cond-mat.mtrl-sciAug 22, 2026
SaveCross-Temperature Defect Identification in Atomistic Simulations via Multi-Level Domain Alignment
Organizations: Rutgers Artificial Intelligence and Data Science (RAD) Collaboratory, Rutgers University, Piscataway, 08854, NJ, USA. · Department of Industrial and Systems Engineering, Rutgers University, Piscataway, 08854, NJ, USA. · Department of Materials Science and Engineering, Rutgers University, Piscataway, 08854, NJ, USA.
Abstract
Identifying atomic defects at elevated temperature is difficult because thermal fluctuations blur the local symmetry that both geometric heuristics and supervised classifiers rely on: trustworthy labels exist in low-temperature reference configurations, while the high-temperature regime where robust analysis matters most is effectively unlabeled. We cast this as a cross-temperature domain-shift problem and align the two domains at three levels: an equivariant denoiser at the input level, cross-temperature contrastive learning at the representation level, and a morphology-aware regularizer that steers predictions toward the compact geometry of physical defect structures. Because no atom-wise truth exists at temperature, we further introduce a label-free evaluation suite that scores predicted defect structures along five spatial and physics-based axes, enabling model assessment and selection without high-temperature labels. Near the melting point, the framework identifies vacancies and self-interstitial atoms across face-centered-cubic, body-centered-cubic, and hexagonal-close-packed iron systems with every interstitial localized and zero false detections in every vacancy system against Wigner-Seitz ground truth, with no high-temperature labels used in training. It sustains this fidelity on a million-atom, 2.5 ns trajectory, resolving single vacancy hops and complete Frenkel-pair recombination, and captures grain-boundary phase transformations in aluminum bicrystals, distinguishing two nucleation modes. Multi-level domain alignment thus offers a practical, label-efficient route to temperature-robust structural analysis of large-scale molecular dynamics.
Figures & tables
Figure 1: Defect detection by the full model (MLP with the contrastive and morphology terms) across all six systems at the melting temperature. Each panel shows one representative test snapshot (raw thermal positions); colored atoms are those the deployed pipeline flags as defective, gray atoms are a subsample of the remaining bulk. Top row: vacancy-containing systems; bottom row: self-interstitial-atom-containing systems. In every system the flagged atoms form a single compact cluster at the defect site, with no scattered false detections elsewhere in the box; the elongated shape of the interstitial clusters reflects the dumbbell geometry of the defect. Quantitative per-system results are given in Table 1 .
| System | Recall | Precision | F1 | FP |
|---|---|---|---|---|
| Panel A: Pristine crystals | ||||
| Perfect FCC | ||||
| Perfect BCC | ||||
| Perfect HCP | ||||
| Panel B: Vacancy systems | ||||
| FCC + vacancy | ||||
Table 1: Ground-truth evaluation of the deployed pipeline at the melting temperature. Detection is scored at the defect level against atom-tracked Wigner–Seitz occupancy labels: predicted defect objects (connected clusters of flagged atoms) are matched one-to-one to true defect sites by center-of-mass proximity (Methods), and we report object-level recall, precision, F1, and false objects per snapshot (FP). Entries are mean standard deviation across independent runs; ground truth is used for evaluation only, never for training. Ladder comparisons appear in Table 2 .
Figure 2: Temperature robustness for the vacancy task. (a, c, e) Physics-consistency score (agreement with the denoiser+PTM reference; Methods) as a function of homologous temperature for FCC, BCC, and HCP. (b, d, f) The same score at for the model ladder, from the geometric baseline (PTM) through descriptor-based classification (ACE + MLP), input-level denoising (+ denoiser), and the full model. The complete rung-by-rung dissection, including the intermediate + contrastive configuration, is given in Table 2 . Shaded bands denote one standard deviation across independent runs. Raw geometric and descriptor-only classification degrade sharply with temperature; denoising restores most of the reference consistency in FCC and BCC but much less in HCP, where the full model’s alignment terms are decisive.
| Structure | Model | Recall | Precision | F1 | FP |
|---|---|---|---|---|---|
| FCC | PTM | ||||
| ACE + MLP | |||||
| + denoiser | |||||
| + contrastive | |||||
| + morphology | |||||
| BCC | PTM |
Table 2: Ablation study at the melting temperature for vacancy-containing FCC, BCC, and HCP systems, scored against Wigner–Seitz ground truth at the defect-object level (protocol of Table 1 ). The rows form a ladder aligned with the three levels of the framework: the geometric baseline (PTM) and descriptor-based classification (ACE + MLP) operate on raw thermal coordinates; + denoiser adds input-level alignment; + contrastive adds representation-level alignment; and the full model (+ morphology) adds the prediction-level morphology term. For recall, precision, and F1, higher is better ( ); FP counts false predicted defect objects per snapshot, so lower is better ( ). Best results per group are in bold .
Figure 3: Latent-space organization across the model ladder (HCP vacancy system at the melting temperature). Each panel shows a 2-D UMAP embedding of the last-hidden-layer representations of one model: (a) plain MLP, (b) MLP with the contrastive term, (c) MLP with the contrastive and morphology terms. All three models are trained on identical noise-matched training data; only the training objective differs. All three operate on denoised coordinates, so panels (a)–(c) correspond to the + denoiser, + contrastive, and full-model rungs of Table 2 , respectively. Blue points are bulk atoms (training and test pooled), orange points are the defect examples seen during training, and red crosses are the defect atoms of the unseen MD test snapshot (labels from PTM on the denoised configuration). Class separation is the distance between the bulk and defect class centroids in the full latent space after per-dimension standardization and normalization (range 0–2). Adding the two alignment terms increases the separation monotonically ( ): in (a) the test defects lie in the contact region between the bulk and defect manifolds, whereas in (b) and (c) the classes form well-separated manifolds and the unseen test defects fall on the manifold spanned by the training defects, indicating that the learned separation transfers to the true MD test domain. The same trend appears in detection performance, where false positives at fixed recall drop from 3,639 (a) to 19 (b) to 0 (c). UMAP ( n_neighbors = 50, min_dist = 0.4) is used for visualization only: it preserves which points are neighbors, but distances in the 2-D layout carry no quantitative meaning, which is why the class-separation values quoted above are computed in the full latent space rather than measured from the plot.
Figure 4: The classifier tracks point defects through 2.5 ns of annealing with no retraining. All panels show classifier predictions only; no ground truth enters the figure. (a) Predicted defect objects (clusters of predicted atoms, shown as one point per defect) in the 1M-atom FCC Fe frame at ps, 20 ps, and 2.49 ns. The predicted counts (802/710/424 vacancies, 481/344/6 SIAs) track the Wigner–Seitz truth (796/707/423 and 433/307/0 defect groups) to within 1% for vacancies at every time. (b) Predicted vacancies in a Å slab at 10 ps (light) and 20 ps (dark); arrows connect each vacancy to its matched position one frame later, resolving individual lattice hops. (c) Displacement distribution of the matched vacancies (34 unchanged, 591 moved within ). (d) Predicted defect-object counts versus time: vacancies and SIAs disappear in near-equal numbers, and by 2.49 ns the model reports an SIA-free crystal ( residual objects, 36 atoms out of ), reproducing the complete Frenkel-pair recombination that the ground truth confirms ( vs. 453 surviving vacancies). Scored against the Wigner–Seitz truth ( core+halo), the pipeline finds 1054/1054 vacancies and 597/599 interstitials at 10 ps, with 15 residual false vacancy atoms per million.
Figure 5: A grain-boundary phase transformation captured in progress ( , ). Per-atom classification of boundary structure along the MD trajectory: frames are denoised, per-atom ACE descriptors computed, and boundary atoms classified by a classifier trained on the two minimized reference phases (orange = diamond, green = ladder). (a) Fractions of boundary atoms in each phase versus timestep. The diamond ladder transformation proceeds gradually over steps 87k–117k (shaded), with transient partial reversals. Below: edge-on maps at representative times, flanked by the reference structures (dashed outlines); counts and fractions above each map, with each trajectory map outlined in the color of its dashed time marker in the curve. (b) The mid-cell boundary viewed face-on (all its atoms in the y–z plane): conversion proceeds row by row — each new ladder row runs nearly the full width of the boundary within one frame interval, rows stack one after another, and the in-fill between them completes the plane. The simulation cell’s second boundary converts by the same mechanism, earlier; both show transient near-total retreats before locking in at 117k. Classifier validation: 0.944 leave-one-realization-out; clean references read at 99.8%/0.1%; results unchanged under an independently trained denoiser.
Figure 6: GB phase/complexion transformation in a different mode: avalanche conversion under load ( symmetric tilt, ). Layout and color convention as in Fig. 5 (orange = kite, green = L). (a) The kite→L transformation completes in a single sharp step between steps 48k and 51k (shaded). The curve ends before the high-temperature regime where the boundary thickens and per-atom labels become unreliable. (b) Face-on view of the mid-cell boundary: L-classified atoms remain small, scattered seeds through 48k (largest connected cluster 12 atoms at 18% converted), then the entire plane converts within one frame interval — a collective avalanche, in contrast to the sequential row-by-row conversion of Fig. 5 b. The boundary thickens upon transforming (192 → 288 atoms on this plane). Classifier validation: 0.996 leave-one-snapshot-out; clean references read at 100%/ 0%.
| Defect-structure metrics | |||||
| System | Coh. | Frag. | Comp. | Bound. | Phys. |
| Panel A: Vacancy systems (cross-temperature transfer) | |||||
| FCC + vacancy | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| BCC + vacancy | 0.90 | 0.87 | 0.97 | 0.79 | 0.98 |
| HCP + vacancy | 1.00 | 0.99 | 1.00 | 1.00 | 1.00 |
| Random | 0.78 | 0.09 | 0.81 | 0.57 | 0.06 |
Table 3: Defect structure fidelity across defect types. Each entry is the closeness between a defect structure metric evaluated on the predicted structure and on the PTM + denoiser reference, for coherence (Coh.), fragmentation (Frag.), compact geometry (Comp.), boundary (Bound.), and physics consistency (Phys.); higher is better, with 1 indicating exact agreement with the reference. Panels A and B use the full model, trained at and evaluated at the melting temperature; entries are means over independent MD seeds. Panel C evaluates the pipeline on the two bicrystals of Section 2.4 , GB1 (Fig. 6 ) and GB49 (Fig. 5 ), scoring the two competing phases of each boundary separately at its respective temperature, one trajectory each. Random rows report the same closeness for random permutations of each model’s per-atom defect probabilities (25 permutations, pooled within each panel). For the extended planar defects of Panel C, Comp. measures agreement of the defect-region shape statistics with the reference rather than compactness per se.
Figure 7: Overview of the framework. A labeled source domain (low-temperature references with bulk and defect classes, broadened by synthetic perturbations) and an unlabeled target domain (high-temperature snapshots) are aligned at three levels: an equivariant denoiser aligns the domains in input space, a contrastive objective on matched cold–hot atom pairs aligns their latent representations, and a morphology regularizer aligns target-domain predictions with the compact, coherent geometry of physical defect fields. All terms are optimized end-to-end through the shared encoder.
Appendix figures & tables1 asset
Supplementary material from the paper’s appendix.
Appendix
Figure 8: A denoiser trained only on perfect crystals erases interstitials; retraining it with defect examples fixes this. (a) Separation of the two atoms forming each interstitial dumbbell, in units of the nearest-neighbor distance , for the same 598 interstitial pairs identified by Wigner–Seitz analysis of the 1M-atom FCC Fe test frame ( , 3 GPa). In the raw MD frame the pairs sit near (green), matching the low-temperature training geometry (dashed line, 0.84). The crystal-trained denoiser reads the two-atoms-on-one-site compression as noise and merges each pair: the distribution collapses to a mean of (orange), largely below (shaded), where the pair is effectively a single atom on a normal lattice site. The defect-trained denoiser restores the physical geometry (blue, mean ). (b, c) One representative pair (raw separation ) after each denoiser, with the surrounding FCC lattice in gray. The crystal-trained model fuses the two atoms into what appears to be one (b, ); the defect-trained model preserves the dumbbell (c, ). The collapse in (b) is what made SIAs invisible to the downstream classifier; all classification results in this work use the defect-trained denoiser.
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