Coherent beam combining (CBC) by active phase control is an efficient way to power scale fiber amplifiers but its bandwidth of operation of CBC can be limited. Deep-learning techniques offer some capability for fast retrieval of the laser phases from the shape of the interference pattern generated through combining, in order to increase the speed and bandwidth of operation of CBC. In this paper, we present the development and numerical tests of a Convolutional Neural Network (CNN) used for such fast phase retrieval. After numerically generating tens of thousands of interference patterns corresponding to different phase sets for the combined lasers, we learned the CNN to retrieve the phase set corresponding to a given shape of interference pattern. Unfortunately, due to the central symmetry of the tiled-aperture hexagonal geometry of the array of fiber outputs, there’s not a unique set of phases for the combined lasers that can lead to a given shape of interference pattern. We demonstrate that acquiring the image of the interference pattern in a plane that is not perfectly located in the far-field offers a simple solution to get rid of this non-uniqueness ambiguity. After demonstrating numerically that with this addition, the CNN learning approach operates well resulting in low values for the CBC residual phase error, we explain how it’s possible to transfer this learning that has been done numerically to a real experiment.