Bio-inspired computing platform for reliable solution of Bratu-type equations arising in the modeling of electrically conducting solids

摘要

In this study, a bio-inspired computing approach is developed to solve Bratu-type equations arising in modeling of electrically conducting solids and various other physical phenomena. We employ feed-forward artificial neural networks (ANN) optimized with genetic algorithm (GA) and the active-set method (ASM). The mathematical formulation consists of an ANN with an unsupervised error, which is minimized by tuning weights of the network. The evolutionary technique based on GAs is used as a tool for global search of the weights in conjunction with the ASM for rapid local convergence. The designed methodology is applied to solve a number of initial and boundary value problems based on Bratu equations. Monte Carlo simulations and their statistical analyses are used to validate accuracy, convergence and effectiveness of the scheme. Comparison of results is made with exact solutions, the fully explicit Runge-Kutta numerical method, and other reported solutions of analytical and numerical solvers to establish correctness of the designed scheme.