For natural guide star adaptive optics (AO) systems, pyramid wavefront sensors (PWFSs) can provide a significant increase in sensitivity over the traditional Shack-Hartmann but at the cost of a reduced linear range. When using a linear reconstructor, nonlinearities result in wavefront estimation errors, which can have a significant impact on the image quality delivered by the AO system. We simulate a wavefront passing through a PWFS under varying observing conditions to explore the possibility of using a nonlinear machine learning model to estimate wavefront errors and compare with a linear reconstruction. We find significant potential improvements in delivered image quality even with computationally simple models, underscoring the need for further investigation of this approach.