Estimating Parameters of Governing Equations of Non-Linear Systems from Data Using Synchronisation and Machine Learning

Abstract

Deriving governing equations from a measured time series is an ongoing topic of research across different disciplines in science. One method studied can derive the form of governing equations, however it cannot infer the coefficients in front of each term. This is where our work comes in: given the form of governing equations and a measured time series, we propose an algorithm for finding the correct coefficients of the governing equations describing the observed data best. We achieve this by treating the data as primary system and coupling a secondary system to it. Then by inducing synchronisation, we can change the parameters of the secondary system in the direction minimising a loss function. After the loss has reached its minimum, the found parameters are a good estimation of the real parameters producing the data. We applied our algorithm successfully on a number on synthetic systems and even found a method for reconstructing signals masked by chaotic data.