The design and tuning of accelerators are both complicated processes involving many physical effects. Of these, the modeling of coherent synchrotron radiation has long been one of the most complicated and time consuming. This is especially true when modeling two and three-dimensional CSR, which is often neglected in state-of-the-art accelerator modeling due to its time consuming nature. We present a neural network designed to model 2D CSR, demonstrating both faithful accuracy to the physics and a dramatic speedup over even the fastest existing codes. We study its performance in the context of the last bunch compressor of the FACET-II facility, where the intense short pulse demands at least a 2D treatment, and find that we can reproduce the results of more standard tracking codes in a fraction of the time.