Reconstruction of polynomial systems from noisy time-series measurements using genetic programming

The problem of functional reconstruction of a polynomial system from its noisy time-series measurement is addressed in this paper. The reconstruction requires the determination of the embedding dimension and the unknown polynomial structure. The authors propose the use of genetic programming (GP) to find the exact functional form and embedding dimension of an unknown polynomial system from its time-series measurement. Using functional operators of addition, multiplication and time delay, they use GP to reconstruct the exact polynomial system and its embedding dimension. The proposed GP approach uses an improved least-squares (ILS) method to determine the parameters of a polynomial system. The ILS method is based on the orthogonal Euclidean distance to obtain an accurate parameter estimate when the series is corrupted by measurement noise. Simulations show that the proposed ILS-GP method can successfully reconstruct a polynomial system from its noisy time-series measurements