Stochastic computing with Levenberg–Marquardt neural networks for the study of radiative transportation phenomena in three-dimensional Carreau nanofluid model subjected to activation energy and porous medium

The objective of this research is to establish the modelling and evaluation of a differential mathematical system for the radiated Carreau nanofluid model (RCNFM) by exploiting the skills of stochastic computing with Levenberg–Marquardt neural networks (SCLMNNs).The reference dataset is created using the Adams technique in the Mathematica software by variation of various physical quantities. The reference data results are trained using a split of seventy percent for training and thirty percent for validation and testing methods. This approach aims to enhance and compare the estimated outcomes with established solutions. The precision and efficacy of the developed stochastic computing with Levenberg–Marquardt neural networks are illustrated by a comparison of the results obtained from the dataset using Adams technique. This comparison includes variations in values of several influential parameters including Magnetic number, Weissenberg Numbers, Porosity parameter, Brownian movement, Prandtl number, Unsteady parameter, Temperature Difference Parameter, Stretching/shrinking parameter, and Lewis Number. The reference data results are trained by assigning 70% for training, 15 % for validation and 15 % for testing. Fitness curves of mean square error, regression studies, error evaluated with histogram plots, and evaluation on absolute errors all authenticate the reliability and precision of stochastic computing with Levenberg–Marquardt neural networks. Performance metrics in terms of mean square error are excellent at the levels 1.19E⁻¹⁰, 1.92E⁻¹⁰, 9.60E⁻¹¹, 1.02E⁻¹⁰, 7.09E⁻¹¹, 2.07E⁻⁰⁹, 1.66E⁻¹⁰, 8.34E⁻¹¹, and 1.17E⁻¹³against 117, 194, 144, 117, 237, 260, 96, 128, and 74 epochs. The error analysis of the designed and reference datasets suggests that the stochastic computing with Levenberg–Marquardt neural networks is accurate and reliable, with values ranging from E⁻⁰⁸ to E⁻⁰⁴ across all scenarios. Radiative transport in three dimensional Carreau nanofluids with activation energy in porous media improves the following domains: biomedical engineering, energy systems, chemical process, environmental engineering, thermal management and material science.