Computing intelligence for the magnetised chemically reactive bidirectional radiative nanofluid flow through the Bayesian regularisation back-propagated neural network

This research work aims to explain the model and assessment of a differential mathematical system of the magneto-bioconvection of the Williamson nanofluid model (MBWNFM) by capitalising on the strength of the stochastic technique through computational intelligence of Bayesian regularisation back-propagated neural networks (CIBRB-NNs). This facilitates a more accurate, reliable and proficient computation of the dynamics. A reference dataset is built using the Adams technique in the Mathematica software to depict multiple situations and account for numerous influential parameters of the MBWNFM. The reference data results are split into 70% for training and 30% for validation and testing methods. This approach aims to enhance the accuracy of the approximated results and enable them to be compared with established solutions. The demonstration of the accuracy and efficiency of the created CIBRB-NNs involves a comparison of the results obtained from the dataset using the Adams approach, by adjusting several influential parameters which include magnetic parameter ( \(M\) $M$ ), bioconvection Lewis Number ( \(L_{b}\) $L_b$ ), thermal diffusivity ( \(\alpha\) $\alpha$ ) and thermal Biot number ( \(\gamma\) $\gamma$ ). The stability and accuracy of CIBRB-NNs are validated using various methodologies, including the analysis of fitness curves depicting mean square error, regression studies, evaluation of error using histogram plots and measurement of absolute errors. The excellent measures of performance in terms of MSE are achieved at levels 4.50e-12, 6.73e-13, 1.07e-13, 7.08e-13, 4.77e-13 and 1.70e-13 against 82, 150, 98, 83, 170 and 189 epochs. The error analysis of the proposed and reference datasets shows that CIBRB-NNS is authentic and precise, ranging from e-09 to e-04 for all scenarios.