Predicting and Interpreting Energy Barriers of Metallic Glasses with Graph Neural Networks

TL;DR

The paper tackles predicting energy barriers (EBs) in metallic glasses (MGs) by casting EB prediction as node regression on atomic graphs. It introduces SymGNN, a two-module graph neural network with a symmetrization mechanism that achieves $E(3)$-invariance in expectation, enabling accurate and scalable EB predictions with fast inference. The approach outperforms molecular-dynamics-based local sampling and a range of ML baselines, and it includes an extended GNNExplainer to provide edge-level explanations that align with the medium-range order (MRO) hypothesis and topological features captured by persistent homology (PH). The work delivers a new MG EB dataset, demonstrates substantial computational savings, and offers interpretable insights that can spur scientific discoveries in MG structure–property relationships.

Abstract

Metallic Glasses (MGs) are widely used materials that are stronger than steel while being shapeable as plastic. While understanding the structure-property relationship of MGs remains a challenge in materials science, studying their energy barriers (EBs) as an intermediary step shows promise. In this work, we utilize Graph Neural Networks (GNNs) to model MGs and study EBs. We contribute a new dataset for EB prediction and a novel Symmetrized GNN (SymGNN) model that is E(3)-invariant in expectation. SymGNN handles invariance by aggregating over orthogonal transformations of the graph structure. When applied to EB prediction, SymGNN are more accurate than molecular dynamics (MD) local-sampling methods and other machine-learning models. Compared to precise MD simulations, SymGNN reduces the inference time on new MGs from roughly 41 days to less than one second. We apply explanation algorithms to reveal the relationship between structures and EBs. The structures that we identify through explanations match the medium-range order (MRO) hypothesis and possess unique topological properties. Our work enables effective prediction and interpretation of MG EBs, bolstering material science research.

Figures (7)

• Figure 1: EBs represent mobility, which can further influence the MG dynamics and their physical properties.
• Figure 2: Example graphs demonstrating model expressiveness. SchNet cannot distinguish the embeddings of node 1 in these two graphs but SymGNN can.
• Figure 3: Illustration of the SymGNN framework. Given an input graph with node features being atom types and edge feature the relative distance, the symmetrization module of SymGNN aggregates encoding results on various orthogonally transformed graphs sampled from a learnable distribution to achieve ${\mathrm{O}}(3)$-invariant in expectation. The invariant embeddings are then passed to message-passing layers with attention to aggregate information and predict label.
• Figure 4: Global explanation visualization. We notice that many of selected edges are of 2 hop neighborhood from the central node.
• Figure 5: (a) Distribution of distance to the prediction target (central node) of important atoms identified by our explanation vs. all atoms. (b)Distribution of the number of cycles involved in important edges identified in our explanation vs. randomly selected edges.

Theorems & Definitions (13)

• Definition 3.1: Orthogonal Transformation
• Lemma 3.2: ${\mathrm{O}}(3)$ Decomposition
• Theorem 3.3
• Definition 3.4: Invariant/Equivariant Transformation
• Lemma 4.1
• proof
• Lemma 4.2
• proof
• Theorem 4.3
• proof