The problem of wavefront reconstruction by its slopes, related to the the phase recovery of a light wave based on Shack-Hartmann sensor data, is considered. A reconstruction method based on the application of physics-informed neural networks to slope measurement data on both regular and irregular grids in two modifications WRPINN and WRRADPINN is proposed. A comparison with the reconstruction method based on the variational approach combined with the projection method using a fractional smoothness stabilizer on typical smooth, nonsmooth, and discontinuous wavefronts defined on a regular grid is given. The results of the method’s performance on irregular grids and with partially missing data are analyzed, leading to the conclusion about its effectiveness in handling such data.