Symmetry-Constrained Multi-Scale Physics-Informed Neural Networks for Graphene Electronic Band Structure Prediction

• URL: http://arxiv.org/abs/2508.10718v1
• Date: Thu, 14 Aug 2025 14:59:10 GMT
• Title: Symmetry-Constrained Multi-Scale Physics-Informed Neural Networks for Graphene Electronic Band Structure Prediction
• Abstract summary: We present the Symmetry-Constrained Multi-Scale Physics-Informed Neural Network (SCMS-PINN) v35.<n>It directly learns graphene band structures while rigorously enforcing crystallographic symmetries.<n>The model predicts Dirac point gaps within 30.3 $mu$eV of theoretical zero and average errors of 53.9 meV (valence) and 40.5 meV (conduction) across the Brillouin zone.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Accurate prediction of electronic band structures in two-dimensional materials remains a fundamental challenge, with existing methods struggling to balance computational efficiency and physical accuracy. We present the Symmetry-Constrained Multi-Scale Physics-Informed Neural Network (SCMS-PINN) v35, which directly learns graphene band structures while rigorously enforcing crystallographic symmetries through a multi-head architecture. Our approach introduces three specialized ResNet-6 pathways -- K-head for Dirac physics, M-head for saddle points, and General head for smooth interpolation -- operating on 31 physics-informed features extracted from k-points. Progressive Dirac constraint scheduling systematically increases the weight parameter from 5.0 to 25.0, enabling hierarchical learning from global topology to local critical physics. Training on 10,000 k-points over 300 epochs achieves 99.99\% reduction in training loss (34.597 to 0.003) with validation loss of 0.0085. The model predicts Dirac point gaps within 30.3 $\mu$eV of theoretical zero and achieves average errors of 53.9 meV (valence) and 40.5 meV (conduction) across the Brillouin zone. All twelve C$_{6v}$ operations are enforced through systematic averaging, guaranteeing exact symmetry preservation. This framework establishes a foundation for extending physics-informed learning to broader two-dimensional materials for accelerated discovery.

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