Application of machine learning for numerical analysis of mixed convective Falkner–Skan flow of cross nanofluid through predictive neural networks algorithm

This work represents the numerical computing and analysis of Falkner–Skan flow of Cross nanofluid with melting phenomena through Artificial Intelligence Neural Network (AI-NN). The dominant factors influencing the motion, temperature and mass diffusion of the fluid are thermophoresis impact and Brownian motion impact, along with magnetic forces (MHD). Initially movement of the mass through the fluid is supposed to be zero on the expanding surface. The mechanism is mathematically defined by the Cross nanofluid model and partial differential equations (PDEs) are developed using the pre-supposed conditions. Further, relevant transformations are applied to convert the obtained nonlinear PDEs to the nonlinear ordinary differential equations (ODEs). The famous Adam Numerical Technique (ANT) helps to extract the desired data set of different parameters for different cases by exploiting ‘ND Solve’ routine in Mathematica code. Interesting trends are recorded for varying thermophoresis [Formula: see text] and Prandtl number [Formula: see text] parameters, unsteady parameter [Formula: see text], and melting parameter [Formula: see text]. The acquired results are put into the analysis process utilizing MATLAB with the help of Levenberg–Marquardt Backpropagation Neural Network Technique (LMB-NNT). This tool trains the data and gives output in the form of fitness of function, training graphs, regression analysis, error histograms and performance analysis. The mean squared error is recorded for all scenarios. All the intensive simulation-based calculations of fitness of function, training graphs, regression analysis, error histograms and performance analysis authenticate that the proposed methodology, i.e. AI-NN is effective, accurate and reliable for solving FS-CN.