Prediction of dynamical systems using geometric constraints imposed by observations

TL;DR

This paper presents a data-driven method to improve dynamical system models by leveraging geometric constraints from observations, effectively estimating unmodeled forces to enhance prediction accuracy in applications like satellite orbit and heat conduction.

Contribution

It introduces a novel approach that uses geometric constraints from data to estimate unmodeled forcing terms, improving dynamical model predictions.

Findings

Reduced satellite orbit prediction error to 12% of original

Enhanced temperature predictions over the heat equation

Applicable to various dynamical systems with observational data

Abstract

Solution of Ordinary Differential Equation (ODE) model of dynamical system may not agree with its observed values. Often this discrepancy can be attributed to unmodeled forcings in the evolution rule of the dynamical system. In this article, an approach for data-based model improvement is described which exploits the geometric constraints imposed by the system observations to estimate these unmodeled terms. The nominal model is augmented using these extra forcing terms to make predictions. This approach is applied to navigational satellite orbit prediction to bring down the error to approximately 12% of the error when using the nominal force model for a 2-hour prediction. In another example improved temperature predictions over the nominal heat equation are obtained for one-dimensional conduction.