This paper describes a computational statistical tool to efficiently obtain a phase map from multi-scale experimental measurement profiles obtained from high-throughput small-angle X-ray scattering experiments of polymer blend systems. We show that learned metric geometry can efficiently differentiate ordered phase regions with shifted, missing, and broad Bragg peaks along with features related to non-Bragg behavior of soft-matter systems. The metric geometry allows us to define a shape distance between scattering profiles invariant to phase-independent transformations thus valuable for obtaining a phase map.