Additive Manufacturing (AM) is a revolutionary fabrication process that is a key aspect of the Industry 4.0 environment. In addition, Industry 4.0 aims to have a fully connected environment with numerous sensors for capturing process data. One of the challenges in AM currently is the geometric inaccuracy of parts during fabrication. This has inhibited the widespread use of AM in many suitable applications, such as maintenance and biomedical. Geometric inaccuracies (i.e. distortion) can be reduced through compensation plans, however, compensation plans require accurate predictions of expected distortion. Here we develop a novel Deep Learning approach that accurately predicts distortion well within AM tolerance limits (30-40 microns). We utilize a Convolutional Neural Network to analyze thermal images captured during the process and an Artificial Neural Network to incorporate various design and process parameters. The Deep Learning approach can be applied to any AM quality criterion that is measured pointwise (i.e. porosity). Our Deep Learning approach not only gives highly accurate predictions, but also fits into the Industry 4.0 framework of analyzing big data from a large number of sensors.