In this research article,we introduce a numerical investigation through artificial neural networks(ANN)integrated with evolutionary algorithm especially Archimedean optimization algorithm(AOA)hybrid with the water cyc...In this research article,we introduce a numerical investigation through artificial neural networks(ANN)integrated with evolutionary algorithm especially Archimedean optimization algorithm(AOA)hybrid with the water cycle algorithm(WCA)to address and enhance the analysis of the non-linear magneto-hydrodynamic(MHD)Jeffery-Hamel problem,especially stretching/shrinking in convergent and divergent channel.This combined technique is referred to as ANN-AOA-WCA.The complex nonlinear magneto-hydrodynamic Jeffery-Hamel problem based partial differential equations are transformed into non-linear system of ordinary differential equations for velocity and temperature.We formulate the ANN based fitness function to find the solution of non-linear differential.Subsequently,we employ a novel hybridization of AOA and WCA(AOA-WCA)to optimize the ANN based fitness function and identify the best optimal weights and biases for ANN.To demonstrate the effectiveness and versatility of our proposed hybrid method,we explore MHD models across a range of Reynolds numbers,channel angles and stretchable boundary value leading to the development of two distinct cases.ANN-AOA-WCA numerical results closely align with reference solutions(NDSOLVE)and the absolute error between NDSOLVE and ANN-AOA-WCA is up to 3.35´10^(-8),particularly critical to the understanding of stretchable convergent and divergent channel.Furthermore,to validate the ANN-AOA-WCA technique,we conducted a statistical analysis over 150 independence runs to find the fitness value.展开更多
文摘In this research article,we introduce a numerical investigation through artificial neural networks(ANN)integrated with evolutionary algorithm especially Archimedean optimization algorithm(AOA)hybrid with the water cycle algorithm(WCA)to address and enhance the analysis of the non-linear magneto-hydrodynamic(MHD)Jeffery-Hamel problem,especially stretching/shrinking in convergent and divergent channel.This combined technique is referred to as ANN-AOA-WCA.The complex nonlinear magneto-hydrodynamic Jeffery-Hamel problem based partial differential equations are transformed into non-linear system of ordinary differential equations for velocity and temperature.We formulate the ANN based fitness function to find the solution of non-linear differential.Subsequently,we employ a novel hybridization of AOA and WCA(AOA-WCA)to optimize the ANN based fitness function and identify the best optimal weights and biases for ANN.To demonstrate the effectiveness and versatility of our proposed hybrid method,we explore MHD models across a range of Reynolds numbers,channel angles and stretchable boundary value leading to the development of two distinct cases.ANN-AOA-WCA numerical results closely align with reference solutions(NDSOLVE)and the absolute error between NDSOLVE and ANN-AOA-WCA is up to 3.35´10^(-8),particularly critical to the understanding of stretchable convergent and divergent channel.Furthermore,to validate the ANN-AOA-WCA technique,we conducted a statistical analysis over 150 independence runs to find the fitness value.
