The Disturbance Storm Time (Dst) index quantifies geomagnetic storm intensity by measuring global magnetic field variations. In this study, we apply interpretable machine-learning (ML) techniques to derive data-driven models describing the temporal evolution of the Dst index. We use historical data from the NASA OMNIWeb database, including solar wind density, bulk velocity, convective electric field, dynamic pressure, and magnetic pressure. We employ KAN networks and the symbolic regression framework PyOperon, based on an evolutionary algorithm, to identify closed-form expressions linking (Formula presented) to key solar wind parameters. The equations obtained via symbolic regression form a hierarchy of complexity levels and capture nonlinear dependencies and threshold effects in Dst evolution. In addition, we use a conventional MLP network as a reference black-box model. We benchmark all ML models against observed Dst data and compare their performance with empirical formulations such as the Burton-McPherron–Russell and O’Brien-McPherron models. The performance evaluation on historical storm events includes the 2003 Halloween storm, the 2015 St. Patrick’s Day storm, a moderate storm in 2017, and the extreme storm of May 2024. The data-driven models, particularly the MLP, demonstrate superior accuracy in most cases. While the symbolic regression expressions provide insight into the underlying physics, the results highlight an intrinsic trade-off between model interpretability and predictive accuracy. This is an extended version of a previous work presented in Markidis et al. (2025) [1].