Inertial and Doppler velocity log sensors are commonly used to provide the navigation solution for autonomous underwater vehicles (AUV). To this end, a nonlinear filter is adopted for the fusion task. The filter's process noise covariance matrix is critical for filter accuracy and robustness. While this matrix varies over time during the AUV mission, the filter assumes a constant matrix. Several models and learning approaches in the literature suggest tuning the process noise covariance during operation. In this work, we propose ProNet, a hybrid, adaptive process, noise estimation approach for a velocity-aided navigation filter. ProNet requires only the inertial sensor reading to regress the process noise covariance. Once learned, it is fed into the model-based navigation filter, resulting in a hybrid filter. Simulation results show the benefits of our approach compared to other models and learning adaptive approaches.