  Predictive wavefront control is an important and rapidly developing field of
adaptive optics (AO). Through the prediction of future wavefront effects, the
inherent AO system servo-lag caused by the measurement, computation, and
application of the wavefront correction can be significantly mitigated. This
lag can impact the final delivered science image, including reduced strehl and
contrast, and inhibits our ability to reliably use faint guidestars. We
summarize here a novel method for training deep neural networks for predictive
control based on an adversarial prior. Unlike previous methods in the
literature, which have shown results based on previously generated data or for
open-loop systems, we demonstrate our network's performance simulated in closed
loop. Our models are able to both reduce effects induced by servo-lag and push
the faint end of reliable control with natural guidestars, improving K-band
Strehl performance compared to classical methods by over 55% for 16th magnitude
guide stars on an 8-meter telescope. We further show that LSTM based approaches
may be better suited in high-contrast scenarios where servo-lag error is most
pronounced, while traditional feed forward models are better suited for high
noise scenarios. Finally, we discuss future strategies for implementing our
system in real-time and on astronomical telescope systems.
