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Over the past decade, reversed gradient polarity (RGP) methods have become a popular approach for correcting susceptibility artifacts in echo-planar imaging (EPI). Although several post-processing tools for RGP are available, their implementations do not fully leverage recent hardware, algorithmic, and computational advances, leading to correction times of several minutes per image volume. To enable 3D RGP correction in seconds, we introduce PyTorch Hyperelastic Susceptibility Correction (PyHySCO), a user-friendly EPI distortion correction tool implemented in PyTorch that enables multi-threading and efficient use of graphics processing units (GPUs). PyHySCO uses a time-tested physical distortion model and mathematical formulation and is, therefore, reliable without training. An algorithmic improvement in PyHySCO is its use of the one-dimensional distortion correction method by Chang and Fitzpatrick to initialize the non-linear optimization. PyHySCO is published under the GNU public license and can be used from the command line or its Python interface. Our extensive numerical validation using 3T and 7T data from the Human Connectome Project suggests that PyHySCO can achieve accuracy comparable to that of leading RGP tools at a fraction of the cost. We also validate the new initialization scheme, compare different optimization algorithms, and test the algorithm on different hardware and arithmetic precisions.