Artificial neural network-based prediction of hydromagnetic boundary layer nanofluid fluid flow and heat transportation over a porous wedge with brownian motion

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The primary objective of the present study is to explore two dimensional steady MHD boundary layer nanofluid flow and heat transportation towards a wedge under the inspiration of a magnetic field, porosity parameter, thermophoresis and Brownian motion parameters. The nonlinear PDEs of momentum, energy and concentration are transformed into an ordinary differential equations (ODEs) by applying the similarity approach. The resulting system of ODEs is solved numerically with Bvp4c approach. For further assessment the predictive capability, of the numerical solutions, a Levenberg–Marquardt artificial neural network (LMA-ANN) model is developed using generated dataset, which is split into 15% validation, 15% testing and 70% training. Outcomes elucidates that increasing the magnetic parameter $$\:M$$ suppresses velocity due to the opposing Lorentz (resistive) force while higher Lewis number $$\:Le$$ significantly reduces concentration profiles, while enhancing the Sherwood number. The close agreement between the numerical and ANN forecasts demonstrates high accuracy and predictive performance of the proposed LMA–ANN model. Specifically, the present model provides a high regression coefficient and a low mean squared error for the velocity profile, confirming its effectiveness in accurately predicting the flow characteristics. The impact of pertinent constraints on temperature, velocity, and concentration fields is discussed graphically and in tabular form in detail. Key findings from the ANN predictions and the computed physical quantities. In particular, the best validation MSE for the ANN is 4.77 × 10⁻⁹ at epoch 150, with regression coefficients approaching R = 1, demonstrating excellent agreement between the ANN predictions and the BVP4C results. For the representative parameter set, the computed skin-friction coefficient, heat-transfer rate, and mass-transfer rate are \:-f\:\:(0)\:=\:1.9338 , \:-θ\:\:(0)\:=\:0.2737 , and \:-φ\:\:(0)\:=\:0.1769 .