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.