Not yet reviewed by Pith; the record is open.

The pyramid wavefront sensor (PyWFS) has become increasingly popular to use in adaptive optics (AO) systems due to its high sensitivity. The main drawback of the PyWFS is that it is inherently nonlinear, which means that classic linear wavefront reconstruction techniques face a significant reduction in performance at high wavefront errors, particularly when the pyramid is unmodulated. In this paper, we consider the potential use of neural networks (NNs) to replace the widely used matrix vector multiplication (MVM) control. We aim to test the hypothesis that the neural network (NN)'s ability to model nonlinearities will give it a distinct advantage over MVM control. We compare the performance of a MVM linear reconstructor against a dense NN, using daytime data acquired on the Subaru Coronagraphic Extreme Adaptive Optics system (SCExAO) instrument. In a first set of experiments, we produce wavefronts generated from 14 Zernike modes and the PyWFS responses at different modulation radii (25, 50, 75, and 100 mas). We find that the NN allows for a far more precise wavefront reconstruction at all modulations, with differences in performance increasing in the regime where the PyWFS nonlinearity becomes significant. In a second set of experiments, we generate a dataset of atmosphere-like wavefronts, and confirm that the NN outperforms the linear reconstructor. The SCExAO real-time computer software is used as baseline for the latter. These results suggest that NNs are well positioned to improve upon linear reconstructors and stand to bring about a leap forward in AO performance in the near future.