A Machine Learning Approach for Increased Throughput of Density Functional Theory Substitutional Alloy Studies

In this study, a machine learning based technique is developed to reduce the computational cost required to explore large design spaces of substitional alloys. The first advancement is based on a neural network approach to predict the initial position of ions for both minority and majority ions prior to ion relaxation. The second advancement is to allow the neural network to predict the total energy for every possibility minority ion position and select the most stable configuration in the absence of relaxing each trial position. This study a bismuth oxide materials system, (Bi$_{x}$La$_{y}$Yb$_{z}$)$_2$ MoO$_6$, is used as an model system to demonstrate the developed method and potential computational speedup. Comparing a brute force method that requires calculation of every possible minority concentration location and subsequent relaxation there is a 1.3x speedup if the NN is allowed to predict the initial position prior to relaxation. This speedup is a result in an average decrease of 4 hour reduction in supercell relaxation wall time for all trials. Implementation of the second advancement allowed the NN to predict the total energy for all possible trials prior to relaxation resulting in a speed up of approximately 37x. Validation was done by comparing both position and energy between the NN to DFT calculation. A maximum vector mean squared error (MSE) of 1.6x10$^{-2}$ and a maximum energy MSE of 2.3x10$^{-7}$ was predicted. This method demonstrates a significant computational that even more impressive for larger design spaces where the size of the design space is a function of a factorial number of minority components.