Discovering Unmodeled Components in Astrodynamics with Symbolic Regression

Abstract

The paper explores the use of symbolic regression to discover missing parts of the dynamics of space objects from tracking data. The starting assumption is that the differential equations governing the motion of an observable object are incomplete and do not allow a correct prediction of the future state of that object. Symbolic regression, making use of Genetic Programming (GP), coupled with a sensitivity analysis-based parameter estimation, is proposed to reconstruct the missing parts of the dynamic equations from sparse measurements of position and velocity. Furthermore, the paper explores the effect of uncertainty in tracking measurements on the ability of GP to recover the correct structure of the dynamic equations. The paper presents a simple, yet representative, example of incomplete orbital dynamics to test the use of symbolic regression.