PhaseMatcher: Autoregressive Phase-Set Identification with Spectral Decomposition

Zhonglong Peng; Qiuliang Liu; Chang Chen; Geng Zhong; Qi Li; Lihong Wang; Lan Jiang; Shifeng Jin

cs.CEOct 5, 2026

PhaseMatcher: Autoregressive Phase-Set Identification with Spectral Decomposition

Authors: Zhonglong Peng, Qiuliang Liu, Chang Chen, Geng Zhong, Qi Li, Lihong Wang, Lan Jiang, Shifeng Jin

Organizations: Institute of Physics, Chinese Academy of Sciences · University of the Chinese Academy of Sciences · Xi’an Jiaotong University · Beijing University of Posts and Telecommunications

Abstract

Recovering complete phase sets from powder X-ray diffraction (PXRD) is challenging when weak-phase peaks overlap stronger signals. A natural strategy is to identify phases iteratively, removing the contribution of each identified phase from the observed pattern before predicting the next. However, even after a phase is correctly identified, misestimating its contribution can distort the residual and cause subsequent errors. We introduce PhaseMatcher, an autoregressive framework for complete phase-set identification with physics-guided spectral decomposition. After each phase prediction, PhaseMatcher re-estimates the contributions of all selected phases and the residual from the original observation and all selected reference patterns, accounting for physically plausible variation between reference patterns and the corresponding phase contributions in the observation. The resulting residual guides subsequent phase identification, while a separate stopping module determines when the phase set is complete. On synthetic mixtures and controlled mixtures constructed from measured single-phase patterns, PhaseMatcher improves complete-set identification over the evaluated baselines. On PhaseMix-135K, it also estimates contributions and residuals more accurately than scalar subtraction.

Figures & tables

Figure 1: Autoregressive construction of a phase set. (a) A language model predicts one token at a time until STOP. (b) PhaseMatcher predicts one phase at a time until STOP, updating the residual after each phase prediction.

Figure 2: PhaseMatcher identifies phases while jointly re-estimating contributions. (a) Identification and contribution re-estimation loop. (b) Sequential subtraction fixes each earlier contribution, while joint re-estimation recomputes all selected contributions.

Figure 3: Reference-conditioned spectral decomposition. (a) Physical-parameter prediction. (b) Reference-conditioned allocation of observed intensity to phase contributions and the residual.

(a) PhaseMix-135K
Method	Exact-set@1 (%)	Phase recall (%)	Count acc. (%)	Exact-set@10 (%)
PhaseDifformer	4.06	34.90	44.33	-
Iterative database matching	13.85	49.98	24.39	15.86
XDecomposer	14.63	51.10	34.95	18.52
PhaseMatcher, scalar Greedy	67.98	88.22	87.59	-
PhaseMatcher, scalar Beam	69.57	88.47	86.07	88.79

Table 1: Complete-set identification on both benchmarks. For iterative matching, Exact-set@10 uses Beam-10; the other metrics use Greedy. A dash denotes an unreported metric.

(a) PhaseMix-135K
Exact-set@1 / Phase recall (%)	1 phase	2 phases	3 phases	4 phases
PhaseDifformer	24.18 / 72.43	7.77 / 47.18	0.28 / 31.08	0.01 / 22.26
Iterative database matching	54.21 / 81.22	26.44 / 60.43	8.19 / 47.92	1.70 / 38.49
XDecomposer	72.17 / 74.67	29.21 / 59.21	5.23 / 49.47	0.00 / 42.37
PhaseMatcher, scalar Greedy	93.80 / 93.96	84.09 / 91.70	69.28 / 88.50	52.50 / 84.84
PhaseMatcher, scalar Beam	95.72 / 95.79	86.64 / 93.06	71.75 / 89.31	52.88 / 83.72

Table 2: Identification by phase count on both benchmarks.

Figure 4: Contribution and residual quality by phase count. (a) Automatic Greedy predictions at termination. (b) Both methods receive all correct phases. Residual targets subtract the correctly selected true contributions from the observation and clip at zero; both methods use the same target in (b).

Method	Cosine similarity $\uparrow$	MAE ( $10^{-4}$ ) $\downarrow$
PhaseDifformer	0.4683	64.6040
XDecomposer	0.6319	32.8429
PhaseMatcher, scalar Greedy	0.8807	32.4846
PhaseMatcher, scalar Beam	0.8701	32.5473
PhaseMatcher, Greedy	0.9735	3.4209
PhaseMatcher, Beam	0.9765	3.0280

Table 3: Automatic contribution reconstruction on PhaseMix-135K. Beam uses the first-ranked path.

Figure 5: Physics guidance across sequential updates. (a–c) Two-, three-, and four-phase samples with correct phases supplied. Contribution scores average the selected phases within each sample; open markers denote the complete set.

Appendix figures & tables53 assets

Supplementary material from the paper’s appendix.

Appendix

Quantity	PhaseMix-135K	RRUFF mixtures	Convention
Reference IDs	135,258	740	Full candidate library at inference
Training mixtures	12,135,258	100,000	Observation realizations 0, 1, 2
Validation mixtures	100,000	7,400	Observation realization 3
Test mixtures	100,000	7,400	Observation realization 4
Test $K=1$	10,000	740	One selected ID
Test $K=2$	20,000	1,480	Two distinct IDs

Appendix

Table 4: Reference libraries and mixture manifests. Realizations index observation profiles of the same library ID.

Level	Parameter	Distribution / setting	Operation
Reference	Gaussian FWHM	$0.10^{\circ}$	Clean theoretical profile rendering
Phase	Wavelength in perturbation formulas	$1.5406$ Å	Scherrer broadening and thermal attenuation
Phase	Crystallite size	$U[80,250]$ nm	Gaussian broadening; Scherrer width at $2\theta=45^{\circ}$
Phase	Isotropic strain	$U[-0.0015,0.0015]$	Bragg-law coordinate warp
Phase	Thermal root-mean-square displacement	$U[0.01,0.10]$ Å	Angle-dependent intensity attenuation
Phase	Relative-intensity envelope	Six anchors from $U[-0.1,0.1]$	Linear interpolation of multiplicative modulation

Appendix

Table 5: Data-construction parameters.

U[a,b]

denotes independent uniform sampling. Peak-relative quantities use the maximum of the mixture before background and noise.

Array	Shape	Type	Meaning
Clean patterns.npy	$N\times L$	float32	Candidate reference spectra
Perturbed patterns.npy	$N\times R\times L$	float16	Five observation profiles per ID
entry.npy	$N$	Unicode	Record IDs in reference-row order
axis_two_theta.npy	$L$	float32	Angular grid in degrees
$s$ _ids.npy	$M\times 4$	int32	Selected library-row IDs
$s$ _weights.npy	$M\times 4$	float32	Mixture weights

Appendix

Table 6: PhaseMix-135K arrays on disk. Clean and perturbed banks use separate directories. A split prefix

s

is train , val , or test .

Field	Batched shape	Meaning / use
mixture	$B\times 1\times L$	Max-normalized observation
phase_ids	$B\times 4$	True IDs in decreasing-weight order; padding $-1$
phase_weights	$B\times 4$	Mixture weights; padding 0
counts	$B$	True phase count $K$
targets	$B\times 5$	$K$ phase IDs, a termination marker, then padding $-1$
reference_patterns	$B\times 4\times 1\times L$	Clean references for the true history

Appendix

Table 7: Joint-training batch fields. Common-scale spectra share the observation’s maximum as denominator. True contributions and residuals supply supervision; the Phase Head receives a model-generated residual.

Module	Configuration
Spectrum encoder: convolutions	Four stride-two layers; kernels 15, 11, 7, 5; channels 256, 512, 512, 512; projection to width 512
Spectrum encoder: Transformer	Learned positional embeddings; 3 layers; 8 heads; feed-forward width 2,048; dropout 0.05
Single-phase classifier	Learned attention pooling; normalized feature and classifier rows; learned logit scale; $135{,}258\times 512$ class matrix
Phase Head / STOP Head	6 / 2 Transformer decoder layers; width 512; 8 heads; feed-forward width 2,048; dropout 0.05
Decomposition encoders	Separate observation and reference pyramids; input channels $x$ and $\log(1+9x)/\log 10$ ; channels 24, 48, 96, 192
Local correlation	One $8\times 21$ cosine-similarity table per observation–reference pair: 8 angular regions and offsets $-10$ to $10$ bins; output $B\times t\times 8\times 21$

Appendix

Table 8: Network configuration. The shared spectrum encoder produces 219 tokens of width 512 from a 3,501-point spectrum. The classifier size below refers to PhaseMix-135K.

Figure 6: Dual-head network architecture. The upper panel shows the shared encoder and each head’s inputs and outputs. The lower panels expand the decoder layers into causal self-attention, cross-attention, and feed-forward blocks.

Term $\mathcal{L}_{m}$	$\alpha_{m}$	Definition
Component intensity	1	Weighted pointwise SmoothL1 between $\widehat{c}_{k}$ and $y_{k}^{}$ ; transition parameter 0.02; point weight $0.05+\sqrt{\bar{y}_{k}^{}}$ . Padding masks exclude absent references.
Component shape	0.1	Mean cosine distance between $\widehat{c}_{k}$ and $y_{k}^{*}$ over valid references with nonzero target norm.
Total selected-phase intensity	2	Weighted SmoothL1 between $\widehat{u}$ and $u^{}$ , with transition parameter 0.02 and point weight $0.05+\sqrt{\bar{u}^{}}$ .
Source allocation	1	Kullback–Leibler divergence from target fractions $(y_{1}^{},\ldots,y_{t}^{},r^{})/x$ to predicted fractions. Point weight $0.05+\sqrt{\bar{x}}+2\sqrt{\bar{u}^{}}$ ; bins with $x\leq 10^{-8}$ have zero weight.
Integrated selected-phase intensity	0.1	Mean $\left\|\sum_{\ell}\widehat{u}_{\ell}-\sum_{\ell}u_{\ell}^{}\right\|/\max(\sum_{\ell}u_{\ell}^{},0.01)$ .
Residual shape	0.2	Cosine distance between max-normalized $\widehat{r}$ and $r^{*}$ .

Appendix

Table 9: Spectral decomposition loss terms and internal weights. All intensity comparisons use the common observation scale.

Setting	Single-phase pretraining	Multiphase joint training	Joint training with STOP
Trainable modules	Spectrum encoder and classifier	Encoder, phase table, Phase Head, decomposition	Stage-two modules and STOP Head
Initialization	New model	Single-phase encoder and class matrix; new Phase Head and decomposition parameters	Final stage-two weights
Objective	Phase cross-entropy	$\lambda_{\mathrm{phase}}\mathcal{L}_{\mathrm{phase}}+\lambda_{\mathrm{decomp}}\mathcal{L}_{\mathrm{decomp}}$	$\lambda_{\mathrm{phase}}\mathcal{L}_{\mathrm{phase}}+\lambda_{\mathrm{stop}}\mathcal{L}_{\mathrm{stop}}+\lambda_{\mathrm{decomp}}\mathcal{L}_{\mathrm{decomp}}$
Optimizer	AdamW	AdamW	Fresh AdamW
Initial learning rate	$2\times 10^{-4}$	$5\times 10^{-5}$ in both parameter groups	$5\times 10^{-5}$ in both parameter groups
Weight decay	0.01	$10^{-4}$	$10^{-4}$

Appendix

Table 10: PhaseMix-135K three-stage training. Outer loss weights are all 1. Batch-size products give GPU count, per-GPU batch size, and accumulation steps where applicable.

Setting	PhaseMix-135K	RRUFF mixtures
Phase-stage updates / batch size	120,000 / 128	1,750 / 128
STOP-stage updates / batch size	40,000 / 224	1,250 / 128
Checkpoint for STOP / evaluation	Final phase / final STOP	Final phase / final STOP

Appendix

Table 11: Scalar PhaseMatcher optimization. Both datasets use AdamW, weight decay

10^{-4}

, initial learning rate

5\times 10^{-5}

, and BF16 mixed precision.

	Input: observations $x_{i}$ , ordered true-ID sequences $J_{i}$ of length $K_{i}$ , true contributions, and stage $s\in\{2,3\}$ .
1	Sample one candidate set containing all batch-positive IDs and negative proposals.
2	Initialize phase-loss list $A$ , STOP-loss list $T$ , weighted decomposition sum $d=0$ , and prefix count $q=0$ .
3	For $t=0,\ldots,\max_{i}K_{i}$ :
4	Select samples $I_{t}=\{i:K_{i}\geq t\}$ ; let $H_{i}$ contain the first $t$ IDs of $J_{i}$ (the empty sequence when $t=0$ ).
5	If $t=0$ , set each residual query $r_{i}=x_{i}$ .
6	If $t>0$ : compute $(\widehat{\mathbf{c}}_{i},\widehat{r}_{i})=D(x_{i},P_{H_{i}})$ and set $r_{i}=\widehat{r}_{i}$ .

Appendix

Algorithm 1 One joint-training batch (stage two or three)

	Input: normalized observation $x$ , full reference library, maximum count $K_{\max}=4$ , and width $W$ (1 for Greedy; 10 for Beam).
	State: an ordered history $H$ , its residual query $r$ , and cumulative action log probability $s$ .
1	Initialize active paths $A=\{((),x,0)\}$ and completed paths $F=\varnothing$ .
2	While $A$ is nonempty:
3	Initialize next active candidates $C=\varnothing$ .
4	For each $(H,r,s)\in A$ :
5	Compute phase logits from $r,H$ and the STOP logit from $x,H$ .

Appendix

Algorithm 2 Greedy and Beam inference with spectral decomposition

Figure 7: (a) Greedy follows one path. (b) Beam expands multiple paths. Solid and dashed arrows denote retained and discarded branches; this illustration uses width three.

Setting	PhaseMix-135K	RRUFF mixtures
Optimizer updates	106,000	13,380 (30 epochs)
Global batch size	1,024	224
Peak learning rate	$2\times 10^{-4}$	$5\times 10^{-5}$
Warmup updates	2,120	429
Encoder	Frozen	Fine-tuned
Selected update	106,000	13,380

Appendix

Table 12: XDecomposer decomposition training and RRUFF fine-tuning.

Dataset	Retrieval	Threshold	Exact-set@1	Phase recall	Count acc.
PhaseMix-135K	Reranked	0.800	11.015	46.180	46.392
	Cosine	0.800	13.904	53.340	46.179
	Cosine	0.850	14.572	51.850	38.569
	Cosine	0.870	14.680	51.101	34.952
	Reranked	0.870	11.652	44.232	35.092
RRUFF	Cosine	0.800	14.608	59.303	44.986

Appendix

Table 13: XDecomposer configuration comparison on the validation sets (%).

Dataset	Retrieval, threshold	Exact-set@1	Phase recall	Count acc.	Exact-set@10
PhaseMix-135K	Reranked, 0.800	10.87	46.16	46.22	14.15
	Cosine, 0.870 (selected)	14.63	51.10	34.95	18.52
RRUFF	Cosine, 0.800	14.49	59.54	44.47	17.36
	Cosine, 0.868 (selected)	15.46	56.52	35.27	18.11
	Reranked, 0.800	12.07	52.73	45.00	16.86

Appendix

Table 14: XDecomposer test configurations (%). Selected rows supply the main identification tables.

Phase count	Paper component Top-1	Our component Top-1	Phase recall	Exact-set@1
2	$65.31\pm 2.62$	78.41	66.79	34.32
3	$53.49\pm 1.48$	61.17	53.66	1.26
4	$41.90\pm 1.74$	51.96	46.54	0.03

Appendix

Table 15: RRUFF component retrieval and automatic set recovery (%).

Module	Updates	Peak LR	Val. interval	Selected step
Unguided predictor	213,000	$1.5\times 10^{-4}$	2,000	142,000 / 78,000
Guided predictor	213,000	$1.5\times 10^{-4}$	2,000	78,000 / 98,000
Confidence estimator	7,100	$10^{-5}$	500	7,100 / 7,100

Appendix

Table 16: PhaseDifformer training. Budgets apply to each dataset; the last column lists selected steps for PhaseMix-135K / RRUFF. All intervals count optimizer updates.

Item	Setting
Observation generation	Seeds: 20260826 for PhaseMix-135K and 20260909 for RRUFF. PhaseMix-135K shares mixture identities and weights across baselines; differing observation seeds produce different noise realizations.
Gaussian representation	Filter-first NNLS targets; FWHM $0.125^{\circ}$ on PhaseMix-135K and $0.15^{\circ}$ on RRUFF, shared by target fitting and inference rendering.
Normalization	Observed dense-spectrum maximum, rather than a ground-truth coefficient scale. Remaining coefficients are rendered before forming subsequent peak-height conditions.
Peak augmentation	Position standard deviation $0.1^{\circ}$ follows the paper, rather than the released configuration’s $1.0^{\circ}$ ; relative-height standard deviation is 0.1.
Confidence objective	Noise error plus $0.005$ candidate BCE over all five candidates; the released configuration uses zero diffusion weight and its top-candidate path.
Diffusion and clipping	The denoising diffusion probabilistic model (DDPM) uses all 1,000 indices for training and sampling, $0,\ldots,999$ . Generated coefficients are nonnegative, without a peak-height upper bound.

Appendix

Table 17: PhaseDifformer coefficient-target protocol and benchmark adaptations.

Dataset	Protocol	Exact-set@1 (%)	Phase recall (%)	Count acc. (%)
PhaseMix-135K	Peak height	4.84	29.09	38.21
	Coefficient (main)	4.06	34.90	44.33
RRUFF mixtures	Peak height	8.27	42.51	27.46
	Coefficient (main)	2.12	47.04	37.51

Appendix

Table 18: PhaseDifformer protocol comparison. The coefficient-target protocol supplies all main-text results.

Phase count	1	2	3	4
Count accuracy (%)	98.78	90.41	64.50	43.65
Exact-set@10 (%)	100.00	94.80	81.04	63.99

Appendix

Table 19: Additional Scalar Beam-10 metrics on RRUFF mixtures.

Cosine / MAE ( $10^{-4}$ )	1 phase	2 phases	3 phases	4 phases
PhaseDifformer	0.5464 / 31.47	0.5061 / 49.37	0.4548 / 65.94	0.4400 / 79.50
XDecomposer ( $\tau=0.8$ )	0.9270 / 10.66	0.7428 / 24.98	0.6239 / 32.27	0.5597 / 39.50
XDecomposer ( $\tau=0.870$ )	0.9342 / 13.74	0.7323 / 27.56	0.6062 / 33.99	0.5253 / 39.40
PhaseMatcher, scalar Greedy	0.9233 / 49.99	0.9052 / 36.06	0.8828 / 30.62	0.8561 / 27.72
PhaseMatcher, scalar Beam	0.9239 / 50.20	0.9050 / 36.11	0.8754 / 30.64	0.8352 / 27.78
PhaseMatcher, Greedy	0.9969 / 2.63	0.9848 / 3.20	0.9740 / 3.73	0.9616 / 3.50

Appendix

Table 20: Automatic contribution reconstruction by phase count on PhaseMix-135K.

Dataset	Test mixtures	Cosine similarity $\uparrow$	MAE ( $10^{-4}$ ) $\downarrow$
PhaseMix-135K	100,000	0.4683	64.6040
RRUFF mixtures	7,400	0.4189	125.7769

Appendix

Table 21: PhaseDifformer automatic contribution reconstruction.

Automatic Greedy, at termination
Method	Phases	Contribution		Residual
		Cosine	MAE	Cosine	MAE
Scalar	1	0.9233	49.9854	0.3770	50.8714
Scalar	2	0.9052	36.0601	0.3724	67.4130
Scalar	3	0.8828	30.6208	0.3719	79.6533
Scalar	4	0.8561	27.7196	0.3714	89.0785

Appendix

Table 22: Contribution and residual reconstruction by phase count. Each setting includes 10,000, 20,000, 30,000, and 40,000 samples for one through four phases. MAE is in units of

10^{-4}

Figure 8: Automatic Greedy trajectories for a selected two-phase sample. (a) Library references. (b,c) A’s first and final contributions. (d) The residual after A. (e) Terminal residuals, shown against the common complete-set background/noise target. The local windows in (a–c) use unchanged reference or observation scales. Neither method receives the mixture’s phase identities or phase count.

History	Update	Cosine similarity	MAE ( $10^{-4}$ )
Incomplete	Scalar	0.6634	65.6803
Incomplete	PhaseMatcher	0.9928	5.1114
Complete	Scalar	0.3508	75.8484
Complete	PhaseMatcher	0.9770	3.8705

Appendix

Table 23: Residual reconstruction under identical true-phase histories.

Figure 9: Residual quality with the same correct phases supplied sequentially. (a) MAE on a shared logarithmic scale. (b) Cosine similarity on a shared linear scale. Each column follows a fixed group of two-, three-, or four-phase samples; points are test-set means and open markers denote the complete set.

$K$	$t$	Samples	Scalar		PhaseMatcher
			Cosine	MAE ( $10^{-4}$ )	Cosine	MAE ( $10^{-4}$ )
1	1	10,000	0.3514	50.1147	0.9870	2.0867
2	1	20,000	0.6855	51.0897	0.9962	3.3403
2	2	20,000	0.3487	66.0129	0.9806	3.1298
3	1	30,000	0.8002	51.5527	0.9982	4.1955
3	2	30,000	0.5347	71.7535	0.9902	4.7662

Appendix

Table 24: Residual reconstruction by total phase count

K

and true-history length

t

. MAE uses the original observation scale.

Figure 10: Joint re-estimation of an initially misallocated peak in a selected PhaseMix test sample under the true history A, then A/B. (a) Reference spectra. (b) Initial and re-estimated A contributions. (c) B contributions after selection. Vertical dotted lines mark

26.96^{\circ}

; reference and contribution intensities retain their respective original scales.

Figure 11: Initial over-allocation and subsequent joint re-estimation in a selected PhaseMix sample. (a) References. (b,c) Initial A estimates and residuals. (d,e) Joint A and B estimates after adding B. (f) Scalar’s B estimate when the first removal uses true A. Dotted lines mark

55.72^{\circ}

. References retain their library scale; contributions and residuals retain the observation scale.

	Contribution		Residual
Update	Cosine $\uparrow$	MAE $\downarrow$	Cosine $\uparrow$	MAE $\downarrow$
Sequential scalar	0.9202	40.5222	0.5336	65.0384
Joint scalar	0.8909	51.3037	0.5330	64.7952
Joint scalar, proportional clipping	0.9222	39.9904	0.5330	64.7952
PhaseMatcher	0.9983	3.6447	0.9874	4.2546

Appendix

Table 25: Correct-phase reconstruction on the 1,000-sample subset. MAE is in units of

10^{-4}

Update	Step 1	Step 2	Step 3	Step 4
Sequential scalar	51.6661	74.1393	82.7750	84.8074
Joint scalar	51.6661	73.5152	82.2667	84.9592
PhaseMatcher	4.8220	5.8917	6.1350	4.3864

Appendix

Table 26: Residual MAE (

10^{-4}

) over the 250 four-phase samples.

Model	Search	Exact-set (%)		Phase recall (%)	Contribution
		@1	@10		Cosine	MAE ( $10^{-4}$ )
Without physics guidance	Greedy	76.79	-	91.37	0.9725	3.7602
Full model	Greedy	77.15	-	91.50	0.9735	3.4209
Without physics guidance	Beam-10	81.36	94.49	93.31	0.9738	3.4133
Full model	Beam-10	81.98	94.73	93.59	0.9765	3.0280

Appendix

Table 27: Physics-guidance ablation on PhaseMix-135K. Contribution scores use the first-ranked predicted set.

		Contribution		Residual
History	Physics guidance	Cosine	MAE	Cosine	MAE
Incomplete	Without	0.9988	5.3124	0.9895	6.5233
Incomplete	With	0.9989	4.4417	0.9928	5.1121
Complete	Without	0.9964	3.1938	0.9734	4.0841
Complete	With	0.9966	2.8534	0.9770	3.8709

Appendix

Table 28: Correct-phase reconstruction with and without physics guidance, averaged over all test prefixes of each type. MAE is in units of

10^{-4}

		Contribution		Residual
$K$	Step	Cosine	MAE	Cosine	MAE
1	1	1.0000 / 1.0000	2.7705 / 2.4017	0.9836 / 0.9870	2.4554 / 2.0867
2	1	0.9997 / 0.9998	4.3979 / 3.5523	0.9950 / 0.9962	4.1862 / 3.3406
2	2	0.9977 / 0.9977	3.2255 / 2.8268	0.9750 / 0.9806	3.6667 / 3.1297
3	1	0.9995 / 0.9997	5.4680 / 4.3406	0.9975 / 0.9982	5.3233 / 4.1959
3	2	0.9988 / 0.9987	4.5791 / 3.9769	0.9861 / 0.9902	6.0940 / 4.7667

Appendix

Table 29: Contribution and residual reconstruction. Metric pairs: without physics guidance (left), full model (right).

K

denotes phase count; MAE uses units of

10^{-4}

Figure 12: Newly added phase contributions with correct phases supplied. (a–c) Two-, three-, and four-phase test samples. Points are sample means; open markers denote the last update. Cosine axes are zoomed.

Figure 13: Weakest-phase identification on PhaseMix-135K. (a–c) Recall by weakest-phase intensity share. (d–f) Recall by overlap tertile among mixtures with weakest-phase share below 5%. Columns correspond to two-, three-, and four-phase mixtures. Points show recall with 95% mixture-bootstrap confidence intervals; some intervals are smaller than the markers. Group sizes appear in Table 30 .

(a) Weakest-phase intensity share
$K$	Group	$n$	Database	PhaseDifformer	XDecomposer	Scalar	PM
2	$<5\%$	2,688	0.26	2.42	4.32	62.39	75.37
	$5$ – $10\%$	2,353	2.85	8.50	18.49	85.81	88.65
	$10$ – $20\%$	4,098	17.86	11.01	26.96	87.92	90.04
	$\geq 20\%$	10,861	41.26	7.71	38.54	87.63	89.55
3	$<5\%$	10,614	0.10	0.05	0.63	51.74	69.52

Appendix

Table 30: Exact-set@1 (%) in the groups of Figure 13 . Database denotes iterative database matching and PM denotes PhaseMatcher. The two PhaseMatcher variants and database matching use Greedy.

Phase count	1	2	3	4
Time (s/mixture)	0.0250	0.0401	0.0551	0.0685

Appendix

Table 31: Single-GPU Greedy inference time on PhaseMix-135K.

Figure 14: Two-phase RRUFF-based mixture 956. Weakest-phase share: 3.39%; overlap: 0.108.

Figure 15: Two-phase RRUFF-based mixture 1571. Weakest-phase share: 35.31%; overlap: 0.013.

Figure 16: Two-phase RRUFF-based mixture 2098. Weakest-phase share: 43.63%; overlap: 0.481.

Figure 17: Three-phase RRUFF-based mixture 2597. Weakest-phase share: 11.02%; overlap: 0.286.

Figure 18: Three-phase RRUFF-based mixture 2686. Weakest-phase share: 20.10%; overlap: 0.033.

Figure 19: Three-phase RRUFF-based mixture 2912. Weakest-phase share: 2.97%; overlap: 0.081.

Figure 20: Three-phase RRUFF-based mixture 3892. Weakest-phase share: 15.40%; overlap: 0.264.

Figure 21: Three-phase RRUFF-based mixture 4009. Weakest-phase share: 2.97%; overlap: 0.122.

Figure 22: Three-phase RRUFF-based mixture 4364. Weakest-phase share: 11.74%; overlap: 0.086.

Figure 23: Four-phase RRUFF-based mixture 4449. Weakest-phase share: 3.84%; overlap: 0.168.

Figure 24: Four-phase RRUFF-based mixture 4845. Weakest-phase share: 7.95%; overlap: 0.077.

Figure 25: Four-phase RRUFF-based mixture 5418. Weakest-phase share: 9.34%; overlap: 0.112.

Figure 26: Four-phase RRUFF-based mixture 5805. Weakest-phase share: 0.34%; overlap: 0.080. Beam misses ID 39 and adds ID 550.

Figure 27: Four-phase RRUFF-based mixture 5941. Weakest-phase share: 2.16%; overlap: 0.071.

Figure 28: Four-phase RRUFF-based mixture 5984. Weakest-phase share: 4.57%; overlap: 0.102.

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May 7, 2026cs.AI

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

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

Hanyu Gao, Bin Cao, Yunyue Su +2

New Laboratory of Pattern Recognition (NLPR), Institute of Automation, Chinese Academy of Sciences (CASIA) · School of Advanced Interdisciplinary Sciences, University of Chinese Academy of Sciences · Guangzhou Municipal Key Laboratory of Materials Informatics, The Hong Kong University of Science and Technology (Guangzhou) +1

Powder X-Ray Diffraction Decomposition

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Oct 6, 2026cond-mat.mtrl-sci

A self-learning scientific agent for X-ray diffraction

A central challenge for scientific agents is to turn analytical experience into reusable expertise grounded in physical evidence. Here we introduce Gan Jiang, a self-learning agent for powder X-ray diffraction built on a diffraction-analysis ecosystem we developed: XMatcher, XQueryer, XDecomposer and WPEM. Together, these engines span phase identification, multiphase decomposition and physics-constrained whole-pattern modelling. Gan Jiang converts analytical experience into executable skills by diagnosing failures, revising skill instructions and code, and validating revisions before reuse, without retraining the language model or changing the underlying physical models. Skills selected using development data and frozen before held-out evaluation achieve higher refinement scores than the original expert-designed skills across FullProf, GSAS-II and PyWPEM. The agent resolves strongly overlapping reflections, quantifies a five-phase ancient Egyptian cosmetic, tracks lattice evolution in an operating battery and compares atomic configurations in a disordered oxide catalyst. On DeltaXRDbench, it leads the evaluated methods in single- and multiphase identification across simulated and experimental data. Without supplied composition, single-phase top-1 accuracies reach 96.30%, 81.78% and 40.83% on MP500, RRUFF and opXRD, respectively, compared with 58.00%, 58.47% and 26.45% for the strongest comparator. These results demonstrate how an integrated scientific tool ecosystem can support agents that extract structural knowledge from measurements while accumulating validated analytical expertise that transfers to new samples.

Bin Cao, Huichi Zhou, Runyu Yang +7

The Hong Kong University of Science and Technology (Guangzhou), China · University College London, United Kingdom · AI Lab, The Yangtze River Delta, China +1

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Jun 12, 2026cond-mat.mtrl-sci

XRDiff: Crystal Structure Prediction from Powder X-Ray Diffraction Data Using Diffusion Models

Determining the crystal structure of a material from its powder X-ray diffraction (PXRD) pattern is a central challenge in materials science. PXRD is an accessible and widely used characterization technique, yet recovering the atomic structure from diffraction data requires solving an underdetermined inverse problem due to the loss of phase information. Generative modeling can provide a prior over atomic structure and learn the mapping from PXRD patterns to crystal structures via simulated structure-spectrum pairs. We present XRDiff, a diffusion model that recovers crystal structures from PXRD given either the stoichiometry or, in a more challenging setting, the elemental constituents and total number of atoms in the unit cell. We evaluate on datasets where each stoichiometry has multiple polymorphs and all polymorphs of a given composition are held out together, ensuring that high performance reflects genuine use of the diffraction signal. XRDiff achieves strong structure recovery rates on simulated benchmarks, indicating that the model learns a spectrum-to-structure mapping precise enough to differentiate between polymorphs. To address generalization to experimental data, we compare a full-spectrum encoding against an encoding based on peak descriptors. The peak-based encoding generalizes substantially better, outperforming even a model trained on full spectra with augmentations fitted to the experimental noise distribution. These results demonstrate that representations robust to the noise and artifacts present in real-world PXRD offer a practical and scalable path toward closing the simulation-to-experiment gap, enabling zero-shot crystal structure solution from experimental PXRD with full or partial chemical composition input.

Nofit Segal, Mingda Li, Benjamin Kurt Miller +1

Department of Materials Science and Engineering, MIT, Cambridge, MA, USA. · Department of Nuclear Science and Engineering, MIT, Cambridge, MA, USA. · FAIR, Meta, San Francisco, CA, USA.

Powder X-Ray Diffraction Crystal Structure Prediction Diffusion Models Spectral

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