Artificial Intelligence based modeling for unsteady cross nanofluid flow over a stretching sheet

The present research focuses on the outcome of Artificial Intelligence technique Levenberg-Marquardt Algorithm with Non-linear Auto Regressive Exogenous on cross-section of nanofluid movement built across a contracting cylinder. This study examines the characteristics of a field of magnetic attraction, the attributes of nanoparticles via Brownian motion and the thermophoresis effect. Improved accuracy and dependability results from this approach guarantees model's efficient training, validation, and assessment. To provide a dataset for training the Levenberg Marquardt algorithm using a Nonlinear Autoregressive Network with Exogenous Inputs modified ordinary differential equations are solved in Mathematica and data set is generated. By comparing the Levenberg-Marquardt Algorithm with Non-linear Auto Regressive Exogenous model output with conventional reference solutions while varying significant parameters its accuracy is evaluated. Partitioning of the dataset into 80%, 10% and 10% training, validation, and testing respectively helped improve the prediction efficiency, allowing for efficient training and evaluation of the model. Validation of the accuracy of the Levenberg-Marquardt Algorithm with Non-linear Auto Regressive Exogenous model was done by comparing the results against the Adams method data based on the parameters such as unsteadiness, magnetic, viscosities ratio, Biot number 1, thermophoretic, temperature difference, reaction rate and fitted rate coefficients. Stability and accuracy were proven by the mean square deviation fitness curve analysis, regression analysis, histogram error plot analysis and absolute error analysis. The best mean square deviation performance levels obtained were 7.3018E-11, 6.6303E-11, 9.9254E-11, 6.0943E-13, 2.2896E-08, 9.4438E-11, 5.7583E-10, and 1.2855E-13 within 1000 epochs. Velocity is inversely proportional to unsteadiness and magnetic coefficient but directly proportional to viscosity ratio; temperature is inversely proportional to Biot and thermophoretic coefficients; concentration is directly proportional to temperature.