The Kolmogorov-Arnold representation of a continuous multivariate function is a decomposition of the function into a structure of inner and outer functions of a single variable. It can be a convenient tool for tasks where it is required to obtain a predictive model that maps some vector input of a black box system into a scalar output. However, the construction of such representation based on the recorded input-output data is a challenging task. In the present paper, it is suggested to decompose the underlying functions of the representation into continuous basis functions and parameters. A novel lightweight algorithm for parameter identification is then proposed. The algorithm is based on the Newton-Kaczmarz method for solving non-linear systems of equations and is locally convergent. Numerical examples show that it is more robust with respect to the section of the initial guess for the parameters than the straightforward application of the Gauss-Newton method for parameter identification.

翻译：连续多变量函数的Kolmogorov-Arnold表示是将该函数分解为单变量内函数与外函数结构的形式。在需要建立将黑箱系统的向量输入映射为标量输出的预测模型的任务中，该表示可成为一种便捷工具。然而，基于记录的输入输出数据构造此类表示是一项具有挑战性的任务。本文提出将该表示中的底层函数分解为连续基函数与参数，并进一步提出一种新颖的轻量级参数辨识算法。该算法基于用于求解非线性方程组的Newton-Kaczmarz方法，且具有局部收敛性。数值算例表明，相比于直接应用Gauss-Newton方法进行参数辨识，该算法对参数初始猜测的选取具有更强的鲁棒性。