A Sniffer Technique for an Efficient Deduction of Model Dynamical Equations Using Genetic Programming

Abstract

A novel heuristic technique that enhances the search facility of the standard genetic programming (GP) algorithm is presented. The method provides a dynamic sniffing facility to optimize the local search in the vicinity of the current best chromosomes that emerge during GP iterations. Such a hybrid approach, that combines the GP method with the sniffer technique, is found to be very effective in the solution of inverse problems where one is trying to construct model dynamical equations from either finite time series data or knowledge of an analytic solution function. As illustrative examples, some special function ordinary differential equations (ODEs) and integrable nonlinear partial differential equations (PDEs) are shown to be efficiently and exactly recovered from known solution data. The method can also be used effectively for solution of model equations (the direct problem) and as a tool for generating multiple dynamical systems that share the same solution space.