In this paper, a down-to-earth approach to purely data-based modelling of unknown dynamical systems is presented. Starting from a classical, explicit ODE formulation y′=f(t,y) of a dynamical system, a method determining the unknown right-hand side f(t,y) from some trajectory data yk(tj), possibly very sparse, is given. As illustrative examples, a semi-standard predator-prey model is reconstructed from a data set describing the population numbers of hares and lynxes over a period of twenty years, and a simple damped pendulum system with a highly non-linear right-hand side is recovered from some artificial but very sparse data.
@article{arxiv.1512.03357,
title = {Construction of ODE systems from time series data by a highly flexible modelling approach},
author = {Thomas Dierkes},
journal= {arXiv preprint arXiv:1512.03357},
year = {2015}
}