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Predicting and Interpreting Energy Barriers of Metallic Glasses with Graph Neural Networks
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Proposes SymGNN, an approximately O(3)-invariant GNN with learned von Mises sampling of orthogonal transformations, plus a GNNExplainer variant, to predict metallic glass energy barriers from atomic structure, and releases a new Cu64Zr36 EB dataset.
Problem
Predicting per-atom energy barriers (EBs) in metallic glasses is accurate but computationally prohibitive with ARTn (about 41 days for a 3,000-atom system), and the EB target should be invariant to Euclidean transformations.
Approach
Achieve E(3)/O(3) invariance in expectation by symmetrizing a message-passing encoder over many orthogonal transformations of the graph, sampled from learnable von Mises distributions over Euler angles, combined with attention over edges; explanations are obtained by adapting GNNExplainer's mask objective from entropy to MSE for regression.
Key results
- SymGNN reaches 0.7859 test Pearson on Cu64Zr36, versus 0.3614 for MD local sampling and 0.7588 for SchNet, the best ML baseline.
- SymGNN achieves 0.6084 and 0.5862 on Cu80Zr20 and Cu50Zr50, versus 0.5489 and 0.1571 for the strongest baselines (EGAT and SchNet respectively).
- Inference on a 3,000-atom MG takes 0.26 seconds for SymGNN, compared with about 41 days for ARTn and 150 minutes for MD local sampling.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add the SymGNN symmetrization module (ablation) | SymGNN · Cu64Zr36 | Pearson correlation: 0.2669 ± 0.0371 -> 0.7859 ± 0.0056 | Helped |
| add the SymGNN symmetrization module (ablation) | SymGNN · Cu80Zr20 | Pearson correlation: 0.2283 ± 0.0256 -> 0.6084 ± 0.0167 | Helped |
| add the SymGNN symmetrization module (ablation) | SymGNN · Cu50Zr50 | Pearson correlation: 0.1135 ± 0.0129 -> 0.5862 ± 0.0277 | Helped |
| use learned symmetrization instead of aggregation over three fixed orthogonal transformations (ablation) | SymGNN · Cu64Zr36 | Pearson correlation: 0.6614 ± 0.0285 -> 0.7859 ± 0.0056 | Helped |
| use learned symmetrization instead of aggregation over three fixed orthogonal transformations (ablation) | SymGNN · Cu80Zr20 | Pearson correlation: 0.3304 ± 0.0201 -> 0.6084 ± 0.0167 | Helped |
| use learned symmetrization instead of aggregation over three fixed orthogonal transformations (ablation) | SymGNN · Cu50Zr50 | Pearson correlation: 0.2135 ± 0.0337 -> 0.5862 ± 0.0277 | Helped |
| use 2 instead of 6 orthogonal transformations (ablation) | SymGNN · Cu64Zr36 | Pearson correlation: 0.7858 -> 0.7901 | No clear effect |
| use 4 instead of 6 orthogonal transformations (ablation) | SymGNN · Cu64Zr36 | Pearson correlation: 0.7858 -> 0.7778 | No clear effect |
| use a learned von Mises distribution instead of a uniform angle distribution | SymGNN · metallic-glass energy-barrier prediction | Pearson correlation | Helped |
| use SymGNN instead of SchNet | energy-barrier prediction models · Cu64Zr36 | Pearson correlation: 0.7588 ± 0.0088 -> 0.7859 ± 0.0056 | Helped |
| use SymGNN instead of SchNet | energy-barrier prediction models · Cu80Zr20 | Pearson correlation: 0.2505 ± 0.0128 -> 0.6084 ± 0.0167 | Helped |
| use SymGNN instead of SchNet | energy-barrier prediction models · Cu50Zr50 | Pearson correlation: 0.1808 ± 0.0106 -> 0.5862 ± 0.0277 | Helped |
Surprising findings
- Removing the symmetrization module drops SymGNN test Pearson from 0.7859 to 0.2669 on Cu64Zr36.
- SchNet explanations show no meaningful difference in optimal-cycle counts between high- and low-importance edges (1.312 vs 1.240), unlike SymGNN explanations (4.130 vs 0.874).
Limitations
- Equiformer, DimeNet, and Torch-MD Net could not be trained within 2 days on the large graphs, so their comparisons are incomplete.
- Only Cu-based metallic glasses are studied; generalization to other MG compositions is not established beyond the Cu-Zr dataset.
- The invariance is only approximate, holding in expectation over finite sampled transformations (k=6).
Experimental setup
Datasets: Cu64Zr36 EB dataset (own, ARTn-simulated) Cu-Zr MG dataset from prior work (Cu80Zr20, Cu50Zr50)
Benchmarks: Cu64Zr36 EB dataset Cu80Zr20 and Cu50Zr50 Cu-Zr MG dataset
Metrics: Pearson correlation coefficient inference time training time per epoch
Baselines: GCN with edge features EGNN MLP SchNet MGCN FAENet EGAT (edge length as 1D feature) MD local sampling
Builds on: GNNExplainer EGAT Euler angle decomposition ARTn
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