High costs for the repair of concrete structures can be prevented if damage at an early stage of degradation is detected and precautionary maintenance measures are applied. To this end, we use numerical wave propagation simulations to identify simulated damage in concrete using convolutional neural networks. Damage in concrete subjected to compression is modeled at the mesoscale using the discrete element method. Ultrasonic wave propagation simulation on the damaged concrete specimens is performed using the rotated staggered finite-difference grid method. The simulated ultrasonic signals are used to train a CNN-based classifier capable of classifying three different damage stages (microcrack initiation, microcrack growth and microcrack coalescence leading to macrocracks) with an overall accuracy of 77%. The performance of the classifier is improved by refining the dataset via an analysis of the averaged envelope of the signal. The classifier using the refined dataset has an overall accuracy of 90%.