Publications Details

USING DEEP NEURAL NETWORKS TO PREDICT MATERIAL TYPES IN CONDITIONAL POINT SAMPLING APPLIED TO MARKOVIAN MIXTURE MODELS

Davis, Warren L.; Olson, Aaron J.; Popoola, Gabriel A.; Bolintineanu, Dan S.; Rodgers, Theron R.; Vu, Emily

Conditional Point Sampling (CoPS) is a recently developed stochastic media transport algorithm that has demonstrated a high degree of accuracy in 1-D and 3-D calculations for binary mixtures with Markovian mixing statistics. In theory, CoPS has the capacity to be accurate for material structures beyond just those with Markovian statistics. However, realizing this capability will require development of conditional probability functions (CPFs) that are based, not on explicit Markovian properties, but rather on latent properties extracted from material structures. Here, we describe a first step towards extracting these properties by developing CPFs using deep neural networks (DNNs). Our new approach lays the groundwork for enabling accurate transport on many classes of stochastic media. We train DNNs on ternary stochastic media with Markovian mixing statistics and compare their CPF predictions to those made by existing CoPS CPFs, which are derived based on Markovian mixing properties. We find that the DNN CPF predictions usually outperform the existing approximate CPF predictions, but with wider variance. In addition, even when trained on only one material volume realization, the DNN CPFs are shown to make accurate predictions on other realizations that have the same internal mixing behavior. We show that it is possible to form a useful CoPS CPF by using a DNN to extract correlation properties from realizations of stochastically mixed media, thus establishing a foundation for creating CPFs for mixtures other than those with Markovian mixing, where it may not be possible to derive an accurate analytical CPF.