  Polarized neutron reflectometry 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 polarized neutron
reflectometry 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-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 reflectometry profile of the topological insulator-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.
