Machine Learning Surrogate Models to Accelerate Monte-Carlo Calculation

While modern Monte-Carlo algorithms are highly efficient for computational statistical mechanics in many systems, it is desirable for many materials simulations to utilize energies that are evaluated using density functional theory to capture the complex interactions in multicomponent systems. In the past we have performed calculations by combining our LSMS first principles code with Wang-Landau Monte-Carlo calculations. The number of Monte-Carlo steps limits the applicability of this method even on high-performance computer systems. Thus, we are integrating a machine learning derived surrogate model with Monte-Carlo calculations. Here we present our results of deriving surrogate models from total energy calculations that replicate the behavior of first principles calculations of alloy ordering transitions. In addition to evaluating the attainable speedup, we explore strategies for reducing the dimensionality of the surrogate model as well as the impact of the model on the accuracy of the Monte-Carlo results.