Learning nonparametric ordinary differential equations from noisy data

2022/06/30 by Kamel Lahouel, Lahouel, Kamel, Michael Wells +9 · 3 citations
Engineering · Physics and Astronomy · #62G05 #65L70 #68U99 #Advanced Numerical Analysis Techniques #Control Systems and Identification #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks

paper · pdf · doi:10.48550/arxiv.2206.15215

openalex publication_date 2022/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• A joint optimization approach to identifying sparse dynamics using least squares kernel collocation
• Discovering Interpretable Ordinary Differential Equations from Noisy Data
• The Stochastic Occupation Kernel (SOCK) Method for Learning Stochastic Differential Equations

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