The surface detector array of the Pierre Auger Observatory measures the footprint of air showers induced by ultra-high energy cosmic rays. The reconstruction of event-by-event information sensitive to the cosmic-ray mass, is a challenging task and so far mainly based on fluorescence detector observations with their duty cycle of $\approx 15 \%$.
Recently, great progress has been made in multiple fields of machine learning using deep neural networks and associated techniques. Applying these new techniques to air-shower physics opens up possibilities for improved reconstruction, including an estimation of the cosmic-ray composition.
In this contribution, we show that deep convolutional neural networks can be used for air-shower reconstruction, using surface-detector data. The focus of the machine-learning algorithm is to reconstruct depths of shower maximum. In contrast to traditional reconstruction methods, the algorithm learns to extract the essential information from the signal and arrival-time distributions of the secondary particles. We present the neural-network architecture, describe the training, and assess the performance using simulated air showers.