RECONSTRUCTION OF ORDINARY DIFFERENTIAL EQUATIONS FROM IRREGULARLY DISTRIBUTED TIME- SERIES DATA

The present paper aims to develop a reconstruction method for the right side of a system of ODEs inpolynomial form from sparse and irregularly distributed time-series data. This method doesn’t requireany additional knowledge about the system and has several steps. The scarcity of the data through thetrajectory length is compensated by the artificially generated points using approximatingtrigonometrical polynomials. Then, we get uniformly spread data points with the step conditioned bythe desired accuracy of derivatives approximation in ODEs. This let to further use conventionalreconstruction algorithms described in the literature. We test the proposed method on time series datagenerated from known ODE models in a two-dimensional system. We quantify the accuracy of thereconstruction for the system of ODEs as a function of the amount of data used by the method.Further, we solve the reconstructed system of ODEs and compare the solution to the original timeseries data. The method developed and validated here can now be applied to large data sets forphysical and biological systems for which there is no known system of ODEs.