Data-Driven Sparse Approximation for the Identification of Nonlinear Dynamical Systems - Application in Astrodynamics

Abstract

This work aims to provide a unified and automatic framework to discover governing equations underlying a dynamical system from data measurements. In an appropriate basis, and based on the assumption that the structure of the dynamical model is governed by only a few important terms, the equations are sparse in nature and the resulting model is parsimonious. Solving a well-posed constrained one-norm optimization problem, we obtain a satisfactory zero-norm approximation solution and determine the most prevalent terms in the dynamic governing equations required to accurately represent the collected data. Considering the well-known problem of identifying the central force field from position only observation data, we validate the developed approach by comparing the sparse solution with classical least-squares regression techniques and deep learning approaches.