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 substitutional alloys. The first advancement is based on a neural network approach to predict the initial position of ions for both minority and majority ions before 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. In this study, a bismuth oxide materials system, (Bi$_{x}$La$_{y}$Yb$_{z}$)$_2$ MoO$_6$, is used as the model system to demonstrate the developed method and potential computational speedup. Comparing a brute force method that requires the calculation of every possible minority concentration location and subsequent relaxation there was a 1.3x speedup if the neural network (NN) was allowed to predict the initial position prior to relaxation. This speedup is a result in an average decrease of 4 wall hour (64 cpu-hrs) reduction in relaxation for individual calculations. Implementation of the second advancement allowed the NN to predict the total energy for all possible trials prior to relaxation, resulting in a speedup of approximately 37x. Validation was done by comparing both position and energy between the NN to DFT calculations. 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 speedup, which has the potential for significant computational savings for larger compositional design spaces.