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PXRD-Bench: How Close Are We to Determining Crystal Structures from Powder Diffraction?

Dongyeop Woo, Nofit Segal, Nayoung Kim, Minkyu Kim, Rafael Gomez-Bombarelli, Sungsoo Ahn

arXiv:2610.16480v1cs.AIcond-mat.mtrl-sci

TL;DR

PXRD patterns compress three-dimensional crystal information into one dimension, where peak overlap and measurement distortions complicate structure determination. PXRD-Bench broadens evaluation across compositions, prototypes, and two-phase mixtures, and Bragglite provides a PXRD-conditioned baseline. Bragglite improves experimental recovery over prior methods, but prototype generalization and multiphase recovery remain challenging.

  • Problem

    PXRD compresses three-dimensional structural information into one-dimensional patterns where different structures can yield similar signals, complicating routine structure determination.

    Source: §1 · p. 1

  • Method

    The paper introduces PXRD-Bench for broader PXRD structure-recovery evaluation and develops Bragglite, a PXRD-conditioned baseline informed by systematic modeling studies.

    Source: §1 · p. 2, §3.1 · pp. 3–4, §6 · p. 10

  • Results

    Bragglite substantially improves experimental structure recovery over prior methods, while robust use of experimental PXRD, unseen-prototype generalization, and multiphase recovery remain challenging.

    Source: §6 · p. 10

  • Takeaways & Limitations

    PXRD-Bench establishes a controlled framework for measuring progress toward practical PXRD-based structure determination and identifying persistent limitations.

    Source: §6 · p. 10

    The benchmark provides primitive-cell atom counts as oracle input, so the element-set and two-phase settings do not test inference of total atom count.

    Source: F Scope and limitations · p. 37

Abstract

from arXiv · show

Determining crystal structures from powder X-ray diffraction (PXRD) would enable routine characterization of newly synthesized materials, including those absent from reference databases. Generative models offer a promising approach, but existing evaluations remain fragmented and largely assume single-phase samples with known composition. To fill this gap, we introduce PXRD-Bench, a unified benchmark that extends evaluation to unknown per-element atom counts and recovery of both structures in two-phase mixtures. It provides approximately 4.1 million training structures with simulated PXRD, tests generalization to unseen compositions and structural prototypes, and evaluates recovery from experimental PXRD after excluding structurally matching training entries. To provide a strong reference baseline, we also introduce Bragglite, a PXRD-to-structure model developed through a systematic study of PXRD modeling choices. It achieves a 44.2\% Top-1 match rate on experimental RRUFF patterns with known composition, 24.6\% above the strongest prior baseline. Further analysis yields several key findings: some models fail to benefit from experimental PXRD, while generalization to unseen structural prototypes and recovery from two-phase mixtures remain challenging. Together, our benchmark, systematic studies, and Bragglite clarify the capabilities and limitations of current PXRD-to-structure models.

1 Introduction

PXRD can support routine characterization, but its one-dimensional patterns make structure recovery ambiguous and conventional analysis often needs substantial expert guidance. PXRD-Bench broadens evaluation beyond known-composition, single-phase settings, while Bragglite and the benchmark expose continuing challenges in experimental transfer and structural novelty.

1 Introduction

  • The 1D diffraction pattern can obscure 3D structure through peak overlap and similar patterns from different structures, while noise, broadening, intensity distortion, and multiple phases further complicate interpretation.Conventional analysis combines crystallographic analysis, structure search, and refinement, often requiring substantial expert guidance.Source: §1 · p. 1
  • Existing evaluations use fragmented datasets and protocols and largely assume single-phase samples with known composition, leaving unknown atom counts and multiphase structure recovery underexplored.Unseen-composition testing alone does not establish recovery of unfamiliar structural arrangements when prototypes may remain represented in training.Source: §1 · pp. 1–2
  • PXRD-Bench combines a 4.2-million-structure simulated corpus with experimental RRUFF and opXRD data, simulated two-phase mixtures, and experimental GALAXI mixtures.Its protocols hold out compositions, structural prototypes, or composition–prototype pairs and extend evaluation to element-set conditioning and two-phase recovery.Source: §1 · p. 2
  • Bragglite provides a strong PXRD-conditioned baseline, and the benchmark reveals persistent limits in experimental diffraction use, unseen-prototype generalization, and recovery of multiple phases.Models struggle more with unseen structural prototypes than with unseen compositions; several existing PXRD-conditioned models also underperform composition-only DiffCSP on experimental RRUFF patterns.Source: §1 · pp. 2–3

2 Related Work

Prior PXRD-to-structure work varies in data, chemical inputs, and refinement, limiting direct comparisons. This section situates the benchmark across model evaluation, experimental transfer, and multiphase analysis.

PXRD-to-structure models

  • Prior PXRD-to-structure evaluations vary in training data, chemical inputs, and post-generation refinement, and largely emphasize in-distribution or composition-level generalization.The benchmark compares models under controlled data and evaluation settings, with held-out compositions, prototypes, and composition–prototype pairs.Source: §2 · p. 3

Transfer to experimental PXRD

  • Experimental-transfer strategies have been tested across different models, settings, and benchmarks, sometimes without separate validation and test sets.The paper compares representation and augmentation choices under a common protocol and excludes training structures matching experimental references.Source: §2 · p. 3

Multiphase PXRD analysis

  • Prior multiphase learning focuses on identifying known phases or decomposing signals rather than recovering constituent atomic structures.The paper extends this work to generating a structure for each of two decomposed components and evaluates transfer on GALAXI experimental mixtures.Source: §2 · p. 3

3 Benchmark design

PXRD-Bench evaluates complementary structure-recovery tasks, simulation-to-experiment transfer, and generalization beyond training data. Its protocols cover single-phase and two-phase settings with controlled held-out splits and experimental datasets.

3 Benchmark design

  • The benchmark targets practical task extensions, simulation-to-experiment transfer, and generalization beyond the training distribution.The three tasks are known-composition single-phase recovery, element-set-conditioned recovery, and two-phase recovery.Source: §3 · p. 3, §3.1 · p. 3

3.1 Task formulations

  • In element-set conditioning, the model receives the elements and total atom count but must infer element multiplicities, coordinates, and lattice; two-phase recovery requires assigning elements and recovering both structures from a mixed pattern.For the mixture task, the inputs include the combined element set and the atom count of each phase, but not either phase’s composition.Source: §3.1 · pp. 3–4

3.2 Single-phase PXRD benchmarks

  • The single-phase benchmarks pair simulated PXRD with structures and test in-distribution recovery plus held-out composition, prototype, and composition–prototype generalization.Experimental transfer uses RRUFF and opXRD validation and test sets, with structurally matching training entries excluded; predictions are evaluated unrefined using structural matching.Source: §3.2 · pp. 4–5

3.3 Multiphase PXRD benchmark

  • The two-phase benchmark uses thermodynamically plausible simulated mixtures and 21 experimental GALAXI test samples, measuring dominant-, minor-, and all-phase recovery.An all-phase match requires both constituent phases to be recovered within their respective candidate sets.Source: §3.3 · p. 5

4 Bragglite: A baseline for PXRD-to-structure generation

Bragglite is a PXRD-conditioned baseline built on a crystal-structure diffusion model. Its input representation combines peak features, while training augmentations perturb simulated diffraction to resemble measurement distortions.

4 Bragglite: A baseline for PXRD-to-structure generation

  • Bragglite builds on Crystalite’s diffusion Transformer with pair-geometry attention biases and adds a Transformer PXRD encoder for diffraction conditioning.The model is presented as a reference baseline developed through systematic study of PXRD representation, encoding, and augmentation choices.Source: §4 · p. 5

4.1 PXRD representation and conditioning

  • The PXRD representation uses detected peaks with position, intensity, width, and prominence, and the study compares 2θ, d, and q positions, using q by default.Relative intensity is used because absolute scale varies with experimental conditions; prominence and width capture background/noise context and peak broadening.Source: §4.1 · pp. 5–6

4.2 PXRD augmentation

  • Training augmentation perturbs simulated reflections and dense profiles to model missing peaks, position errors, intensity variation, broadening, background scattering, and noise.After profile augmentation, peaks are redetected and their positions, intensities, widths, and prominences are supplied to the model.Source: §4.2 · p. 6, Figure 3 · p. 6

5 Experiments

The experiments show Bragglite outperforming baselines across single-phase settings, while revealing persistent challenges in experimental transfer, unseen structural prototypes, and two-phase recovery.

5.1 Single-phase benchmark results

  • Bragglite outperforms baselines across all settings, including known-composition and element-set single-phase recovery.Source: §5.1 · p. 7
  • Crystalite beats PXRD-conditioned baselines on MP-20 and RRUFF, but performs substantially worse on polymorph-rich PXRD-Bench.The contrast suggests composition alone can recover references when polymorph ambiguity is limited, whereas PXRD helps distinguish structures sharing a composition.Source: §5.1 · pp. 7–8
  • Performance remains strong on unseen composition–prototype pairings and compositions, but drops substantially for unseen structural prototypes.Bragglite nevertheless substantially outperforms its composition-only counterpart on unseen prototypes.Source: §5.1 · p. 8, Table 2 · p. 8
  • Top-1 match rates improve across simulated splits and experimental RRUFF as training data scale increases, with diminishing gains at larger scales.Source: Figure 4 · p. 8, §5.1 · p. 8

5.3 Two-phase recovery

  • Bragglite outperforms the reference methods in most two-phase recovery settings on simulated MP-20 and experimental GALAXI mixtures.MatterGen is not leakage-controlled against the evaluation sets, while XRDiff receives phase-specific element sets, so these are not strictly controlled baselines.Source: Table 4 · p. 9, §5.3 · p. 10

5.2 Understanding sim-to-real transfer

  • Adding PXRD augmentations improves experimental RRUFF performance while generally reducing simulated accuracy, and component effectiveness varies across experimental datasets.Source: §5.2 · p. 9, Figure 5 · p. 9
  • No augmentation and peak-only augmentation show little experimental improvement as simulated performance rises, while both full-augmentation settings show positive trends.The proposed full-augmentation magnitudes yield larger experimental gains than the reduced magnitudes.Source: §5.2 · p. 9, Figure 5 · p. 9
  • Despite its smaller size, MP-20 transfers better to RRUFF than PXRD-Bench, and oversampling Si/O-containing structures further improves RRUFF performance.The authors suggest distribution-aware fine-tuning toward the target domain may further improve downstream experimental performance.Source: §5.2 · p. 9, Table 3 · p. 9

6 Conclusion

The conclusion presents PXRD-Bench and Bragglite as tools for evaluating PXRD-based structure determination, while noting unresolved limits in experimental transfer, prototype generalization, and multiphase recovery.

6 Conclusion

  • PXRD-Bench spans simulation-to-experiment transfer, out-of-distribution generalization, element-set conditioning, and two-phase recovery; Bragglite is a strong PXRD-conditioned baseline.Experiments show improved experimental structure recovery over prior methods, but robust experimental PXRD use, unseen-prototype generalization, and multiple-phase recovery remain challenging.Source: §6 · p. 10

AI use statement

  • The authors report using ChatGPT and Codex across implementation, analysis, figure and table preparation, and manuscript drafting, with authors reviewing outputs and retaining responsibility.Source: AI use statement · p. 10

Reproducibility statement

  • The paper identifies benchmark construction, splits, leakage controls, metrics, model specifications, training settings, baselines, seeds, and compute resources as reproducibility details, with code and configurations in supplementary material.Source: Reproducibility statement · p. 10

A Benchmark details

  • Appendix A provides additional details on benchmark dataset construction, curation, and evaluation metrics.Source: A Benchmark details · p. 14

A.1.1 Dataset construction

The dataset pipeline selects and validates source structures, filters compositions, deduplicates records, and applies atom-count and chemical curation before finalizing the benchmark corpus.

A.1.1 Dataset construction

  • Energy-based selection on MP, OQMD, and Alexandria, but not AFLOW, retains 5,634,620 candidate records from source snapshots totaling approximately 9.78 million input records.The aggregate input count includes repeated AFLOW API records and should not be read as a unique-structure count.Source: §A.1.1 · p. 14
  • Structural validation retains three-dimensionally periodic structures with fully occupied, ordered sites, while excluding invalid structures and primitive cells exceeding 208 atoms.The subsequent composition-bucket step discards buckets with more than 128 records, then performs cross-source representative-centered structural deduplication using fixed source priority.Source: §A.1.1 · p. 14
  • The benchmark further limits primitive cells to at most 52 atoms and excludes molecular crystals and structures with evidence of organic components.The authors characterize this as a conservative operational exclusion policy, not a guarantee that all remaining structures are free of molecular or organic content.Source: §A.1.1 · p. 14
  • After filtering and split-consistency checks, the benchmark contains 4,262,691 structures, including an effective training set of 4,107,627 structures.Source: §A.1.1 · p. 14

A.1.2 Dataset splits and overlap audits

The corpus is split into IID and three OOD evaluations using intact structural similarity groups, with holdout constraints rechecked after filtering. Final audits verify split separation and zero training overlap with the external benchmarks.

A.1.2 Dataset splits and overlap audits

  • Prototype-, composition-, and composition–prototype-pair OOD holdouts are constructed before IID holdouts, preserving the novelty unit for each evaluation.Prototype and composition holdouts require their associated composition or prototype to remain represented in training; pair holdouts preserve both and cannot split a structural similarity group.Source: §A.1.2 · pp. 14–15
  • Structural prototypes use space group, primitive-cell site count, and species-anonymized Wyckoff-orbit patterns, while matching groups keep similar structures together across splits.Similarity groups are connected components of a species-aware matching graph and remain intact during splitting.Source: §A.1.2 · pp. 14–15
  • The curated corpus contains 4,262,691 structures, including 4,107,627 training structures after curation and split-consistency filtering.Any validation or test structures that no longer satisfy their defining OOD condition after filtering are removed.Source: Table 5 · p. 15, §A.1.2 · p. 15
  • IID validation and test sets hold out structural similarity groups without explicitly enforcing novelty in composition or prototype; OOD holdout units remain intact across validation and test.Each OOD validation/test subset and each IID subset targets approximately 20,000 structures; rare compositions or prototypes can occur only in IID evaluation.Source: §A.1.2 · p. 15
  • Audits of finalized splits found no structural similarity group shared across splits and, after excluding matches to RRUFF-148 or opXRD-123, no training structure matching either reference.Exclusion matching required identical element species and used primitive-cell conversion and lattice scaling, without supercell or subset matching; tolerances were (ltol, stol, angle_tol) = (0.3, 0.5, 10°). Figure 6 reports finalized split sizes.Source: §A.1.2 · pp. 15–16

A.1.3 Additional dataset coverage statistics

The curated corpus spans varied cell sizes and compositions, but structural-family coverage is highly uneven and simulated diffraction profiles vary substantially in complexity.

A.1.3 Additional dataset coverage statistics

  • Primitive cells contain a median of 6 atoms and a 95th-percentile size of 22; ternary and quaternary compositions account for 69.5% and 20.4% of structures.Figure 7 summarizes cell-size and composition-arity distributions.Source: §A.1.3 · p. 16, Figure 7 · p. 17
  • Among 46,658 structural prototypes, 41.4% occur only once, leaving structural-family coverage highly nonuniform despite the corpus scale.The prototype-frequency distribution is strongly long-tailed.Source: §A.1.3 · p. 16, Figure 7 · p. 17
  • Simulated Bragg-line counts span a long-tailed range beyond the 128- and 512-line budgets, and calculator lines may merge multiple reflections.The counts cover 2θ ∈[5°, 90°] and need not equal experimentally resolved peak counts; the distribution motivates testing fixed-size peak representations.Source: §A.1.3 · p. 16, Figure 7 · p. 17
  • Figure 6 reports finalized training, validation, and test sizes for IID, pair-OOD, prototype-OOD, and composition-OOD evaluations on a logarithmic axis.No structural similarity group is shared across splits.Source: Figure 6 · p. 17

A.2 Construction of the Multiphase Dataset

The appendix constructs two-phase mixtures from plausible phase pairs, defines recovery metrics and reference datasets, and tests PXRD representation choices. The representation study favors q-based peak features with shape information and log16 Fourier encoding.

A.2 Construction of the Multiphase Dataset

  • Two-phase candidates use nine complementary phase weight fractions and are retained if they are equilibrium adjacent stable phases or satisfy the stated near-hull criteria.Near-hull mixtures must lie within 50 meV/atom of the convex hull, and each constituent phase must also meet its stability criterion.Source: §A.2 · p. 18
  • The dataset combines constituent PXRD profiles using scale factors derived from phase weight fractions, then maximum-intensity normalizes the mixture.The final dataset contains 125,064 mixtures; recovery experiments use 10,657 non-tie test mixtures.Source: §A.2 · p. 18

A.3 Evaluation Metrics

  • Single-phase Top-K match rates count recovery when at least one of the first K candidates matches the reference under StructureMatcher.The benchmark reports Top-1 and Top-20 match rates.Source: §A.3 · p. 19
  • Two-phase evaluation reports dominant-, minor-, and all-phase rates; an all-phase success requires both structures to be recovered and is not an average of the phase-specific rates.Rates are reported at Top-1 and Top-20.Source: §A.3 · p. 19

A.4 Existing datasets used in additional experiments

  • MP-20 supplies a compact reference training corpus, while MP-20-polymorph-split groups every structure with the same reduced composition into one split.The composition-grouped split removes composition overlap while retaining the MP-20 structure collection and overall composition-arity distribution.Source: §A.4 · p. 20

B.1 PXRD representation study

  • Log16 Fourier features give the best overall validation results, while increasing the maximum frequency to 64 reduces performance on both RRUFF and opXRD.The final representation uses q, intensity, width, prominence, and log16 Fourier encoding of physical peak position.Source: Table 6 · p. 21, §B.1 · p. 21
  • Among 2θ, d-spacing, and q-spacing with intensity, q gives the strongest validation performance overall and is independent of measurement wavelength.The study keeps model architecture and size fixed and compares Top-1 validation match rates on RRUFF and opXRD.Source: §B.1 · p. 21, Table 6 · p. 21
  • Adding peak width and prominence to q and intensity improves validation performance on both RRUFF and opXRD.These descriptors encode local peak shape and distinguish peaks that may share similar positions and intensities.Source: §B.1 · p. 21

B.2 Architecture ablation

This section examines Bragglite’s architecture choices and their effects on structure recovery, alongside the model configuration and benchmark evaluation details. It describes a shared geometry-enhancement module, symmetry-aware element-set token ordering, and EDM-preconditioned denoising outputs.

B.2 Architecture ablation

  • On the MP-20 validation set, removing GEM causes a larger match-rate drop, particularly in Top-1, than removing in-context fusion; the Transformer PXRD encoder improves Top-1 and Top-20 match rates over the MLP.Source: Table 7 · p. 22, §B.2 · p. 22, Table 8 · p. 22

B.3 In-depth analysis of benchmark results

  • Across RRUFF and opXRD, Bragglite recovers most baseline Top-1 successes while solving additional cases; overlap is lower against XRDiff with element-set conditioning.The analysis attributes Bragglite’s higher aggregate match rate primarily to additional recoveries rather than losing cases solved by prior methods.Source: §B.3 · p. 22, Figure 8 · p. 23

B.4 Detailed two-phase recovery results; B.5 Benchmark results on MP-20-polymorph-split

  • The two-phase results separate dominant-, minor-, and all-phase recovery, while the polymorph-split evaluation uses MP-20-polymorph-split training and its held-out test set.All-phase recovery requires recovering both constituent phases; the supplied passages describe these evaluations but do not report their result values.Source: §B.4 · p. 22, §B.5 · p. 22, Table 9 · p. 23

C. Bragglite model details; C.1 Crystalite backbone

  • Bragglite retains Crystalite’s diffusion and EDM backbone, which represents atomic sites and the lattice as tokens and uses GEM to inject periodic geometry into attention.Atom types are fixed under exact-stoichiometry conditioning, but are denoised and decoded within the supplied element set under element-set conditioning.Source: C Bragglite model details · p. 24, §C.1 · p. 24

C.2 PXRD encoding and in-context conditioning

  • The PXRD encoder represents up to 128 peaks with peak features and Fourier position encoding, then uses a Transformer to produce context tokens jointly processed with crystal tokens during denoising.The encoder uses a [CLS] representation and eight learned-position context tokens; the context is reused across diffusion steps.Source: §C.2 · pp. 24–25

C.3 PXRD augmentation

  • Training augmentation perturbs reflection presence, position, and intensity, then adds profile-level broadening, background, and noise; independent intensity scaling is not a crystallographic preferred-orientation model.The augmentation pipeline renders perturbed reflections with randomized pseudo-Voigt shapes before profile-level processing.Source: §C.3 · pp. 25–26

C.4 Multiphase recovery pipeline

  • For two-phase recovery, XDecomposer produces ordered dominant- and minor-phase profiles, which Bragglite processes separately using the mixture element set and each phase’s oracle atom count.Bragglite must infer each phase’s elements and multiplicities; XRDiff receives phase-specific element sets, while MatterGen does not use the decomposed PXRD profiles.Source: §C.4 · pp. 27–28

D.1 Model configurations

  • The experimental configurations use separate Bragglite models for known-composition and element-set settings, with a 512-dimensional, 14-layer backbone and a four-layer, eight-head PXRD Transformer.The PXRD encoder has hidden dimension 256, and the backbone uses 16 attention heads.Source: §D.1 · p. 29
  • Fractional coordinates use independent axis-wise Fourier features at integer frequencies 1–32, mapped from 192 dimensions to the 512-dimensional backbone space.The mapping is 192 → 512 → 512 with a SiLU activation between linear layers.Source: §D.1 · p. 29
  • Noise conditioning encodes the transformed noise level into 256 sinusoidal features, duplicates the embedding across two noise-input slots, and maps the concatenated vector for adaLN-Zero modulation.The two slots form a 512-dimensional vector processed by a 512 → 512 → 512 MLP with SiLU activation.Source: §D.1 · p. 29
  • A single GEM computes head-specific biases from noisy coordinates, lattice, and noise level once, then reuses them across all 14 Transformer layers.The distance bias, edge-bias MLP, and noise gate are shared across layers.Source: §D.1 · p. 29
  • The element-set model orders atoms by symmetry orbit, electronegativity, and Wyckoff letter, then applies training-time orbit and within-orbit permutations without changing the structure or PXRD pattern.Sinusoidal atom-slot positional encodings are added after ordering and permutation; they are distinct from the fractional-coordinate Fourier encoding.Source: §D.1 · pp. 29–30
  • Separate linear heads predict atom types, coordinates, and lattice latents; EDM preconditioning yields continuous denoising outputs rather than categorical logits or coordinate velocities.The heads map token features 512 → 16 and 512 → 3, and lattice-token features 512 → 6.Source: §D.1 · p. 30

D.2 Training objective and optimization

The appendix specifies Bragglite’s diffusion objectives, optimization and sampling protocols, baseline configurations, computational costs, and qualitative examples.

D.2 Training objective and optimization

  • Known-composition models keep atom types fixed, while element-set models jointly denoise atom types, coordinates, and lattice parameters with setting-specific losses and noise distributions.The table summarizes loss weights and EDM noise-distribution parameters for the two settings.Source: §D.2 · p. 32, Table 12 · p. 32
  • Training budgets vary by corpus, and ablations use controlled settings, with independent training seeds for augmentation studies and fixed settings for representation and encoding studies.MP-20 and PXRD-Bench models use different step and batch-size budgets; ablations use 200K steps unless specified otherwise.Source: §D.2 · pp. 32–33

D.3 Sampling and checkpoint selection

  • Inference uses 150 stochastic Heun sampling steps to generate 20 candidates per pattern, while checkpoints are selected by validation Top-1 match rate.Checkpoint selection evaluates one candidate for each of 512 simulated validation structures every 10K steps.Source: §D.3 · p. 33, Table 16 · p. 34

D.4 Baseline configurations

  • Baseline training uses EMA evaluation checkpoints and validation-based learning-rate schedules, with separate patience and step limits for PXRD-Bench and MP-20 training.Baselines use Adam with zero weight decay; MP-20 training runs for at most 300K optimizer steps.Source: §D.4 · p. 34
  • Baseline configurations span composition-only generation and PXRD-conditioned models using profile, peak-feature, or Bragg-stick representations, with method-specific augmentation.DiffCSP receives no PXRD input, while XRDiff, RealPXRD-Solver, PXRDGen, and Crystalyze use different PXRD encodings or augmentations.Source: §D.4 · pp. 34–35
  • Baseline samplers retain each public implementation’s default procedure, ranging from 200-step Euler integration to 5,000-step annealed Langevin dynamics.DiffCSP, XRDiff, and PXRDGen use 1,000 predictor–corrector steps.Source: §D.4 · p. 35

D.5 Compute resources

  • The main Bragglite configurations’ training time and peak GPU memory are reported for runs on one RTX 3090 GPU.The referenced table reports training configuration and computational cost.Source: §D.5 · p. 35, Table 17 · p. 35

E Qualitative examples

  • Figure 9 compares generated structures and their simulated PXRD patterns with reference structures and experimental patterns for Skutterudite and Stolzite examples.The examples are from the RRUFF test split, and r denotes correlation between simulated and experimental profiles.Source: Figure 9 · p. 36, E Qualitative examples · p. 36

F Scope and limitations

The benchmark evaluates candidate generation rather than complete end-to-end structure determination, and it relies on oracle atom counts and limited labeled experimental PXRD data.

F Scope and limitations

  • Top-K structural match rate evaluates generated structures before refinement, so it is not equivalent to end-to-end success against measured patterns.Unmatched candidates may still refine to the correct structure, while matched candidates do not guarantee successful refinement.Source: F Scope and limitations · p. 37
  • The benchmark supplies primitive-cell atom counts, so element-set models infer elemental multiplicities but not total atom count.The two-phase setting supplies the count for each constituent phase; inferring counts jointly with structure is left as a more general formulation.Source: F Scope and limitations · p. 37
  • Limited measured PXRD patterns with reliable structural labels constrain experimental benchmark coverage and study of adaptation on measured data.The paper identifies larger datasets with reliable, traceable annotations as needed for broader evaluation and adaptation studies.Source: F Scope and limitations · p. 37
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