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Nonlinear iris texture deformations due to pupil size variations are one of the main factors responsible for within-class variance of genuine comparison scores in iris recognition. In dominant approaches to iris recognition, the size of a ring-shaped iris region is linearly scaled to a canonical rectangle, used further in encoding and matching. However, the biological complexity of the iris sphincter and dilator muscles causes the movements of iris features to be nonlinear in a function of pupil size, and not solely organized along radial paths. Alternatively to the existing theoretical models based on the biomechanics of iris musculature, in this paper we propose a novel deep autoencoder-based model that can effectively learn complex movements of iris texture features directly from the data. The proposed model takes two inputs, (a) an ISO-compliant near-infrared iris image with initial pupil size, and (b) the binary mask defining the target shape of the iris. The model makes all the necessary nonlinear deformations to the iris texture to match the shape of the iris in an image (a) with the shape provided by the target mask (b). The identity-preservation component of the loss function helps the model in finding deformations that preserve identity and not only the visual realism of the generated samples. We also demonstrate two immediate applications of this model: better compensation for iris texture deformations in iris recognition algorithms, compared to linear models, and the creation of a generative algorithm that can aid human forensic examiners, who may need to compare iris images with a large difference in pupil dilation. We offer the source codes and model weights available along with this paper.