mlsanityData to 7 Oct 2026

Learning nonparametric ordinary differential equations from noisy data

arXiv 2206.15215 ↗First posted 30 Jun 2022stat.ML cs.LGcited by 4

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Abstract (arXiv)

Learning nonparametric systems of Ordinary Differential Equations (ODEs) dot x = f(t,x) from noisy data is an emerging machine learning topic. We use the well-developed theory of Reproducing Kernel Hilbert Spaces (RKHS) to define candidates for f for which the solution of the ODE exists and is unique. Learning f consists of solving a constrained optimization problem in an RKHS. We propose a penalty method that iteratively uses the Representer theorem and Euler approximations to provide a numerical solution. We prove a generalization bound for the L2 distance between x and its estimator and provide experimental comparisons with the state-of-the-art.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 11 of its 44 references that are in the map. First posted on arXiv 30 Jun 2022.

Builds on

11 of 44 references.

References · 11

  1. 2018Neural Ordinary Differential Equationscited by 3,733
  2. 2018Gaussian Processes and Kernel Methods: A Review on Connections and Equivalencescited by 188
  3. 2017Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systemscited by 125
  4. 2018Data Driven Governing Equations Approximation Using Deep Neural Networkscited by 94
  5. 2018Learning unknown ODE models with Gaussian processescited by 54
  6. 2018A Unified Framework for Sparse Relaxed Regularized Regression: SR3cited by 36
  7. 2017Gaussian Quadrature for Kernel Featurescited by 21
  8. 2020Revealing hidden dynamics from time-series data by ODENetcited by 17
  9. 2020Kernel Analog Forecasting: Multiscale Test Problemscited by 11
  10. 2018Diffeomorphic Learningcited by 5
  11. 2020Kernel Ordinary Differential Equationscited by 5

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Cited by year

Citing papers per year: 2025: 4.

4 papers.

  1. 2025Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysiscited by 6
  2. 2025The Stochastic Occupation Kernel (SOCK) Method for Learning Stochastic Differential Equationscited by 0
  3. 2025Discovering Interpretable Ordinary Differential Equations from Noisy Datacited by 0
  4. 2025A joint optimization approach to identifying sparse dynamics using least squares kernel collocationcited by 0