Dynamics of waste discharge pollutant concentration and heat source/sink effects across a nonlinear stretching surface conveying tri-hybrid nanofluids: a multi-output MLP-ANN surrogate approach

The analysis of nanofluid circulation over a nonlinear stretching surface plays an important role in areas such as thermal engineering, pollutant control systems, polymer processing, coating technology, cooling equipment, and advanced manufacturing processes. Motivated by the above applications, the present study investigates the combined effects of heat source/sink, porous medium, activation energy, pollutant discharge concentration, velocity slip, and thermal slip effects of a tri-hybrid nanofluid flow over a nonlinear stretching surface. The governing flow equations are converted into a system of nonlinear ordinary differential equations and solved computationally with the help of the RKF-45 algorithm together with a shooting procedure. A multi-output multilayer perceptron artificial neural network is subsequently developed as a data-driven surrogate for the simultaneous prediction of engineering factors. The proposed model achieved a mean testing normalized root mean square error (NRMSE) of 1.0705 × 10 − 6 and a mean testing mean absolute percentage error (MAPE) of 1.2560 × 10 − 4 %. Comparative evaluation against radial basis function neural network (RBFNN), Gaussian support vector regression (SVR), sparse Gaussian process regression (GPR), and LSBoost models demonstrated that the multi-output multi-layer perceptron artificial neural network (MO-MLP-ANN) provided the lowest testing error within the examined one-at-a-time sampled domain.