Data-driven electrical conductivities of dense plasmas

Abstract

A wide range of theoretical and computational models have been developed to predict the electrical transport properties of dense plasmas, in part because dense plasma experiments explore order-of-magnitude excursions in temperature and density; in experiments with mixing, there may also be excursions in stoichiometry. In contrast, because high pressures create transient and heterogeneous plasmas, data from experiments that isolate transport are relatively rare. However, the aggregate of our datasets continues to increase in size and plays a key role in the validation of transport models. This trend suggests the possibility of using the data directly to make predictions, either alone or in combination with models, thereby creating a predictive capability with a controllable level of agreement with the data. Here, such a data-driven model is constructed by combining a theoretical model with extant data, using electrical conductivity as an example. Discrepancy learning is employed with a theoretical model appropriate for dense plasmas over wide ranges of conditions and a dataset of electrical conductivities in the solid to expanded warm dense matter regimes. The resulting discrepancy is learned via a radial basis function neural network. Regularization of the network is included through centers chosen with silhouette scores from k-means clustering. The covariance properties of each cluster are used with a scaled Mahalanobis distance metric to construct anisotropic basis functions for the network. The scale is used as a hyperparameter that is used to optimize prediction quality. The resulting predictions agree with the data and smoothly transition to the theoretical model away from the data. Detailed appendices describe the electrical conductivity model and compare various machine-learning methods. The electrical conductivity data and a library that yields the model are available at GitHub.