Machine learning for atomic forces in a crystalline solid: Transferability to various temperatures

Recently, machine learning has emerged as an alternative, powerful approach for predicting quantum‐mechanical properties of molecules and solids. Here, using kernel ridge regression and atomic fingerprints representing local environments of atoms, we trained a machine‐learning model on a crystalline silicon system to directly predict the atomic forces at a wide range of temperatures. Our idea is to construct a machine‐learning model using a quantum‐mechanical dataset taken from canonical‐ensemble simulations at a higher temperature, or an upper bound of the temperature range. With our model, the force prediction errors were about 2% or smaller with respect to the corresponding force ranges, in the temperature region between 300 K and 1650 K. We also verified the applicability to a larger system, ensuring the transferability with respect to system size. A machine‐learning model on crystalline silicon to predict the atomic forces is constructed using a quantum‐mechanical dataset taken from canonical‐ensemble simulations at a higher temperature, or an upper bound of the temperature range. With this model, the force prediction errors are about 2% or smaller with respect to the corresponding force ranges, in the temperature region between 300 K and 1650 K for systems containing 64 and 512 atoms.