Neural Network Potential for Lattice Dynamics Calculations and Thermal Conductivity Prediction

Lattice dynamics calculations can predict the phonon properties of insulating and semi-conducting crystals, with force constants as the primary input. Density functional theory (DFT) allows for an ab initio method to obtain these force constants accurately. These DFT calculations, however, can be computationally expensive. This is not an issue in simple materials (high symmetry and small primitive cell), where relatively few DFT calculations are necessary. In more complex materials, however, the number of calculations required will increase significantly and tax computational resources.

We address this issue by training a high-dimensional neural network potential to calculate force constants with a training set that is smaller than the required number of calculations. We used silicon as a test case, with accuracy quantified using phonon frequencies and thermal conductivity in addition to the standard force and energy metrics. We find that accurate forces, energies, and frequencies do not guarantee an accurate thermal conductivity. In addition, a single training set and hyperparameters can result in a range of thermal conductivities, with an accurate average value but significant variance. We attempt to reduce the variance in results using an adaptive selection scheme.