MRI-Linacs are new cancer treatment machines integrating radiotherapy with MRI. Dynamically adapting the radiation beam on the basis of MR-detected anatomical changes (e.g. respiratory and cardiac motion) promises to increase the accuracy of MRI-Linac treatments. A key challenge in real-time beam adaptation is accurately reconstructing images in real time. Historically, reconstruction of data acquired with accelerated techniques, such as compressed sensing, has been very slow. Here, we use AUTOMAP, a machine-learning framework, to quickly and accurately reconstruct radial MRI data simulated from a digital thorax phantom. These results will guide development of real-time adaptation technologies on MRI-Linacs.