This study examines the Buongiorno model for the MHD nano‐fluid flow through a rotating disk under the influence of partial slip effects using the Levenberg Marquardt back‐propagation neural networks scheme (LMB‐NNS). The basic system of nonlinear PDEs used to describe the Buongiorno model of MHD nanofluid flow over rotating disk (BM‐MHD‐NRD) model is converted into an analogous nonlinear ODEs system utilizing similarity transformations. A data set for the recommended LMB‐NNS is spawned using the Explicit Runge‐Kutta numerical method for a variety of BM‐MHD‐NRD scenarios by varying the magnetic field number (M), velocity slip parameter (γ), thermophoresis parameter (Nt), Brownian motion parameter (Nb), thermal slip parameter (α) and Schmidt number (Sc). The estimate solution of separate cases has been examined using the LMB‐NNS testing, validation, and training method, and the suggested model has been matched for verification. The MSE, regression analysis, and histogram studies have been used to authenticate the recommended LMB‐NNS. The LMB‐NNS technique has various applications such as disease diagnosis, Robotic control systems, Ecosystem evaluation etc. Analysis of some statistical date like gradient, performance and epoch of the model. With a level of accuracy ranging from 10−09 to 10−12, the suggested approach is differentiated as the closest of the suggested and reference results.

The present works focus on the effects of electric and magnetic fields on the flow of micro-polar nano-fluid between two parallel plates with rotation under the impact of Hall current (EMMN-PPRH) has considered by using Artificial Neural Networks with the scheme of Levenberg–Marquardt backpropagation (ANN-SLMB). The nonlinear PDEs are transformed into nonlinear ODEs by employing similarity variables. By varying different parameters such as coupling parameter, electric parameter, rotation parameter, viscosity parameter, Prandtl number and the Brownian motion parameter, a dataset for recommended ANN-SLMB is produced for numerous scenarios through utilizing homotopy analysis method (HAM). The ANN-SLMB training, testing and validation technique have been used to analyze the approximate solution of individual cases, and the recommended model has matched for confirmation. After that, regression analysis, MSE, and histogram investigations were utilized to validate the proposed ANN-SLMB. The recommended technique is distinguished nearest of the suggested and reference findings, with an accuracy level ranging from 10 −09 to 10 −11 .

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<abstract> <p>The present study aims to design a Levenberg-Marquardt backpropagation neural network (LMB-NN) integrated numerical computing to investigate the problem of fluid mechanics governing the flow of magnetohydrodynamics micro-polar nanofluid flow over a rotating disk (MHD-MNRD) model along with the partial slip condition. In terms of PDEs, the basic system model MHD-MNRD is transformed into a system of non-linear ODEs by applying the similarity of transformations. For MHD-MNRD scenarios, the comparative dataset of the built LMB-NN procedure is formulated with the technique of Adams numerical by variation of micro-polar parameters, Brownian motion, Lewis number, magnetic parameter, velocity slip parameter and thermophoresis parameter. To compute the approximate solution for MHD-MNRD for various scenarios, validation, testing and training procedures are carried out in accordance to adjust the networks under the backpropagation procedure in terms of the mean square error (MSE). The efficiency of the designed LMB-NN methodology is highlighted by comparative study and performance analysis based on error histograms, MSE analysis, regression and correlation.</p> </abstract>

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