A genetic algorithm optimized Morlet wavelet artificial neural network to study the dynamics of nonlinear Troesch's system

In this work, a new stochastic computing technique is developed to study the nonlinear dynamics of Troesch's problem by designing the mathematical models of Morlet Wavelets Artificial Neural Networks (MW-ANNs) optimized with Genetic Algorithm (GA) integrated with Sequential Quadratic Programming (SQP). The differential equation mathematical model for MW-ANNs are designed for Troesch's system by incorporating a windowing kernel based on Morlet Wavelets as an activation function and these networks are constructed to define a fitness function of Troesch's system in the mean squared sense. The unknown adjustable parameters of MW-ANNs are trained initially by an effective global search using GAs hybridized with SQP for rapid local refinement of the results. The proposed scheme is evaluated to solve the Troesch's problems for small and large values of the critical parameter in the system. Comparison of the proposed results with standard reference solutions of Adams method shows good agreement. Validation of accuracy and convergence of the proposed scheme is made using statistical analysis based on a sufficiently large number of independent runs, this is done in terms of performance measures of mean absolute deviation and root mean squared error. (C) 2017 Elsevier B.V. All rights reserved.