Atomistic Line Graph Neural Network for improved materials property predictions

The study addresses the limitation of many existing atomistic GNNs that use primarily interatomic distances while neglecting explicit angular information, despite many materials properties (especially electronic properties such as band gaps) being highly sensitive to bond angles and local geometric distortions. The purpose is to develop a GNN that explicitly incorporates bond angles via a line-graph construction to improve predictive accuracy across materials datasets. The importance lies in providing faster, accurate alternatives to quantum mechanical calculations for solids and molecules, enabling efficient materials discovery and screening.

Prior work includes GNN architectures for molecules and crystals such as SchNet, CGCNN, MEGNet, ICGCNN, OrbNet, and other variants that typically encode elemental properties as node features and distances/bond valences as edge features, implicitly capturing many-body interactions via stacked convolutions. Explicit use of angle-based information has improved models with hand-crafted descriptors (e.g., CFID), and several recent GNNs began incorporating directional or many-body features. However, a general and efficient architecture that directly passes messages over both bonds and bond angles for atomistic systems remained needed.

• Representation: Construct an undirected atomistic bond graph where nodes are atoms and edges are interatomic bonds (periodic 12-nearest-neighbor graph for crystals, expanded to include all atoms in the neighbor shell of the 12th-nearest neighbor). Node input features (9 per atom) include electronegativity, group number, covalent radius, valence electrons, first ionization energy, electron affinity, block, and atomic volume (CGCNN-inspired). Edge inputs are interatomic distances expanded with a radial basis function (RBF) (support 0–8 Å for crystals, up to 5 Å for molecules).
• Line graph: Build the atomistic line graph where nodes correspond to bonds of the original graph, and edges correspond to bond pairs sharing a common atom (i–j–k triplets). Initial line-graph edge features are RBF expansions of bond-angle cosines.
• Shared latent representations: Each bond in the direct graph corresponds to a node in the line graph and shares a latent representation, enabling efficient propagation of angular information to atom and bond features.
• Convolution operator: Use Edge-gated graph convolution to update both node and edge features. The edge gates are normalized and incorporate edge features; pre-aggregated edge messages update edge representations. ALIGNN composes two steps per layer: (1) edge-gated convolution on the line graph to update pair/triplet features; (2) propagate the updated pair features to the direct graph and perform edge-gated convolution on the direct graph to further update atom and bond features.
• Architecture: Stack N ALIGNN layers followed by M edge-gated GCN layers on the bond graph. Use SiLU activations and batch normalization. After NM graph convolutions, perform global average pooling over nodes and map to outputs with a single linear layer.
• Default hyperparameters: ALIGNN layers = 4; GCN layers = 4; edge input features = 80; triplet input features = 40; embedding features = 64; hidden features = 256; batch size = 64; learning rate = 0.001. Losses: MSE for regression, negative log likelihood for classification. Optimizer: AdamW with weight decay 1e-5; one-cycle learning rate schedule; 300 training epochs.
• Datasets and splits: Materials Project (MP 2018.6.1; 69,239 materials; PBE band gaps, formation energies), split 60,000/5,000/4,239; JARVIS-DFT (2021.8.18; 55,722 materials; diverse properties including OptB88vdW and MBJ band gaps, elastic, dielectric, piezoelectric, thermoelectric, EFG, effective masses, etc.), split 80/10/10; QM9 (130,829 molecules), split 110,000/10,000/10,829.
• Implementation: PyTorch + DGL with PyTorch-Ignite; 80 bond RBF and 40 angle RBF inputs; 64-d embeddings for atom/bond/angle to convolution layers; 4 ALIGNN + 4 GCN layers with 256 hidden size. Training on a single Tesla V100 32GB GPU; results for baselines reproduced on same hardware when possible. Hyperparameter tuning via manual experiments and random search (Ray Tune) focused on learning rate, weight decay, and convolution width.

• Materials Project (Table 2): ALIGNN achieves MAE 0.022 eV/atom for formation energy and 0.218 eV for band gap, outperforming CGCNN (0.039, 0.388), MEGNet (0.028, 0.218), and SchNet (0.035, n/a for Eg in table). MAD:MAE ratios indicate strong predictive performance (e.g., 42.27 for Ef).
• JARVIS-DFT (Table 3, 29 properties): ALIGNN consistently outperforms CFID and CGCNN across many targets. Examples: total energy MAE 0.037 eV/atom (MAD:MAE 48.11); formation energy MAE 0.033 eV/atom (MAD:MAE 26.06); Ehull 0.076 eV; OptB88vdW band gap 0.14 eV; MBJ band gap 0.31 eV; bulk modulus Kv 10.40 GPa; shear modulus Gv 9.48 GPa; magnetic moment 0.26 μB; dielectric constants (OPT) εx 19.99–20.40; DFPT dielectric (elec+ionic) 28.15; piezo coefficients: dij 20.57 (CN−1), eij 0.147 (Cm−2); exfoliation energy 51.42 meV/atom; max EFG 19.12×10^21 V m−2; avg me 0.085, mh 0.124; thermoelectric: n-Seebeck 40.92 μV/K, p-Seebeck 42.42 μV/K; n-PF 442.30 μW(mK^2)−1, p-PF 440.26 μW(mK^2)−1. ALIGNN often halves CGCNN error (e.g., OptB88vdW total energy).
• JARVIS-DFT classification (Table 4): High ROC AUCs, e.g., metal/non-metal 0.92 (OPT and MBJ thresholds 0.01 eV), magnetic/non-magnetic 0.91 (0.05 μB), stable/unstable by Ehull 0.94 (0.1 eV), SLME high/low 0.83, spillage high/low 0.80, Seebeck high/low 0.88–0.92, PF high/low 0.74.
• QM9 (Table 5): ALIGNN attains state-of-the-art or competitive MAEs: HOMO 0.0214 eV (better than SchNet/MEGNet/DimeNet++), LUMO 0.0195 eV (ties DimeNet++), dipole moment 0.0146 Debye (best among listed), with similar performance to SchNet on several energy targets.
• Ablation (Table 6; Fig. 3): Including ALIGNN layers yields notable accuracy gains vs GCN-only. Best trade-off near ALIGNN-2/GCN-2 gives ~29% MAE reduction vs GCN-4 with ~2× per-epoch cost; performance saturates around 4 total ALIGNN/GCN layers. Hidden width saturates at 256; edge RBF features around 80 (formation energy) and 40 (band gap); embeddings around 64 (formation energy) and 32 (band gap). Batch vs layer norm trade-offs suggest possible 1.7× speedup with minor accuracy loss. Learning curves show continued gains up to full JARVIS-DFT size; average validation MAE 0.0316 ± 0.0004 eV/atom for formation energy at full training set.

Explicit inclusion of bond-angle information via the line graph substantially improves atomistic GNN performance by better capturing many-body geometric effects critical for properties like band gaps and energies. Alternating message passing on the bond graph and its line graph enables propagation of pair and triplet information to atom representations, yielding lower errors than prior GNNs (CGCNN, MEGNet, SchNet) across multiple datasets and targets. Cross-dataset comparisons suggest that dataset size and underlying DFT protocols influence difficulty; MP is larger and often easier for energy targets, but JARVIS-DFT yields lower MAE for high-throughput band gaps, likely due to methodological differences (functionals, DFT+U, smearing, k-point settings) and distributional biases. Ablation studies confirm that at least two ALIGNN layers are needed to realize most benefits and show a clear accuracy-cost tradeoff. Classification results with high ROC AUCs demonstrate practical utility for screening tasks where regression remains challenging (e.g., electronic properties with lower MAD:MAE). Overall, ALIGNN addresses the initial hypothesis that explicit angular information improves generalization and accuracy in atomistic property prediction.

The paper introduces ALIGNN, a graph neural network that alternates message passing on an atomistic bond graph and its line graph to explicitly encode bond angles. This design significantly improves predictive accuracy across a wide range of solid-state and molecular properties on MP, JARVIS-DFT, and QM9, outperforming or matching strong GNN baselines while maintaining competitive training cost and robustness across datasets. Contributions include the dual-graph architecture, comprehensive benchmarking on 52 properties, ablation analyses elucidating accuracy-cost tradeoffs, and open-source data, code, and web tools. Future directions suggested by the work include comprehensive performance-cost studies with normalization strategies, resolving cross-dataset methodological and distributional discrepancies affecting target difficulty, scaling to larger datasets given favorable learning curves, and improving performance on challenging electronic properties.

• Some electronic-property regression tasks exhibit relatively low MAD:MAE ratios, indicating room for improvement.
• Performance depends on dataset characteristics and underlying DFT methodologies; differences in functionals, DFT+U usage, smearing, and k-point settings introduce label variability and potential bias across datasets (e.g., MP vs JARVIS-DFT).
• TBmBJ-calculated band gaps are underrepresented due to computational cost, potentially limiting supervised signal quality for high-fidelity electronic targets.
• Computational cost increases with ALIGNN layers, though mitigations (fewer layers, layer normalization) help; a full performance-cost study is deferred.
• Results rely on DFT-computed labels, which carry known systematic errors (e.g., PBE band gap underestimation) and may affect generalizability to experimental data.