Multimode fibers are regarded as the key technology for the steady increase in data rates in optical communication. However, light propagation in multimode fibers is complex and can lead to distortions in the transmission of information. Therefore, strategies to control the propagation of light should be developed. These strategies include the measurement of the amplitude and phase of the light field after propagation through the fiber. This is usually done with holographic approaches. In this paper, we discuss the use of a deep neural network to determine the amplitude and phase information from simple intensity-only camera images. A new type of training was developed, which is much more robust and precise than conventional training data designs. We show that the performance of the deep neural network is comparable to digital holography, but requires significantly smaller efforts. The fast characterization of multimode fibers is particularly suitable for high-performance applications like cyberphysical systems in the internet of things.