The mobility and ideal heat transmission of a Williamson fluid through a homogenous porous medium are examined in the present innovative study. The velocity and temperature equations of the appropriate partial differential equations become transmuted into ODEs for symmetry analysis and a novel scaling-group transformation. The numerical technique solved the resulting system of ODEs using the BVP4C solver from the MATLAB program. Graphs and tabular values determined from the outcomes of various physical characteristics in the form of the momentum distribution, thermal fluctuation, the wall friction coefficient ( \(C_{f_{x}}\) ), and the Nusselt factor ( \(N_{u_{x}}\) ). The improvement of the magnetic factor and Weissenberg number dropped the velocity profile shape. When the temperature profile reduces the higher Prandtl number, and the temperature variation elevates the expansion of the heat production attribute. Subsequently, implementing the Multiple Linear Regression (MLR) algorithm towards machine learning (ML) to anticipate the physical significances yielded an excellent accuracy with the standard error of the surface frictional \(1.12*10^{-3}\) and heat transfer coefficients \(1.28*10^{-4}\) being very tiny. Furthermore, the novel technique of an Artificial Neural Network (ANN) achieved a better precision level of \(99\%\) , employed in this study. The significant potential findings of this work demonstrate the future progress in designing, setting up, and optimizing energy-relevant technologies. The outcomes are more comprehensive and have biological applications, including cancer treatment, medication delivery systems, image processing, and blood flow analysis.
