The loss landscape of powder X-ray diffraction-based structure optimization is too rough for gradient descent

Abstract

Solving crystal structures from powder X-ray diffraction (XRD) is a critical inverse problem in materials characterization. This work studies the mapping from diffractogram to crystal structure using gradient-based optimization of the structure with XRD similarity as the objective, and evaluates the retrieval of ground-truth geometries from moderately distorted structures. We find that commonly used XRD similarity metrics result in an ill-posed, highly non-convex loss landscape where high signal agreement does not necessarily imply structural accuracy, a phenomenon driven by spurious peak overlaps. Constraining the optimization to the ground-truth crystal family significantly improves retrieval, and yields higher correlation between structural similarity and XRD similarity. Nevertheless, the landscape may remain non-convex along certain symmetry axes. Finally, we contrast this with the interatomic potential energy landscape, which exhibits smooth, locally convex behavior for identical structural perturbations.