Fig. 2: Neural network architecture of xDeepH.
From: Deep-learning electronic-structure calculation of magnetic superstructures
a, Workflow of the xDeepH model. Initial vertex and edge features are embedded by one-hot encoding and Gaussian expansion, respectively. Features are updated alternately by vertex layer and edge layer with interatomic distance vectors rij equipped with spherical harmonics Ylm. Subsequently, a magnetic moment layer with strict locality is used to include the magnetic moments mi of atoms as input. Finally, a Hamiltonian construction layer is employed to build the DFT Hamiltonian matrix block Hij. b, Details of the vertex layer (top), edge layer (middle) and magnetic moment layer (bottom), containing the ‘Interaction’ block. c, Details of the ‘Interaction’ block. The superscript (L) refers to the Lth layer. ∥ denotes vector concatenation and ⋅ denotes element-wise multiplication. \({\sum }_{{{{\mathcal{N}}}}}\) denotes the summation of neighbors for features, which is only valid for the vertex layer.
