The thesis contains several pioneering results at the intersection of state-of-the-art materials characterization techniques and machine learning. The use of machine learning empowers the information extraction capability of neutron and photon spectroscopies. In particular, new knowledge and new physics insights to aid spectroscopic analysis may hold great promise for next-generation quantum technology. As a prominent example, the so-called proximity effect at topological material interfaces promises to enable spintronics without energy dissipation and quantum computing with fault tolerance, yet the characteristic spectral features to identify the proximity effect have long been elusive. The work presented within permits a fine resolution of its spectroscopic features and a determination of the proximity effect which could aid further experiments with improved interpretability. A few novel machine learning architectures are proposed in this thesis work which leverage the case when the data is scarce and utilize the internal symmetry of the system to improve the training quality. The work sheds light on future pathways to apply machine learning to augment experiments.