Neuro-optimized numerical solution of non-linear problem based on Flierl–Petviashivili equation

Abstract

The article presents, a reliable numerical framework supported by feed-forward Artificial Neural Network (ANN) optimized with hybrid swarm intelligence technique for non-linear system of Flierl–Petviashivili (FP) problem. The universal approximation capabilities of ANN are exploited for mathematical approximation of the system in an unsupervised way based upon various performance metrics like fitness value, absolute error and execution time. The optimization of the cost function is subject to finding the appropriate weights which are highly stochastic in nature for the problem as well as its initial and boundary conditions. Therefore, hybrid approach based on Particle Swarm Optimization (PSO) and Interior Point Algorithm (IPA) is exploited for tuning of the adaptive weights in such a way that exploration is performed by PSO while the exploitation is done using IPA algorithm. The designed scheme is evaluated for standard FP problem along with its variants supported on various scenarios. The reliability, accuracy and robustness of the solvers are validated through a statistical analysis applied on two hundred independent runs.