Motivated by the potential of non-diffraction limited, real-time computational image sharpening with neu7 ral networks in astronomical telescopes, we have studied wavefront sensing with convolutional neural networks basedon a pair of in-focus and out-of-focus point spread functions. By simulation, we generated a large dataset for trainingand validation of neural networks, and trained several networks to estimate Zernike polynomial approximations forthe incoming wavefront. We included the effect of noise, guide star magnitude, blurring by wide band imagining, andbit depth. We conclude that the “ResNet” works well for our purpose, with a wavefront RMS error of 130 nm forr0 = 0.3 m, guide star magnitudes 4–8, and inference time of 8 ms. It can also be applied for closed-loop operation inan adaptive optics system. We also studied the possible use of a Kalman filter or a recurrent neural network and foundthat they were not beneficial to performance of our wavefront sensor