The Loss Landscape of XRD-Based Structure Optimization Is Too Rough for Gradient Descent

Solving crystal structures from powder X-ray diffraction (XRD) is a central challenge in materials characterization. One machine learning approach to inverting XRD involves optimizing a loss function that compares a ground-truth XRD spectrum against an XRD from a generated candidate crystal. We investigate the roughness of this optimization landscape by comparing reference structures with physically motivated distortions. We show that XRD similarity metrics result in a highly non-convex landscape, complicating direct optimization by gradient descent. Constraining the optimization symmetrically within the ground-truth crystal family improves recovery; nevertheless, the landscape may remain non-convex along symmetry axes. While energy-based relaxation excels at locating low-energy configurations, it cannot directly target the specific minima implied by spectra. We therefore advocate incorporating symmetry inductive biases directly into XRD-conditioned generative models, followed by energy relaxation, to enable more reliable reconstruction of phases from diffraction patterns.