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In microscopy employing electron and x-ray beams, advances in instrumentation and techniques have substantially improved the ability to image, track, and characterize materials at ever-higher resolution and precision. However, determining atomistic arrangements (ie configurations) from microscopy data remains a substantial challenge. Whether due to projection of a three-dimensional structure onto one or two dimensions as in pair distribution functions (PDF) and (scanning) transmission electron microscopy (STEM/TEM), or the reduction of a large number of matrix elements into an overall energy-dependent amplitude as in x-ray absorption spectroscopy (XAS) and electron energy loss spectroscopy (EELS), the result is that inversion of this mapping is time consuming, imprecise, and sometimes even fruitless, despite a large number of excellent tools which produces characterization data from input atomistic …