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.