ollmer Processescited by 61
  3. 2021Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systemscited by 44
  4. 2023Estimating Koopman operators with sketching to provably learn large scale dynamical systemscited by 15
  5. 2024Adversarial dynamical systems characterize when data-driven learning succeeds or failscited by 10
  6. 2022QuACK: Accelerating Gradient-Based Quantum Optimization with Koopman Operator Learningcited by 7
  7. 2021On the Correspondence between Gaussian Processes and Geometric Harmonicscited by 3
  8. 2024Random Features Approximation for Control-Affine Systemscited by 3
  9. 2024Linear quadratic control of nonlinear systems with Koopman operator learning and the Nystr"om methodcited by 2
  10. 2023Error Estimation for Random Fourier Featurescited by 1
  11. 2024The Complexity of Sequential Prediction in Dynamical Systemscited by 1
  12. 2024Nonparametric Sparse Online Learning of the Koopman Operatorcited by 1
5 more
  1. 2025Nonparametric Sparse Online Learning of the Koopman Operatorcited by 0
  2. 2025Online Kernel Dynamic Mode Decomposition for Streaming Time Series Forecasting with Adaptive Windowingcited by 0
  3. 2026LISA: Laplacian In-context Spectral Analysiscited by 0
  4. 2026AdaKoop: Efficient Modeling of Nonlinear Dynamics from Nonstationary Data Streams with Koopman Operator Regressioncited by 0
  5. 2026Learning to control switching nonlinear systems with Koopman operator regressioncited by 0