Learning nonparametric ordinary differential equations from noisy data
This work addresses the challenge of modeling dynamic systems from noisy observations, which is incremental as it builds on existing RKHS theory and penalty methods.
The paper tackles the problem of learning nonparametric ordinary differential equations from noisy data by using Reproducing Kernel Hilbert Spaces to define candidates for f and solving a constrained optimization problem with a penalty method, resulting in a proven generalization bound and experimental comparisons with state-of-the-art methods.
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.