A New Stochastic Computing Paradigm for Nonlinear Painleve II Systems in Applications of Random Matrix Theory

Abstract

The aim of the present work is to investigate the stochastic numerical solutions of nonlinear Painleve II systems arising from studies of two-dimensional Yang-Mills theory, growth processes through fluctuation formulas in statistical physics, soft-edge random matrix distributions using the strength of bioinspired heuristics through artificial neural networks (ANNs), genetic algorithm (GA)-based evolutionary computations and interior-point techniques (IPTs). A new mathematical modelling of the system is formulated through ANNs by defining an error function that exactly satisfies the initial conditions. The weights of ANN models optimized through a memetic computing approach that is based on a global search with GAs, and IPTs are used for an efficient local search. The designed scheme is substantiated through comparative analysis with a fully explicit Range-Kutta numerical procedure on nonlinear Painleve II systems by taking different magnitudes of forcing factors. The accuracy and convergence of the proposed scheme are validated through statistics performed on large numbers of simulations.