Design of Bayesian stochastic networks for numerical treatment of Williamson fluid stretching flow model with mixed convected heat generation

Abstract

In the presented article, a stochastic network paradigm through Bayesian Regularization backpropagation neural network (BRB-NN) is designed to interpret the dynamics of the Williamson fluid stretching flow model with mixed convected heat generation (WF-SFM). The governing nonlinear PDEs system of WF-SFM is reduced to a set of ODEs by incorporating appropriate transformations. The reference datasets for the anticipated BRB-NN approach are created with Adams solver for numerical solutions of WF-SFM by varying material variable W e , buoyancy factor λ , temperature characteristic parameter ε , thermal relaxation variable γ , heat source factor δ , and Prandtl numbers P r . The knacks of artificial intelligence (AI) based BRB-NN procedure is then employed on the generated dataset for WF-SFM. The bias training, biased testing, and validation of BRB-NN are conducted to compute the approximate numerical results for WF-SFM for sundry scenarios, and outputs are in good agreement in reference data that validate the worthy performance of the proposed BRB-NN which is further justified by results of absolute error, mean squared error, error histogram illustrations and regression measures. The viable performance in terms of mean square error (MSE) is achieved at levels ranging from E − 11 to E − 13 , consistently for all scenarios of WF-SFM. The accuracy and the justification of performance are effectively proven by the low level of MSE, to optimal regression metric index as well as distribution of instances error on histograms with negligible magnitude.