Shell elements are widely used in industrial sheet metal forming simulations due to their modeling efficiency. However, their predictive accuracy deteriorates in certain loading scenarios, particularly near free edges, which constitute a critical case in sheet metal forming. Despite their high computational cost, solid elements can provide accurate fracture initiation predictions in these regions. This work proposes a neural network-based correction strategy to enhance shell element predictions by approximating solid element accuracy. A database comprising more than 200 hole-expansion simulations of a 2 mm thick AA6111 aluminum sheet with various elliptical holes and punch geometries is created with both shell and solid elements. The material is modeled using a von Mises yield surface with isotropic hardening and Hosford-Coulomb damage indicator [1]. A recurrent neural network is trained to learn the mapping from shell- to solid-element damage indicator. To achieve sufficient predictive capabilities, the mapping uses the mechanical response of the target shell element and its neighborhood, thereby incorporating local strain gradient. As an output, the Hosford-Coulomb damage indicator in the shell element is computed as a function of the full deformation history of the neighboring elements. The neural-network-enhanced shell predictions reduce the average deviation from solid element results by nearly an order of magnitude down to 0.2%. Furthermore, enhanced shell simulations are more than an order of magnitude faster than the corresponding solid element simulations, demonstrating a favorable balance between accuracy and computational efficiency.