Polarized neutron reflectometry (PNR) is a powerful technique to interrogate the structures of multilayered magnetic materials with depth sensitivity and nanometer resolution. However, reflectometry profiles often inhabit a complicated objective function landscape using traditional fitting methods, posing a significant challenge to parameter retrieval. In this work, we develop a data-driven framework to recover the sample parameters from PNR data with minimal user intervention. We train a variational autoencoder to map reflectometry profiles with moderate experimental noise to an interpretable, low-dimensional space from which sample parameters can be extracted with high resolution. We apply our method to recover the scattering length density profiles of the topological insulator (TI)-ferromagnetic insulator heterostructure Bi$_2$Se$_3$/EuS, exhibiting proximity magnetism, in good agreement with the results of conventional fitting. We further analyze a more challenging PNR profile of the TI-antiferromagnet heterostructure (Bi,Sb)$_2$Te$_3$/Cr$_2$O$_3$, and identify possible interfacial proximity magnetism in this material. We anticipate the framework developed here can be applied to resolve hidden interfacial phenomena in a broad range of layered systems.
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