XDecomposer: Learning Prior-Free Set Decomposition for Multiphase X-ray Diffraction

Abstract: Multiphase powder X-ray diffraction (PXRD) analysis remains a fundamental bottleneck in structure identification, as real-world synthesis often produces complex mixtures whose constituent phases (components) cannot be reliably disentangled. While recent advances in representation-based crystal retrieval and generation suggest the possibility of inferring structures directly from PXRD, existing approaches largely assume single-phase inputs and break down in multiphase settings. Here, we present XDecomposer, a prior-free framework for joint decomposition and identification of multiphase XRD patterns without requiring candidate phase lists, structural templates, or prior knowledge of phase number. We formulate multiphase diffraction analysis as a set prediction problem, where the model infers an unordered set of phase-resolved components, their mixture proportions, and corresponding structural representations within a unified architecture. A phase-query-driven decomposition mechanism, together with diffraction-consistent physical reconstruction, enables accurate source separation while preserving crystallographic fidelity. Extensive experiments on both simulated and experimental datasets show that XDecomposer substantially improves reconstruction accuracy and phase identification across diverse chemical systems, while maintaining strong generalization to unseen mixtures. These results provide a practical route toward data-driven, source-resolved multiphase XRD analysis and reduce long-standing dependence on prior-guided iteratively phase matching. The code is openly available at https://github.com/Licht0812/XDecomposer

• The paper introduces XDecomposer, a permutation-invariant model that jointly estimates phase count, patterns, and proportions from one PXRD mixture without a predefined phase list.
• The method combines masked single-phase pretraining, Transformer-based global context, phase-guided queries, and continuous physics-constrained masks, achieving Pearson 0.8322 and 69.68% Top-1 retrieval for four-phase simulated mixtures.
• The model outperforms baselines on the RRUFF benchmark, reaching 0.6956 Pearson correlation and 65.31% Top-1 retrieval for two-phase mixtures, while revealing a persistent sim-to-real gap and a four-phase output limit.

Problem formulation

Multiphase powder X-ray diffraction (PXRD) analysis requires recovering all constituent phases, their individual diffraction patterns, and their relative proportions from a single one-dimensional pattern. Conventional refinement workflows (Rietveld, Pawley, Le Bail) presuppose that the phase list is known a priori, and existing learning-based approaches either restrict predictions to fixed candidate sets or adopt sequential identify-and-subtract strategies that accumulate error under peak overlap. The paper formulates the task as a single-channel blind source separation (BSS) problem with unknown source cardinality: given a mixture $x(\theta)=\sum_k w_k y_k(\theta)+\epsilon(\theta)$, recover the unordered set of component contributions $\{\hat{y}_k\}$ subject to mixture consistency and $1 \le K \le K_{\max}$. This is a permutation-invariant set prediction problem under variable cardinality, distinct from multi-label classification because identities, number, and proportions are all latent.

Architecture

XDecomposer predicts a fixed set of $K_{\max}=4$ output slots, each comprising a reconstructed contribution and an activity probability; inactive slots are pruned at inference by thresholding. The pipeline has three stages:

• Hierarchical encoding and global context modeling: a 1D convolutional analyzer extracts multi-scale local features (peak shapes, widths, intensity perturbations), which are passed to a Transformer encoder capturing long-range dependencies among Bragg reflections of the same phase—dependencies that purely local convolutions cannot represent.
• Phase-guided latent decomposition: learnable phase queries attend to the shared latent sequence via cross-attention. Each slot produces an activity logit and FiLM modulation parameters $(\gamma_k,\beta_k)$; spatial competition weights derived from slot–position similarity, combined with activity gating ($\alpha_{k,t}=w_{k,t}p_k$), yield spatially adaptive modulation of the shared representation before decoding.
• Physics-consistent reconstruction: the decoder predicts soft masks $m_k \in (0,1)^L$, and components are formed as $\hat{y}_k = m_k \odot x$. Because the input is non-negative and masks are bounded in $(0,1)$, outputs satisfy $0 \le \hat{y}_k \le x$ by construction, embedding non-negativity and partial mixture consistency into the output parameterization rather than only into the loss.

Training is two-stage: MAE-style masked reconstruction pretraining of the global-context encoder on ~2M simulated single-phase patterns (100,315 Materials Project structures × 20 perturbation conditions), followed by decomposition training with the encoder frozen (only 3.09M of 9.20M parameters trainable). The Stage II objective combines PIT-aligned separation loss (amplitude, SI-SDR shape, and square-root-domain geometric terms), slot-activity BCE supervision, and an L1 mixture-consistency term. Mixtures are generated online during training via anchor-driven sampling with Dirichlet weights bounded below at 0.15, avoiding storage of a fixed mixture corpus and preventing cross-split leakage since splits are defined at the crystal-ID level.

Empirical results

Evaluation uses five metrics—Pearson correlation, mean peak-position deviation, FWHM error, and Top-1/Top-10 retrieval accuracy—against three domain baselines (XQueryer, XRD_Proportion_Inference, XRDAutoAnalyzer) and three general sequence models (Transformer, iTransformer, PatchTST), all adapted to a unified decomposition protocol.

On simulated mixtures, XDecomposer leads across all metrics at every cardinality. For $\{\hat{y}_k\}$0, it reaches Pearson 0.8322 and Top-1 69.68% versus 0.7491/48.41% for the strongest baseline (Transformer); for $\{\hat{y}_k\}$1, Top-1 is 87.92% versus 76.43%. Degradation with increasing $\{\hat{y}_k\}$2 is markedly gentler than for baselines, attributed to large-scale XRD pretraining. Notably, XRDAutoAnalyzer's sequential strategy collapses almost entirely (Pearson 0.0011 at $\{\hat{y}_k\}$3), providing direct evidence against subtract-and-match pipelines under severe overlap.

On the RRUFF experimental benchmark (662 measured mineral patterns, five-fold cross-validation), all methods degrade substantially, exposing a clear sim-to-real gap that the authors attribute to multiphase fragility: single-phase variations propagate through superposition. XDecomposer still achieves the best Pearson correlation (e.g., 0.6956 ± 0.0091 at $\{\hat{y}_k\}$4 vs. 0.6519 for XQueryer) and dominant retrieval performance (Top-1 65.31% vs. 49.34% for iTransformer; Top-10 97.51% at $\{\hat{y}_k\}$5). An instructive nuance: XQueryer attains better local peak-position and width fidelity on real data, yet this does not translate into better global decomposition or retrieval—supporting the claim that multiphase analysis is not reducible to single-phase identification plus local peak alignment.

The ablation study at $\{\hat{y}_k\}$6 shows every module is load-bearing. Removing multi-scale skip fusion raises $\{\hat{y}_k\}$7FWHM from 5.25° to 17.77°; removing the geometry constraint, phase-guided modulation, or the pretrained encoder drops Top-1 to roughly 12–15%. Reconstruction form matters most: direct regression falls to Pearson 0.3439, and hard (binarized) masking collapses to 0.1916 with Top-1 of 2.35%, indicating that continuous, mixture-aware mask allocation in overlapping regions is essential.

Limitations and open questions

The framework caps output at $\{\hat{y}_k\}$8 slots with activity gating, which suffices for the studied settings but may not accommodate more variable phase counts. Mask-based reconstruction enforces physical plausibility but may be less robust to complex experimental distortions such as strong broadening, shifts, and background variation—the sim-to-real degradation on RRUFF quantifies this gap directly. Although the authors describe results as near-refinement-level quality, XDecomposer does not replace physical refinement; integration with refinement frameworks such as WPEM remains unexplored. Additionally, the experimental evaluation relies on synthetically mixed RRUFF patterns rather than natively measured multiphase samples, so performance on genuinely measured mixtures is an open question.

Conclusion

XDecomposer recasts prior-free multiphase PXRD analysis as permutation-invariant set prediction with physics-constrained mask reconstruction, combining self-supervised single-phase pretraining, query-based latent decomposition, and built-in non-negativity and mixture consistency. It consistently outperforms domain-specific and general-purpose baselines on both simulated and experimental data, with particularly strong retrieval accuracy and graceful degradation at higher phase counts, while ablations confirm that each architectural and loss-design choice contributes materially. The work establishes joint whole-pattern decomposition as a viable alternative to sequential retrieval-based multiphase identification, within the stated constraints of bounded phase cardinality and synthetic-mixture evaluation.