ВИКОРИСТАННЯ БАЗОВОГО РОЗРІДЖЕННОГО НАВЧАННЯ ДЛЯ ВИЗНАЧЕННЯ ПАРАМЕТРІВ МОДЕЛІ

Abstract

We develop a numerical method to reconstruct systems of ordinary differential equations (ODEs) from time series data without a priori knowledge of the underlying ODEs using sparse basis learning and sparse function reconstruction. We show that employing sparse representations provides more accurate ODE reconstruction compared to least-squares reconstruction techniques for a given amount of time series data. We test and validate the ODE reconstruction method on known 1D,2D, and 3D systems of ODEs. The 1D system possesses two stable fixed points; the 2D system possesses an oscillatory fixed point with closed orbits; and the 3D system displays chaotic dynamics on a strange attractor.