To implement autonomous driving, one essential step is to model the vehicle environment based on the sensor inputs. Radars, with their well-known advantages, became a popular option to infer the occupancy state of grid cells surrounding the vehicle. To tackle data sparsity and noise of radar detections, we propose a deep learning-based Inverse Sensor Model (ISM) to learn the mapping from sparse radar detections to polar measurement grids. Improved lidar-based measurement grids are used as reference. The learned radar measurement grids, combined with radar Doppler velocity measurements, are further used to generate a Dynamic Grid Map (DGM). Experiments in real-world highway scenarios show that our approach outperforms the hand-crafted geometric ISMs. In comparison to state-of-the-art deep learning methods, our approach is the first one to learn a single-frame measurement grid in the polar scheme from radars with a limited Field Of View (FOV). The learning framework makes the learned ISM independent of the radar mounting. This enables us to flexibly use one or more radar sensors without network retraining and without requirements on 360{\deg} sensor coverage.