High-energy cosmic rays and gamma quanta colliding with the upper atmosphere produce cascades of secondary particles known as extensive air showers (EASs). These showers can be detected and recorded using a variety of telescopes such as imaging atmospheric Cherenkov telescopes (IACTs), arrays of wide-angle integrating air detectors or water detectors; some experiments such as TAIGA [1] and LHAASO [2] combine several telescope types. The data from these observations can be used to identify the primary particle type and estimate its parameters such as energy and direction. In this paper, we estimate the EAS direction which is of interest because it can identify the gamma radiation source and is important in estimating the energy of the primary particle. Highly accurate shower direction estimates can be obtained from the timing measurements of multiple detectors spread over a large area such as TAIGA HiSCORE [3], LHAASO, or HAWC [4]. We use simulated data from TAIGA HiSCORE which is a non-imaging array of wide field-of-view integrating air Cherenkov detector stations. We use artificial neural networks (ANNs) to obtain shower direction estimates. Convolutional neural networks seem like a natural choice for the problem since the HiSCORE stations are positioned on a grid. However, the previous work using this approach [5, 6] produced estimates that were significantly less accurate than previously developed methods, e.g.