Blind Spot Effect During Genetic Programming Based Inference of Dynamical Model Equations for Chaotic Systems

Abstract A study based on Genetic Programming (GP) framework is carried out for the inference of model equations for some well known dynamical systems that give rise to chaotic time series. The systems studied are Lorenz and Rossler systems (involving nonlinear coupled Ordinary Differential Equations (ODEs)) and Henon attractor (having coupled nonlinear map equations). The solutions of these systems in specific parameter regimes lead to chaotic series that are too sensitive to initial conditions. The inherent nonlinearity and chaotic nature of the time series makes the inference of system equations very challenging and computationally a difficult problem. Additionally, a plausible reason for the difficulty is attributed to an interesting observation regarding an effect, we call as a Blind Spot Effect. Often during the exploration of the standard GP search space, symbolic chromosome structures padded with spurious terms settle down with higher fitness value creating local maxima. Consequently, the GP search method finds it difficult to shed away the spurious terms leading either to a failure, or at most a very slow convergence in getting around such local maxima. A possible solution to this problem is effected in the present work by combining the standard GP search method with routines that directly help get around the blind spot effect. The resulting enhanced GP method is found to be an empirically successful method to deduce the ODE equations with very good accuracy for the systems studied.