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The present communication examines new recurrent neural networks (RNNs) with Levenberg–Marquardt method (RNNs-LMM) based on backpropagation to find the solutions of melting heat transfer analysis in a 3D-MHD Darcy–Forchheimer hybrid nanofluid flow model. The local similarity transformation converts the controlling system partial differential equations (SPDEs) into a connected higher-order system of nonlinear ordinary differential equations (SNODEs). Only the training data with the input vector are used in unsupervised learning. The network creates clusters during training by employing the input patterns to learn new behaviors. The fitting of the data (FT), performance (PF), mean square errors (MSEs), and training (TR) are all assessed using the stochastic numerical technique. The issue has been validated by error histograms (EHs) and regression (RG) tests, demonstrating high conformity with the accuracy of the obtained solutions from Formula: see text to Formula: see text. Graphs and numerical data are used to analyze the behaviors of several key factors. Heat transmission and the skin’s friction coefficient are examined. Numerical and graphical data are provided to show how various hybrid nanofluid and nanofluid instances are affected by changes in temperature and velocities. Numerical data are also used to study the changing trends of the rates of heat transmission and skin friction.
Mahariq et al. (Wed,) studied this question.