论文标题
从嘈杂的数据中学习非参数的普通微分方程
Learning nonparametric ordinary differential equations from noisy data
论文作者
论文摘要
从嘈杂数据中学习普通微分方程（ODES）的非参数系统点x = f（t，x）是一个新兴的机器学习主题。我们使用良好的复制核希尔伯特空间（RKHS）的发达理论来定义ode解决方案的F候选者，并且是独一无二的。学习f包括解决RKHS中约束的优化问题。我们提出了一种惩罚方法，该方法使用代表定理和Euler近似值来提供数值解决方案。我们证明了X与其估计器之间的L2距离的概括，并提供了与最先进的实验比较。
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.
