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BDIP-Net: Dual-Interaction Graph Learning for Property Prediction of Bilayer Materials

An Vuong, Chen Zhao, Jin Hu, Shui-Qing Yu, Xintao Wu

arXiv:2608.14640v1cs.LGcond-mat.mtrl-scics.AI

TL;DR

Large-scale bilayer discovery is limited by costly structure optimization and models that do not explicitly distinguish intra-layer from inter-layer interactions. The paper combines MatterSim-D3 structural optimization with BDIP-Net, achieving comparable structural quality and consistently stronger property prediction across three bilayer datasets.

  • Problem

    Costly multi-stage bilayer structure optimization and limited interaction distinction in existing models constrain efficient large-scale property prediction.

  • Method

    The framework combines MatterSim-D3-based bilayer structure optimization with BDIP-Net, which separately models intra-layer and inter-layer interactions.

  • Results

    MatterSim-D3 closely reproduces DFT-PBE-D3 structures, while BDIP-Net achieves the best performance across four metrics on BiDB, HetDB, and SAMBA.

  • Takeaways & Limitations

    The combined workflow provides an effective and scalable approach for stacked bilayer material structure construction and property prediction.

  • Takeaways & Limitations

    The framework inherits dataset biases, inaccuracies, and limited material diversity that may affect model generalization, so predictions should complement first-principles calculations and experimental validation.

Abstract

from arXiv · show

Stacked bilayer materials exhibit rich stacking-dependent properties driven by the interplay between strong intra-layer bonding and weak inter-layer van der Waals interactions. The computational discovery of such materials is challenging because accurate structure generation typically relies on expensive DFT-based optimization, while existing machine-learning models often fail to explicitly distinguish different interaction types during property prediction. To address these challenges, we propose a machine-learning framework for efficient construction and property prediction of stacked bilayer materials. The framework employs a MatterSim-D3-based structural optimization workflow to generate DFT-quality bilayer structures from monolayer building blocks and stacking configurations at substantially reduced computational cost. For property prediction, we introduce BDIP-Net (Bilayer Dual-Interaction Potential Network), a graph neural network that explicitly models intra-layer and inter-layer interactions through interaction-specific potential representations and adaptive message fusion. We evaluate the proposed framework on BiDB, HetDB, and SAMBA, encompassing homobilayers, heterobilayers, and twisted bilayer systems. Results show that the MatterSim-D3-based workflow closely reproduces DFT-PBE-D3 optimized structures, while BDIP-Net consistently outperforms existing graph neural network and potential-based approaches for bilayer property prediction.

1 Introduction

Stacked bilayer properties depend strongly on stacking configuration and other structural variables, making accurate large-scale discovery computationally expensive. The proposed workflow combines efficient MatterSim-D3 structural optimization with interaction-aware graph learning and is evaluated across three bilayer databases.

  • Motivation: Bilayer properties vary with stacking configuration, interlayer distance, lattice mismatch, and twist angle because weak interlayer coupling interacts with layer structure.These effects can produce electronic and optical properties absent from isolated monolayers.
  • Motivation: Large-scale bilayer screening is limited by multi-stage optimization involving interlayer-distance scans, in-plane registry optimization, atomic relaxation, and subsequent DFT calculations.Numerous stacking configurations, lateral translations, and interlayer distances can arise from a single monolayer pair.
  • Framework: The proposed workflow uses MatterSim with DFT-D3 dispersion corrections as an MLIP-D3 surrogate for costly DFT-D3 structural optimization and supports ML-based band gap prediction.The framework spans bilayer structure construction, efficient structural optimization, and property prediction.
  • Evaluation: The framework is evaluated on BiDB homobilayers, HetDB van der Waals heterobilayers, and SAMBA twisted homo- and heterobilayers.SAMBA provides over 18,000 twisted homo- and hetero-bilayer structures.
  • Results: MatterSim-D3 achieves nearly identical predictive performance to DFT-PBE-D3, supporting efficient MLIP-based optimization combined with interaction-aware potential-based graph learning.The reported combination is presented as an effective and scalable framework for stacked bilayer property prediction.

2 Related Work

Related work uses graph neural networks to predict materials properties by modeling atoms and their interactions, while recent bilayer models explicitly separate intra-layer and inter-layer interactions. However, such bilayer prediction approaches can depend on computationally intensive optimized structures, limiting scalability.

  • Materials Property Prediction: Crystal GNNs represent atoms as nodes and atomic interactions as edges, commonly encoding interatomic distances with radial basis function expansions and learning patterns through message passing.Examples include SchNet, CGCNN, MEGNet, and OrbNet.
  • Materials Property Prediction: PotNet instead transforms interatomic distances into potential values for modeling atomic interactions.
  • Bilayer Materials Prediction: SE-PAINN predicts stacked 2D bilayer properties by separating intra-layer and inter-layer interactions into distinct edge sets and dedicated message-passing branches.Its reliance on optimized bilayer structures generated through computationally intensive structural optimization workflows limits scalability for large-scale applications.

3 Method

The proposed framework has two stages: constructing bilayers from monolayer structures and predicting their properties. It combines MatterSim-D3 structural optimization with BDIP-Net, which explicitly separates and adaptively integrates intra-layer and inter-layer interactions.

  • Framework overview: The workflow comprises bilayer material construction followed by bilayer property prediction.The two stages are illustrated in Figure 1.
  • Bilayer construction: Bilayers are initialized from DFT-relaxed C2DB monolayers transformed by dataset-specific 3 × 3 stacking configuration matrices.The transformations can enlarge monolayers into supercells, rotate layers, and optionally flip them out of plane.
  • Structural optimization: 0.02 eV average bandgap difference is obtained between MatterSim-D3- and DFT-PBE-D3-optimized bilayer structures.MatterSim-D3 was selected because it showed the best overall performance among evaluated MLIP-D3 models for reproducing DFT-PBE-D3-optimized bilayer structures.
  • BDIP-Net inputs: BDIP-Net constructs separate intra-layer and inter-layer edge sets, initializes node embeddings, and computes interaction-specific potential-based edge embeddings.Adaptive layer neighbor search is performed separately under periodic boundary conditions, with cutoffs increased until each atom has at least N_intra or N_inter valid neighbors after filtering.
  • Message passing: BDIP-Net separately aggregates intra-layer and inter-layer messages, then adaptively fuses them to update node representations for property prediction.The intra-layer branch uses same-layer neighbors, whereas the inter-layer branch uses neighbors across different layers.

4 Experiments

Experiments across BiDB, HetDB, and SAMBA show that BDIP-Net delivers consistently stronger bandgap prediction than baselines, with statistically significant improvements. MatterSim-D3 optimization preserves predictive performance while enabling efficient structure generation, and BDIP-Net generalizes better across domains and model ablations.

  • Datasets and evaluation: BiDB, HetDB, and SAMBA provide complementary benchmarks spanning aligned homobilayers, heterobilayers, and twisted bilayers, evaluated with monolayer-pair-level 4-fold cross-validation.SAMBA contributes more than 18,000 generated structures, with 980 bilayers having DFT-optimized structures and bandgap values.
  • Single-domain prediction: BDIP-Net achieves the best MAE, MSE, RMSE, and R2 across all three datasets, increasing R2 over PotNet from 0.65 to 0.73, 0.89 to 0.93, and 0.73 to 0.83.The comparisons are reported for BiDB, HetDB, and SAMBA, respectively.
  • Statistical significance: p< 0.01 for all BDIP-Net comparisons with baseline models across the combined 12 paired observations, indicating statistically significant improvements across evaluation metrics.The observations combine four folds from each of BiDB, HetDB, and SAMBA.
  • Structural optimization: MatterSim-D3 optimization changes bandgap prediction only slightly relative to DFT-PBE-D3 optimization, preserving structural information required for comparable performance.This finding applies to both BDIP-Net and the baseline models.
  • Ablation study: BDIP-Net increases R2 over BDIP-Net− from 0.69 to 0.73 on BiDB, 0.91 to 0.93 on HetDB, and 0.75 to 0.83 on SAMBA.One-sided paired t-tests show statistically significant improvements across all metrics, with p< 0.01.
  • Runtime: 4.5 seconds on BiDB, 3.5 seconds on HetDB, and 13.5 seconds on SAMBA are the average complete MatterSim-D3 structural optimization times per material.Inference efficiency is similar across methods, averaging approximately 0.05 s per sample.

5 Conclusion

The work develops a pipeline for stacked bilayer material property prediction that combines bilayer structure construction, efficient MatterSim-D3-based optimization, and machine-learning property prediction. Unlike Bimat-ML, the workflow adds explicit bilayer construction and structural optimization before prediction.

  • Pipeline: The proposed pipeline integrates bilayer structure construction, MatterSim-D3-based structural optimization, and machine-learning-based property prediction.It covers the workflow from constructing stacked bilayers through optimized structures to predicted properties.
  • Comparison with Bimat-ML: Compared with Bimat-ML, the workflow adds bilayer structure construction and structural optimization beyond using monolayer structures and stacking information.Bimat-ML directly predicts bilayer properties from monolayer structures and stacking information.
  • Efficiency: The added structural optimization step is performed efficiently using MatterSim-D3.The passage identifies MatterSim-D3 as the method used to make this additional workflow step efficient.

Limitations and Ethical Considerations

The study’s evaluation inherits biases, inaccuracies, and limited diversity from public computational materials databases, which may affect generalization. Its predictions are intended to complement, not replace, high-fidelity first-principles calculations and experimental validation; human-participant and privacy concerns do not apply.

  • Dataset limitations: Public computational materials databases may introduce biases, inaccuracies, and limited material diversity that affect model generalization.The evaluation inherits these dataset limitations.
  • Validation requirements: Predictions should complement rather than replace high-fidelity first-principles calculations and experimental validation.This remains necessary despite reduced computational cost for bilayer structure generation and property prediction.
  • Ethical considerations: The study involves no human participants or personal data, so data privacy and informed consent are not applicable.These ethical considerations therefore do not arise in this work.

Generative AI Usage … B.3 SAMBA

The paper reports that generative AI was limited to language editing, while the appendix defines periodic bilayer representations and dataset-specific construction workflows for BiDB, HetDB, and SAMBA. These workflows transform monolayer structures into initial bilayers using stacking operations, compatible supercells, shared lattices, interlayer spacing, and duplicate filtering.

  • Generative AI Usage: Chat-GPT was used solely for language editing, while the authors developed and verified all scientific content, analyses, and conclusions.The tool was not used for research conception, experimental design, data analysis, interpretation, or scientific-content generation.
  • A Background on Stacked 2D Materials Representation: Crystal structures are represented as periodic unit cells containing atom features, Cartesian coordinates, and lattice vectors defining repetition in three-dimensional space.Periodic images are generated through integer combinations of lattice vectors and inherit corresponding atomic features.
  • A Background on Stacked 2D Materials Representation: Stacked 2D materials combine bottom and top monolayers, applying top-layer rotation, translation, or flipping before setting interlayer spacing and relaxing atomic positions.The resulting bilayer combines the layers’ atomic features and positions within a bilayer lattice.
  • B.1 BiDB: BiDB constructs homogeneous bilayers from two identical monolayer copies, leaving the bottom layer unchanged and transforming only the top layer using supplied stacking information.Fractional coordinates are combined after applying the stacking transformation, layer translation, and initial interlayer distance.
  • B.2 HetDB: HetDB identifies compatible top- and bottom-layer supercell matrices, filters candidates by atom count and geometric or strain constraints, and selects the lexicographically best pair.The selected supercells are aligned to a common in-plane lattice before heterogeneous bilayer construction.
  • B.2 HetDB: HetDB constructs heterogeneous bilayers by extending selected supercell transformations, combining a common in-plane lattice with layer thickness, vacuum spacing, and target interlayer distance.The workflow fixes in-plane translations at (𝛿𝑥,𝛿𝑦) = (0, 0) and considers either both layers unflipped or both flipped.
  • B.3 SAMBA: SAMBA generates supercell pairs and filters them using lattice-area, internal-angle, and lattice-vector compatibility constraints before computing twist angles and constructing candidates.Only pairs satisfying all constraints are retained for subsequent three-dimensional construction.
  • B.3 SAMBA: SAMBA preserves the out-of-plane direction, uses fixed interlayer distance and zero in-plane translation, and removes duplicate candidates through RMSD matching with Kabsch alignment and Hungarian correspondence.The final candidates are assembled from top and bottom supercells sharing a common in-plane lattice.

C Structural Optimization … D.3 Adaptive Layer Neighbor Search

The framework constructs DFT-quality bilayer structures through MatterSim-D3 scans and relaxation, then predicts properties with BDIP-Net by separately modeling intra-layer and inter-layer interactions. Its adaptive neighbor search ensures sufficient interaction-specific graph connectivity for both interaction types.

  • C Structural Optimization: MatterSim-D3 optimizes initial bilayer structures using interlayer-distance scans, optional lateral stacking scans, and final relaxation.The z-scan fixes δx = 0 and δy = 0 while varying d; SAMBA additionally performs an xy-scan before relaxation.
  • C Structural Optimization: BiDB uses a unified MatterSim-D3 z-scan for magnetic and non-magnetic systems, starting at d_start = 5.0 Å and decreasing to d_end = 0 Å without energy normalization.This replaces the original workflow’s SciPy minimization for non-magnetic systems and electron-normalized stepwise scan for magnetic systems.
  • C Structural Optimization: HetDB applies MatterSim-D3 z-scans followed by BFGS relaxation, using coarse and fine step sizes of s_coarse = 0.25 Å and s_fine = 0.05 Å.The coarse scan locates an approximate minimum-energy distance, after which the fine scan refines the result.
  • D.1 BDIP-Net Algorithm: BDIP-Net takes structurally optimized bilayers and interaction-specific cutoffs, neighbor counts, potential scaling coefficients, and training properties to produce predicted bilayer properties.Training minimizes MAE loss through backpropagation, while inference returns the forward-pass prediction.
  • D.1 BDIP-Net Algorithm: The model computes separate intra-layer and inter-layer edge embeddings from Coulomb-based and London-based potentials, then performs separate message passing for each interaction type.Interaction-specific node messages are weighted and fused using attention before being added to residual node representations.
  • D.2 Interaction-Specific Radial Basis Function Expansions: Separate RBF expansions encode Coulomb and London dispersion potential values into feature vectors before independently parameterized networks produce edge embeddings.The experiments define the distance interval as d ∈ [d_min,d_max], with d_min = 1 and d_max = 8.
  • D.3 Adaptive Layer Neighbor Search: Adaptive Layer Neighbor Search separates atoms by z_cut, searches within an initial cutoff radius, and filters neighbors according to the specified interaction type.Atoms with z_i > z_cut belong to the top layer, while atoms with z_i ≤ z_cut belong to the bottom layer.
  • D.3 Adaptive Layer Neighbor Search: When an atom lacks N valid neighbors, the search doubles the cutoff radius and repeats until every atom meets the requirement, retaining ties at the N-th-neighbor distance.The resulting filtered lists form the interaction-specific edge set E_η.

E Additional Experimental Results · E.1 Datasets

The evaluation uses BiDB, HetDB, and SAMBA as complementary benchmarks covering aligned homobilayers, heterobilayers, and twisted bilayer systems. The datasets also reveal distinct relationships between bilayer and monolayer bandgaps, especially in HetDB and SAMBA.

  • E.1 Datasets: BiDB, HetDB, and SAMBA together benchmark structural optimization and interaction-aware graph learning across diverse bilayer systems.Their coverage includes aligned homobilayers, heterobilayers, and twisted bilayer systems.
  • E.1 Datasets: BiDB uses the same processed dataset as Bimat-ML [19].The dataset is identified as the Van der Waals Bilayer Database.
  • E.1 Datasets: 76 HetDB bilayers lie within the monolayer bandgap range, compared with 260 outside it.The range is defined by the smaller and larger monolayer bandgaps.
  • E.1 Datasets: 149 HetDB samples are close to the smaller monolayer bandgap, while none are close to the larger one.This distribution applies across all HetDB samples.
  • E.1 Datasets: 435 SAMBA heterobilayers lie within the monolayer bandgap range, compared with 399 outside it.SAMBA therefore includes substantial representation on both sides of the monolayer-defined range.
  • E.1 Datasets: 603 of 605 SAMBA samples close to a monolayer bandgap are close to the smaller bandgap, while only 2 are close to the larger one.The counts concern the SAMBA samples close to either monolayer bandgap.

E.2 Running Time · E.3 Cross-Domain Generalization

BDIP-Net has training runtime comparable to leading alternatives on BiDB, while its combination with MatterSim-D3-based structure generation forms a practical bilayer property-prediction pipeline. The SAMBA dataset contains 63 unique monolayers, with annotations identifying overlap with BiDB and HetDB for cross-domain analysis.

  • E.2 Running Time: Training runtimes are summarized across BiDB, HetDB, and SAMBA in Figure 6.
  • E.2 Running Time: On BiDB, BDIP-Net requires 575 s for training, compared with 550 s for PotNet and 475 s for SE-MEGNET.
  • E.2 Running Time: On BiDB, BDIP-Net’s 575 s training runtime is slower than SE-CGCNN at 400 s and SE-PAINN at 300 s.
  • E.2 Running Time: Training and inference runtimes are nearly identical for structures optimized by DFT-PBE-D3 and MatterSim-D3, so one runtime is reported per dataset and model.
  • E.2 Running Time: BDIP-Net combined with MatterSim-D3-based structure generation provides a computationally practical pipeline for bilayer property prediction.
  • E.3 Cross-Domain Generalization: The SAMBA dataset contains 63 unique monolayers.
  • E.3 Cross-Domain Generalization: Monolayers overlapping with BiDB are marked with subscript (𝐵), while those overlapping with both BiDB and HetDB are marked with (𝐵, 𝐻).
  • E.3 Cross-Domain Generalization: These annotations identify monolayer overlap between training and test datasets in the cross-domain generalization analysis.

E.3.1 Monolayer Overlap.

This setting trains models on all 336 HetDB heterobilayers and evaluates them on all 980 SAMBA test bilayers, including 13 overlapping monolayers. BDIP-Net and PotNet use matched learning-rate and batch-size settings, with other configurations following Section 4.1.

  • 336 heterobilayers from the full HetDB dataset are used for training, while evaluation uses the full SAMBA test set of 980 bilayers.
  • 13 monolayers forming HetDB heterobilayers overlap with monolayers in SAMBA.
  • BDIP-Net and PotNet are trained with a learning rate of 2 × 10−4 and a batch size of 128.Their remaining model configurations follow those described in Section 4.1.

E.3.2 HetDB-to-SAMBA.

In HetDB-to-SAMBA domain generalization, PotNet performs better overall on the full SAMBA test set, whereas BDIP-Net generalizes more strongly to unseen bilayer combinations after controlling for overlap type. Overall performance is limited by the dominance of no-monolayer-overlap and one-monolayer-overlap bilayers.

  • E.3.2 HetDB-to-SAMBA.: PotNet achieves lower full-test-set errors on 980 SAMBA bilayers, with MAE 0.50, MSE 0.39, RMSE 0.63, and R2 −0.50 versus BDIP-Net’s 0.56, 0.50, 0.71, and −0.93.Both models improve as monolayer overlap increases.
  • E.3.2 HetDB-to-SAMBA.: On 70 two-monolayer-overlap bilayers, BDIP-Net achieves MAE 0.12 versus PotNet’s 0.15.Among 36 exact-pair-overlap bilayers, PotNet instead achieves MAE 0.07 versus 0.10 for BDIP-Net.
  • E.3.2 HetDB-to-SAMBA.: After excluding 36 exact-pair-overlap bilayers, BDIP-Net achieves MAE 0.14, RMSE 0.18, and R2 0.98 on the remaining 34, versus PotNet’s 0.24, 0.43, and 0.86.This supports stronger cross-dataset generalization to unseen bilayer combinations of known monolayers.
  • E.3.2 HetDB-to-SAMBA.: Overall HetDB-to-SAMBA performance remains limited because most SAMBA bilayers belong to the no-monolayer-overlap and one-monolayer-overlap subsets.These subsets dominate the test distribution and constrain the aggregate generalization result.
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