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Learning nonparametric ordinary differential equations from noisy data
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DOI：10.1016/j.jcp.2024.112971.png)
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摘要
En 中文
Learning nonparametric systems of Ordinary Differential Equations (ODEs) 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 L 2 distance between x 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.
Keyword:
Nonlinear dynamical systems
System identification
Kernel methods
Penalty method
Amyloid accumulation
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期刊
IF:
3.8
论文数:
1.6W
被引数:
7.4W
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