Quantum cold-atom sensors provide precise measurements of gravitational acceleration and gravity gradients. By matching these measurements to a high-resolution gravity database, a moving platform can derive its position using map matching techniques that fuse gradient observations with inertial navigation. One such fusion technique, particle-filters, are dominated by the cost of evaluating gravity gradients via surface integrals at each location. To overcome this overhead, we introduce a deep-learning model that predicts the vertical gravity gradient from a compact subset of local gravity anomaly samples, eliminating the need for full integral computations. We integrate this neural network into the map-matching framework, benchmark its accuracy against conventional methods, and demonstrate its real-time performance within a simulated inertial navigation system driven by a quantum sensor model.