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In the presence of strong electronic spin correlations, the hyperfine interaction imparts long-range coupling between nuclear spins. Efficient protocols for the extraction of such complex information about electron correlations via magnetic response are not well known. Here we study how machine learning can extract material parameters and help interpret magnetic response experiments. A low-dimensional representation that classifies the strength and range of the interaction is discovered by unsupervised learning. Supervised learning generates models that predict the spatial extent of electronic correlations and the total interaction strength. Our work demonstrates the utility of artificial intelligence in the development of new probes of quantum systems, with applications to experimental studies of strongly correlated materials.