{"ID":2882386,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.10718","arxiv_id":"2508.10718","title":"Symmetry-Constrained Multi-Scale Physics-Informed Neural Networks for Graphene Electronic Band Structure Prediction","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 $μ$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.","short_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 lear...","url_abs":"https://arxiv.org/abs/2508.10718","url_pdf":"https://arxiv.org/pdf/2508.10718v1","authors":"[\"Wei Shan Lee\",\"I Hang Kwok\",\"Kam Ian Leong\",\"Chi Kiu Althina Chau\",\"Kei Chon Sio\"]","published":"2025-08-14T14:59:10Z","proceeding":"cond-mat.mtrl-sci","tasks":"[\"cond-mat.mtrl-sci\",\"cs.LG\",\"physics.comp-ph\"]","methods":"[]","has_code":false}