Construction of ODE systems from time series data by a highly flexible modelling approach

2015/12/10 by Dierkes, Thomas
#37M10 #65L09 #92C42 #92D25 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1512.03357

Abstract

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 y_k(t_j), 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.

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