Published In
Journal of Computational Physics
Document Type
Pre-Print
Publication Date
3-29-2024
Subjects
Differential equations, Linear differential equations, Mathematical analysis
Abstract
Learning nonparametric systems of Ordinary Differential Equations (ODEs) 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 for which the solution of the ODE exists and is unique. Learning 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 distance between and its estimator. Experiments are provided for the FitzHugh-Nagumo oscillator, the Lorenz system, and for predicting the Amyloid level in the cortex of aging subjects. In all cases, we show competitive results compared with the state-of-the-art.
Rights
Copyright (c) 2024 The Authors
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DOI
10.1016/j.jcp.2024.112971
Persistent Identifier
https://archives.pdx.edu/ds/psu/41833
Citation Details
Published as: Lahouel, K., Wells, M., Rielly, V., Lew, E., Lovitz, D., & Jedynak, B. M. (2024). Learning nonparametric ordinary differential equations from noisy data. Journal of Computational Physics, 507, 112971.
Description
This is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published as: Lahouel, K., Wells, M., Rielly, V., Lew, E., Lovitz, D., & Jedynak, B. M. (2024). Learning nonparametric ordinary differential equations from noisy data. Journal of Computational Physics, 507, 112971.