The Loss Landscape of Powder X-Ray Diffraction-Based Structure Optimization Is Too Rough for Gradient Descent

TL;DR

This paper investigates the challenges of using gradient descent to solve crystal structures from powder X-ray diffraction data, revealing a highly non-convex landscape that complicates direct optimization.

Contribution

It demonstrates the non-convexity of the XRD-to-structure mapping and shows that constraining to the correct crystal family improves recovery, highlighting the need for symmetry-aware methods.

Findings

XRD similarity metrics create a highly non-convex landscape.

Constraining to the ground-truth crystal family improves structure recovery.

The landscape remains non-convex along certain symmetry axes.

Abstract

Solving crystal structures from powder X-ray diffraction (XRD) is a central challenge in materials characterization. In this work, we study the powder XRD-to-structure mapping using gradient descent optimization, with the goal of recovering the correct structure from moderately distorted initial states based solely on XRD similarity. We show that commonly used XRD similarity metrics result in a highly non-convex landscape, complicating direct optimization. Constraining the optimization to the ground-truth crystal family significantly improves recovery, yielding higher match rates and increased mutual information and correlation scores between structural similarity and XRD similarity. Nevertheless, the landscape may remain non-convex along certain symmetry axes. These findings suggest that symmetry-aware inductive biases could play a meaningful role in helping learning models navigate the inverse mapping from diffraction to structure.