  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.
