Solid-liquid phase transformation of a phase change material in a rectangular enclosure with corrugated fins is studied. Employing a physics-based model, the influence of fin length, thickness, and wave amplitude on the thermal and fluid flow fields is explored. Incorporating fins into thermal energy storage systems enhances the heat transfer surface area and thermal penetration depth, accelerating the melting process. Corrugated fins generate more flow perturbations than straight fins, improving the melting performance. Longer and thicker fins increase the melting rate, average temperature, and thermal energy storage capacity. However, the effect of fin thickness on the thermal characteristics seems insignificant. Larger fin wave amplitudes increase the heat transfer surface area but disrupt natural convection currents, slowing the melting front progress. A surrogate model based on an artificial neural network in conjunction with the particle swarm optimisation is developed to optimise the fin geometry. The optimised geometry demonstrates a 43% enhancement in thermal energy storage per unit mass compared to the case with planar fins. The data-driven model predicts the liquid fraction with less than 1% difference from the physics-based model. The proposed approach provides a comprehensive understanding of the system behaviour and facilitates the design of thermal energy storage systems.