Multivariate Gaussian process surrogates for predicting basic structural parameters of refractory non-dilute random alloys

Refractory non-dilute random alloys consist of two or more principal refractory metals with complex interactions that modify their basic structural properties such as lattice parameters and elastic constants. Atomistic simulations (ASs) are an effective method to compute such basic structural parameters. However, accurate predictions from ASs are computationally expensive due to the size and number of atomistic structures required. To reduce the computational burden, multivariate Gaussian process regression (MVGPR) is proposed as a surrogate model that only requires computing a small number of configurations for training. The elemental atom percentage in the hyper-spherical coordinates is demonstrated to be an effective feature for surrogate modeling. An additive approximation of the full MVGPR model is also proposed to further reduce computations. To improve surrogate accuracy, active learning is used to select a small number of alloys to simulate. Numerical studies based on AS data show the accuracy of the surrogate methodology and the additive approximation, as well as the effectiveness and robustness of the active learning for selecting new alloy designs to simulate.