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Neural network optimized with evolutionary computing technique for solving the 2-dimensional Bratu problem

Muhammad Asif Zahoor Raja
Organization: International Islamic University
Department: Department of Electronic Engineering
Siraj-ul-Islam Ahmad
Journal / Anthology

Neural Computing & Applications
Year: 2013
Volume: 23
Issue: 7-8
Page range: 2199-2210

In this paper, a stochastic technique is developed to solve 2-dimensional Bratu equations using feedforward artificial neural networks, optimized with genetic and interior-point algorithms. The 2-dimensional equations are first transformed into a 1-dimensional boundary value problem, and a mathematical model of the transformed equation is then formulated with neural networks using an unsupervised error. Network weights are optimized to minimize the error. Evolutionary computing based on genetic algorithms is used as a tool for global search, integrated with an interior-point method for rapid local convergence. The methodology is applied to solve three cases of boundary value problems for the Bratu equations. The accuracy, convergence and effectiveness of the scheme is validated for a large number of simulations. Comparison of results is made with the exact solution derived using MATHEMATICA, and is found to be in good agreement.

*Science > Biology

2-Dimensional Bratu equations  Neural, networks  Genetic algorithms  Nonlinear ODEs  Hybrid, techniques  Interior-point methods