Functional reconstruction of dynamical systems from time series using genetic programming

Reconstruction of a chaotic system from its measurement is a challenging problem. It requires the determination of an embedding dimension and a nonlinear mapping that approximates the underlying unknown dynamics. We propose the use of genetic programming (GP) to find the exact functional form and embedding dimension of an unknown dynamical system automatically. Using functional operators of addition, multiplication, and time-delay, with the least-squares estimation technique, we use GP to reconstruct the exact chaotic polynomial system and its embedding dimension from a time series. If the underlying dynamic does not come from a polynomial system, the proposed GP method will produce an optimal polynomial predictor for the time series. Simulations showed that the GP approach outperformed a radial basis function neural network in predicting both polynomial and nonpolynomial chaotic systems