Fig. 1: Workflow of the TBHCNN.
From: Machine learning method for tight-binding Hamiltonian parameterization from ab-initio band structure
a The workflows of obtaining the TB model for a 1D periodic system and constructing the TB Hamiltonian matrix for a uniform 1D non-periodic system. There are two additional steps for the latter, which are marked with the red arrows. b Structure diagram of the TBHCNN model. The matrix elements layer in the TBHCNN will be initialized according to the number of the reference ab-initio bands and the real-space TB Hamiltonian matrices considered in the desired TB model. The reference bands data are used as the training set, of which the eigenenergies \(\varepsilon _{i,{\mathbf{k}}}^{{\mathrm{Ab}}}\) are encoded within the ab-initio bands layer for computing the loss function by comparing with the TB results encoded in the tight-binding bands layer. The loss function value will be backpropagated to train the value of the neurons in the matrix element layer, which will be used as the matrix elements to construct the considered real-space Hamiltonians. When the loss function cannot touch down the predefined threshold, the TBHCNN model will add new neurons to the matrix element layer and reinitialize the whole layer to start a new round of training.
