Hybrid Gradient Descent Method for Galactic Modelling Using the Enhanced Newtonian Dynamics Framework

This paper presents the first large scale validation of the Enhanced Newtonian Dynamics framework to the Spitzer Photometry and Accurate Rotation Curves (SPARC) dataset. Unlike traditional models that rely on adjustable free parameters or dark matter halos, END derives gravitational attraction solely from the local density distribution and geometric shape of the galaxy. To accommodate the complexity of real-world data, we developed a hybrid optimisation strategy combining gradient descent with an interval search algorithm. This method enables the robust fitting of multi-component models, where galaxies are decomposed into overlapping oblate spheroids to capture intricate density profiles. After applying strict accuracy filters to the SPARC catalog, we demonstrate that END successfully reproduces the rotation curves of 39 disk galaxies across varying morphological types. Our results confirm that a parameter-free, density-driven approach is sufficient to model galactic dynamics without invoking non-baryonic matter.