Neural network analysis of magnetohydrodynamic power-law fluid flow over a porous wedge in a Darcy–Forchheimer medium: local non-similar solution

Purpose The purpose of this study is to analyze the effects of nonlinear thermal radiation, Darcy–Forchheimer dissipation and Joule heating on the flow of a power-law conducting fluid over a stretching porous wedge embedded in a Darcy–Forchheimer porous medium. The study also aims to develop and validate a deep learning framework based on the Levenberg–Marquardt backpropagation algorithm to accurately predict velocity and temperature distributions in complex nonlinear transport phenomena. Design/methodology/approach The governing nonlinear partial differential equations are transformed into nonlinear ordinary differential equations using a second-order local non-similarity approach. The resulting boundary value problem is solved numerically using MATLAB’s bvp4c solver. A deep learning model using the Levenberg–Marquardt algorithm, gradient descent optimization and a hyperbolic tangent sigmoid activation function is used to predict velocity and temperature profiles. Findings The deep learning predictions show excellent agreement with numerical solutions, with absolute errors of order 10−4–10−5 and very low mean squared errors. Increasing radiation and temperature ratio parameters significantly modifies the thermal boundary layer, causing non-monotonic temperature behavior near the wedge surface. Darcy dissipation reduces fluid temperature, while Forchheimer dissipation increases it. Originality/value This study combines nonlinear thermal radiation and Darcy–Forchheimer effects within a second-order local non-similarity framework, alongside a Levenberg–Marquardt-based deep learning model. The hybrid approach delivers highly accurate predictions for complex porous media flows, demonstrating the power of deep learning beyond traditional numerical methods.