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Cross-Temperature Defect Identification in Atomistic Simulations via Multi-Level Domain Alignment
Yating Fang, Jungmin Kim, Qian Qian Zhao, Pallavi Biswas, Joshua M. Gonjon, Ryan B. Sills, Ahmed Aziz Ezzat
TL;DR
Reliable defect identification near melting is hindered by thermal distortion and the lack of trustworthy high-temperature labels. The paper treats this as cross-temperature domain adaptation, combining denoising, contrastive representation alignment, and morphology-aware prediction regularization with label-free evaluation. Near melting, it reports reliable vacancy and interstitial identification across three iron lattices, including zero false vacancy detections and complete interstitial localization against Wigner–Seitz ground truth.
Problem
High-temperature defect identification lacks trustworthy labels while thermal motion blurs the local structures used by geometric heuristics and classifiers.
Method
The framework aligns low- and high-temperature domains through an equivariant denoiser, cross-temperature contrastive learning, and morphology-aware regularization, supplemented by five-axis label-free evaluation.
Results
The framework identifies vacancies and self-interstitial atoms near melting across FCC, BCC, and HCP iron, with every interstitial localized and zero false detections in vacancy systems against Wigner–Seitz ground truth.
Takeaways & Limitations
Multi-level domain alignment provides a label-efficient route to temperature-robust structural analysis of large-scale molecular-dynamics simulations.
Takeaways & Limitations
Strict accuracy evaluation is tied to known parent-lattice registries; beyond that regime, the suite is reference-relative rather than ground-truth accuracy.
Abstract
from arXiv · showhide
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.
1 Introduction
Reliable defect identification becomes difficult near melting because thermal motion blurs local structural signatures and trustworthy labels are unavailable at high temperature. The paper addresses this cross-temperature problem with explicit defect classes, multi-level alignment, and label-free evaluation.
- 1 Introduction: Near melting, thermal motion erodes descriptor-space class boundaries, making defects difficult to distinguish from distorted but intact neighborhoods.Classical CNA, centrosymmetry, bond-order, and PTM methods depend on symmetry, tolerances, or template similarity and are sensitive to thermal motion and disorder.
- 1 Introduction: High-temperature labels are least trustworthy, creating a domain-shift problem for transferring knowledge from confidently labeled low-temperature structures.The paper also asks how to test predictions when elevated-temperature labels do not exist.
- 1 Introduction: Existing supervised approaches improve high-temperature classification but assume target-temperature labels or treat defects as outliers rather than explicit classes.The proposed framework extends this setting across temperatures while making defects a class of interest.
- 1 Introduction: The framework combines score-based denoising, cross-temperature contrastive alignment, and morphological regularization to address thermal noise, domain mismatch, and implausible defect geometry.Denoising is used at the input level, while alignment and morphology terms address remaining representation and prediction challenges.
- 1 Introduction: The label-free evaluation suite scores predicted structures using five complementary spatial and physics-based axes, while ground truth is used where Wigner–Seitz analysis is available.The paper demonstrates the pipeline across near-melting defect systems, large-scale trajectories, and extended-defect phases.
2 Results
Across near-melting point-defect systems and larger trajectories, the framework transfers low-temperature supervision to thermally disordered structures while preserving defect localization and tracking dynamics. It also distinguishes two grain-boundary transformation modes using spatially resolved phase classification.
- Defect identification near melting: The full model flags one compact defect cluster at the correct site in all six near-melting FCC, BCC, and HCP systems.Vacancy clusters are roughly isotropic, while elongated SIA clusters preserve dumbbell geometry.
- Defect identification near melting: Object-level evaluation finds perfect FCC and HCP vacancy detection, BCC F1 of 0.90, zero false vacancy objects, and SIA recall of 1.00 in all lattices.SIA F1 is 0.92 because occasional small spurious clusters remain; ground truth is used only for evaluation.
- Temperature robustness and alignment: At melting, the full model reaches physics-consistency scores of 1.00, 0.98, and 1.00 for FCC, BCC, and HCP, whereas denoising alone reaches 0.95, 0.88, and 0.36.Raw PTM and ACE + MLP scores collapse to 0.04–0.06 and 0.01–0.03, respectively.
- Temperature robustness and alignment: Adding contrastive and morphology terms increases HCP latent class separation from 1.43 to 1.68 to 1.75 while reducing fixed-recall false positives from 3,639 to 19 to 0.The unseen test defects move from the manifold contact region onto the training-defect manifold.
3 Discussion
The framework combines three complementary alignment mechanisms with label-free evaluation to transfer defect identification across temperatures and beyond point defects. Its scope and reliability depend on correspondence, morphology assumptions, reference-relative evaluation, and the diversity of low-temperature training data.
- Why the three levels are complementary rather than redundant: Three coupled levels target different residuals: denoising reduces marginal thermal mismatch, contrastive learning aligns identity-preserved representations, and morphology regularization constrains predicted geometry.The components address input, conditional, and prediction-level discrepancies rather than duplicating one another.
- Why the three levels are complementary rather than redundant: Ablations show denoising restores detection, contrastive learning tightens precision, and morphology regularization eliminates fabricated defect objects, especially in HCP systems.Without denoising, no true defects are detected; denoising alone does not provide trustworthy predictions.
- What the label-free evaluation buys: The label-free closeness suite compares predicted structures with a physics-based reference across five axes, while random-permutation and available ground-truth checks provide safeguards.It supports assessment where high-temperature labels are unavailable, but closeness is reference-relative by construction.
- When the recipe should transfer beyond cross-temperature shift: The decomposition may transfer to pressure, dilute-alloy disorder, or within-trajectory shifts when input corrections remain local and structured; broken correspondence requires distributional alignment alternatives.The denoiser and morphology levels do not require pairing, whereas contrastive learning depends on identity-preserved positive pairs.
- Implications for defect analysis as a learning problem: Explicit defect classes support both cross-temperature transfer and classification of defect-internal structure, including distinct grain-boundary phases or complexions.The authors argue that treating defects as a residual “other” category discards learnable structural information.
- 3.1 Limitations and outlook: The reported point-defect ladder covers single-element FCC, BCC, and HCP systems, while compactness-oriented morphology priors are not directly suited to dislocation lines or stacking faults.Systematic treatment of extended defects with line- and surface-shaped priors remains a follow-up direction.
- Evaluation: Wigner–Seitz ground truth requires a known parent-lattice registry; outside that regime, evaluation measures agreement with a physics-based reference rather than strict accuracy.Broader ground-truth-anchored benchmarks are identified as a worthwhile extension.
- 3.1 Limitations and outlook: Performance depends on low-temperature reference diversity and synthetic perturbations spanning relevant thermal distortions, while stress, chemical disorder, and finite-size effects remain unexplored systematically.These conditions constrain how broadly the reported results should be generalized.
4 Methods
The framework treats high-temperature defect identification as unsupervised cross-temperature domain adaptation, using input, representation, and prediction-level alignment with low-temperature labels. It combines equivariant denoising, contrastive learning, morphology regularization, and label-free evaluation for thermally perturbed structures.
- Problem formulation: The task uses labeled low-temperature environments and unlabeled high-temperature environments, with reliability required on the target distribution without target labels.The source includes bulk-crystal and defect classes, while the target consists of high-temperature environments.
- Framework overview: The workflow denoises high-temperature snapshots, computes ACE descriptors, and applies an MLP classifier to produce per-atom class probabilities.Low-temperature reference structures provide labeled bulk and defect environments, broadened with synthetic Gaussian perturbations during training.
- Denoising backbone: The denoiser predicts a cleaner configuration from thermally perturbed input and is implemented as an equivariant graph neural network applied iteratively at inference.It is trained self-supervised on synthetically perturbed low-temperature reference structures, including defect-containing references.
- Multi-level alignment: Contrastive learning aligns latent representations of matched low- and high-temperature atom environments, while morphology regularization steers target predictions toward compact, coherent defect geometry.The three components reduce mismatch at input, representation, and prediction levels through the shared encoder.
- Evaluation: Wigner–Seitz occupancy analysis supplies point-defect ground truth, whereas extended defects require label-free evaluation because no atom-wise temperature truth exists.The label-free suite triangulates predictions across five spatial and physics-based axes, and denoiser+PTM is only one external reference signal rather than a gold standard.
Declarations
The declarations report funding, a competing-interest disclosure, and author contributions, with several standard applicability statements marked not applicable.
- Funding: The work was funded by the National Science Foundation under Grant No. 2409835.
- Competing interests: RBS is Editor-in-Chief of the Journal of Materials Science: Materials Theory, a Springer Nature journal.
- Other declarations: Ethics approval, consent to participate, consent for publication, and materials availability are reported as not applicable.
- Author contributions: Author contributions span conceptualization, data curation, formal analysis, investigation, methodology, software, validation, visualization, writing, funding, project administration, and supervision.
Appendix A Spatial morphology metrics
The appendix defines morphology components as differentiable functionals of predicted defect-probability fields on spatial graphs, with modular combinations selected by task.
- Metric framework: Morphology components are differentiable functionals of predicted defect-probability fields evaluated on a spatial graph.The implementation can use components individually or in combination.
- Metric framework: The experiments use the cluster-persistence component with its two sub-terms equally weighted, while the broader morphology family remains available for specialization.
A.1 Spatial graph construction
The spatial graph uses mutual k-nearest-neighbor connectivity, distance-based Gaussian weights, and softened thresholded weights to represent multiple spatial scales.
- Graph construction: Atomic coordinates are used to construct a mutual k-nearest-neighbor graph for each neighborhood size k.
- Distance weighting: Gaussian edge weights depend on Euclidean interatomic distance, with σ_k set to the median distance to the k-th nearest neighbor.
- Multi-scale weighting: Softened thresholded weights incorporate multiple spatial scales through a scale parameter t and transition-sharpness parameter α.
A.2 Coherence component Scoh
The coherence component evaluates whether predicted defect probabilities form smooth, spatially compatible regions, while cluster-persistence terms favor localized mass supported by persistent connectivity and suitable cluster shapes.
- A.2 Coherence component Scoh: The coherence component measures smoothness of the predicted defect-probability field using a normalized total-variation formulation.It operates on node probabilities d_i in [0, 1].
- A.2 Coherence component Scoh: Neighbor averaging compares each atom’s defect probability with a weighted average over graph neighbors.High coherence values indicate mutually compatible probabilities among neighboring atoms.
- A.2 Coherence component Scoh: The fragmentation-sensitive term increases when defect probability mass is supported by persistent local connectivity across spatial scales.It uses soft edge affinity and node support to provide a differentiable analogue of connected-component tracking.
- A.2 Coherence component Scoh: The concentration term is large when defect mass remains concentrated on a small number of coherent regions and decreases as it diffuses across weakly connected islands.Concentration is computed after damped, degree-normalized diffusion over the soft thresholded graph.
- A.2 Coherence component Scoh: Cluster persistence combines fragmentation and concentration, while morphology components assess compatible neighborhoods, localization, and cluster shape.The experiments use an isotropic eigenvalue ratio λmin/λmax favoring round clusters; alternative ratios support line- or plane-shaped priors.
A.5 Aggregation across scales
Morphology components are aggregated over selected neighborhood and scale parameters, reducing dependence on any single neighborhood choice and improving practical robustness.
- A.5 Aggregation across scales: Each morphology component is computed across multiple neighborhood sizes k and, where applicable, multiple scale parameters t.The selected values are combined by averaging or weighted averaging; for example, S_coh averages S_coh(k) over k.
- A.5 Aggregation across scales: Multi-scale aggregation reduces sensitivity to a single neighborhood choice and improves robustness in practice.
Appendix B Detailed definition of evaluation metrics
The evaluation suite converts probabilistic predictions into consistent defect sets and scores their graph smoothness, boundary compatibility, and connected-cluster structure.
- Appendix B Detailed definition of evaluation metrics: The five evaluation metrics are discrete, evaluation-time counterparts of the differentiable training components, computed on a weighted mutual k-nearest-neighbor graph.Edge weights use periodic minimum-image distances and a Gaussian scale based on the frame’s median k-nearest-neighbor distance.
- Appendix B Detailed definition of evaluation metrics: The discrete defect set contains the top-m atoms ranked by predicted defect probability, where m matches the predicted total defect mass.This preserves a consistent defect fraction without an externally fixed threshold.
- Appendix B Detailed definition of evaluation metrics: Global coherence measures smoothness through edge-weighted normalized total variation and local averaging consistency.It is the evaluation-time counterpart of S_coh on the same weighted graph.
- Appendix B Detailed definition of evaluation metrics: Boundary consistency penalizes defect atoms whose graph neighbors lie outside the predicted defect set, assigning isolated predictions a score that cannot increase the metric.Atoms with no graph neighbors use the convention b_i = 1.
- Appendix B Detailed definition of evaluation metrics: Cluster structure combines fragmentation from thresholded connected components with concentration from the component-size distribution across swept linking scales.The construction follows the logic of zero-dimensional persistence.
B.5 Geometric compactness
Geometric metrics evaluate predicted clusters using covariance-based compactness and sphericity, while physics consistency compares a reference signal between predicted defects and non-defects.
- B.5 Geometric compactness: Cluster geometry is derived from the covariance matrix of atomic positions relative to each cluster centroid.
- B.5 Geometric compactness: Compactness compares each cluster’s radius of gyration with that of an ideally close-packed cluster of the same size and local spacing.
- B.5 Geometric compactness: Sphericity is the smallest-to-largest covariance eigenvalue ratio, computed for clusters of at least five atoms and otherwise set to zero.Cluster scores are weighted by each cluster’s share of the defect set, then compactness and sphericity are combined.
- B.5 Geometric compactness: Physics consistency uses a denoiser-assisted PTM reference signal to compare predicted defects with their complement.It combines the absolute standardized mean difference with an orientation-independent AUC-based ranking score.
- B.5 Geometric compactness: The resulting physics consistency score lies in the interval [0, 1] by construction.
B.7 Multi-scale aggregation
The evaluation aggregates graph-based defect metrics across multiple neighborhood sizes and, for component-based scores, across cluster-linking thresholds. Metrics are then mapped to a common scale to compare model predictions with reference structures.
- Graph-based metrics are computed for neighborhood sizes k ∈ {8, 10, 12, 14, 16}.
- Fragmentation, concentration, compactness, and sphericity are additionally averaged across cluster-linking thresholds t ∈ {1.1, 1.2, 1.3, 1.4} within each neighborhood size.
- Each score is summarized by its median across the five neighborhood sizes, with component sub-scores aggregated before pairwise combination.
- For GCS, MCPS, MCGS, BCS, and PCS, closeness is computed by comparing metric values on reference defect structures and model predictions.
- Heterogeneous metrics are mapped to a common [0, 1] scale for side-by-side comparison.
Appendix C Collapse of SIA by denoiser
A denoiser trained only on perfect crystals can collapse self-interstitial atoms by forcing atoms onto lattice sites. Structure-specific defect training prevents this failure in the reported example.
- Testing a perfect-crystal-only pre-trained denoiser produced unphysical collapse of self-interstitial atoms.
- The collapse occurs because the denoiser attempts to locate all atoms onto lattice sites, which is incompatible with self-interstitials.
- The observation motivates training structure-specific denoisers for all atomic structures of interest.
- Figure C1 shows that a denoiser trained only on perfect crystals erases interstitials.
- Retraining the denoiser with defect examples fixes the interstitial-erasure failure.