We develop and evaluate a new approach to phase estimation for observational astronomy that can be used for accurate point spread function reconstruction. Phase estimation is required where a terrestrial observatory uses an adaptive optics (AO) system to assist astronomers in acquiring sharp, high-contrast images of faint and distant objects. Our approach is to train a conditional adversarial artificial neural network architecture to predict phase using the wavefront sensor data from a closed-loop AO system. We present a detailed simulation study under different turbulent conditions, using the retrieved residual phase to obtain the point spread function of the simulated instrument. Compared to the state-of-the-art model-based approach in astronomy, our approach is not explicitly limited by modeling assumptions, e.g., independence between terms, such as bandwidth and anisoplanatism—and is conceptually simple and flexible. We use the open-source COMPASS tool for end-to-end simulations. On key quality metrics, specifically the Strehl ratio and Halo distribution in our application domain, our approach achieves results better than the model-based baseline.