SCEGNN DDATASET

Dataset Description Overview This synthetic dataset is constructed strictly following the specifications presented in the paper S-matrix Constrained Equivariant Graph Neural Network for Hamiltonian Inversion of Kagome and Quasiperiodic Non-Hermitian Systems. It serves as a sample dataset defined in the original work, adopting identical generation rules, physical constraints, parameter distributions and data structures. This dataset can be used for model development, algorithm validation, experimental testing and performance evaluation of the S-matrix Constrained Equivariant Graph Neural Network (SCEGNN) and other related methods for non-Hermitian Hamiltonian inversion. Supported Physical Systems The dataset covers two core research systems : the 48-site Kagome periodic supercell and the 50-site Aubry-André-Harper (AAH) quasiperiodic chain. The AAH chain is divided into two cases: uniform dissipation and site-dependent dissipation. All physical parameters are restricted within the physically reasonable ranges proposed in the paper. Physical Parameter Ranges 1. Kagome 48-site Periodic Supercell Onsite potential: \([0.3, 0.7]\) Dissipation coefficient: \([0.02, 0.10]\) Hopping amplitude: \([0.8, 1.2]\) 2. AAH Quasiperiodic Chain (Uniform Dissipation) Modulation amplitude: \([1.5, 2.5]\) Uniform dissipation coefficient: \([0.02, 0.10]\) 3. AAH Quasiperiodic Chain (Site-dependent Dissipation) Modulation amplitude: \([1.5, 2.5]\) Site-specific dissipation coefficient for each lattice site: \([0.02, 0.10]\) Data Structure The dataset consists of multiple standard data sheets, including sample metadata, Hamiltonian parameters, energy grid and transmission spectrum data. All numerical values are rounded to four decimal places to maintain computational precision for quantum simulation. 1. Sample Metadata This sheet records basic information for each data entry, including unique sample ID, system category, dataset partition label (training / validation / test) and the dimension of corresponding Hamiltonian parameters. It also provides index mapping for cross-reference between parameters and spectral data. 2. Hamiltonian Parameter Tables Separate tables store microscopic Hamiltonian parameters for different systems. These parameters are the unknown quantities to be reconstructed via Hamiltonian inversion: · Parameters for the Kagome supercell: 34 independent variables corresponding to onsite potentials, dissipation coefficients and hopping strengths of lattice sites. · Parameters for the AAH chain (uniform dissipation): two independent physical variables. · Parameters for the AAH chain (site-dependent dissipation): 51 independent physical variables containing modulation amplitude and site-wise dissipation coefficients. 3. Energy Grid A unified linear energy grid is applied across all samples: · Energy range: \([-3.5, 3.5]\) · Total energy sampling points: 300 This configuration is fully consistent with the forward scattering solver adopted in the original paper. 4. Transmission Spectrum Data Transmission coefficient \(T(E)\) acts as the macroscopic observable and input data of neural networks. Four types of transmission spectra are generated for each sample: · Clean transmission spectrum (0% Gaussian noise, ground truth) · Spectrum with 2% additive Gaussian noise · Spectrum with 5% additive Gaussian noise · Spectrum with 10% additive Gaussian noise The noise injection scheme strictly complies with the Gaussian noise model described in the paper, which simulates different levels of interference in actual experimental measurements. Data Rules All data fully conform to the requirements of the original paper: 1. Parameter Sampling: Latin Hypercube Sampling (LHS) is utilized to sample parameters uniformly within predefined ranges, ensuring full coverage of the physical parameter space. Fixed random seeds are used to guarantee full reproducibility. 2. Forward Calculation: Based on the non-Hermitian tight-binding Hamiltonian and S-matrix scattering formalism, the standard forward solver is used to compute clean transmission spectra. The wide-band limit approximation is adopted, and the impact of non-Hermitian skin effect is negligible within the given parameter scope. 3. Noise Injection: Additive Gaussian noise is superimposed on clean spectra following the formula in the paper to simulate practical experimental noise. 4. Format Standardization: Data organization, storage format and numerical precision keep consistent with the dataset in the original research. Usage Notes 1. This dataset is applicable for code debugging, small-scale training, ablation studies and preliminary performance tests of SCEGNN, least-squares fitting, Physics-Informed Neural Networks (PINNs) and other baseline algorithms for Hamiltonian inversion. 2. All data follow the wide-band approximation mentioned in the paper, so it is only applicable to systems without prominent non-Hermitian skin effect and narrow-band leads.