Accident-Tolerant Fuels (ATFs) represent a significant advancement in enhancing reactor safety, with dual-cooled designs offering improved thermal–hydraulic performance. The placement of burnable absorber (BA) rods within such assemblies critically influences neutronic behavior, including reactivity control and power distribution. Traditional high-fidelity simulations for evaluating BA configurations are computationally intensive, limiting large-scale parametric studies. This study proposes a data-driven predictive framework using Gene Expression Programming (GEP) to estimate and predict the neutronic effects of BA rod locations in a dual-cooled ATF (DC-ATF) assembly. A comprehensive dataset was generated via MCNP6 Monte Carlo simulations for 50 distinct assembly configurations with varying BA arrangements. The GEP model was trained to establish explicit functional relationships between the BA rod configuration and key neutronic parameters, such as the thermal, fast, and total neutron flux peaking factors. Results demonstrate that the trained GEP model achieves high accuracy on the training data (R2 = 0.92), providing a computationally efficient surrogate for full-scale simulations. Although validation performance indicates a need for further model refinement, the framework successfully identifies optimal BA patterns that promote a flatter neutron flux distribution. This work underscores the potential of GEP as a transparent and efficient tool for accelerating the design and optimization of advanced nuclear fuel assemblies.