# AI-Driven Structure Refinement of X-ray Diffraction

arXiv: https://arxiv.org/abs/2602.16372 · HTML: https://mlsanity.com/paper/2602.16372/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 40 references that are in the map.
- First posted on arXiv 18 Feb 2026.

## Builds on (most cited first, 3 of 3)

- [Space Group Constrained Crystal Generation](https://mlsanity.com/paper/2402.03992/) (2024)
- [End-to-End Crystal Structure Prediction from Powder X-Ray Diffraction](https://mlsanity.com/paper/2401.03862/) (2024)
- [Beyond Structure: Invariant Crystal Property Prediction with Pseudo-Particle Ray Diffraction](https://mlsanity.com/paper/2509.21778/) (2025)

## Built on by (most cited first, 2 of 2)

- [XDecomposer: Learning Prior-Free Set Decomposition for Multiphase X-ray Diffraction](https://mlsanity.com/paper/2605.05866/) (2026)
- [A self-learning scientific agent for X-ray diffraction](https://mlsanity.com/paper/2610.07862/) (2026)

## Abstract (arXiv)

Artificial intelligence can rapidly propose candidate phases and structures from X-ray diffraction (XRD), but these hypotheses often fail in downstream refinement because peak intensities cannot be stably assigned under severe overlap and diffraction consistency is enforced only weakly. Here we introduce the whole-pattern expectation--maximization (WPEM) algorithm, a physics-constrained whole-pattern decomposition and refinement workflow that turns Bragg's law into an explicit constraint within a batch expectation--maximization framework. WPEM models the full profile as a probabilistic mixture density and iteratively infers component-resolved intensities while keeping peak centres Bragg-consistent, producing a continuous, physically admissible intensity representation that remains stable in heavily overlapped regions and in the presence of mixed radiation or multiple phases. We benchmark WPEM on standard reference patterns (PbSO4 and Tb2BaCoO5), where it yields lower Rp/Rwp than widely used packages (FullProf and TOPAS) under matched refinement conditions. We further demonstrate generality across realistic experimental scenarios, including phase-resolved decomposition in multiphase materials, quantitative recovery of mixture compositions, separation of crystalline peaks from amorphous backgrounds in semicrystalline systems, high-throughput operando lattice tracking, automated refinement of compositionally disordered solid solutions, and quantitative phase-resolved analysis of complex archaeological samples from synchrotron powder XRD. By providing Bragg-consistent, uncertainty-aware intensity partitioning as a refinement-ready interface, WPEM closes the gap between AI-generated hypotheses and diffraction-admissible structure refinement on challenging XRD data.