Uncertainty propagation in the equation-of-state model for gold

High-fidelity equation of state (EOS) models is essential in modeling a wide range of material properties under the influence of temperature and pressure. The desired quantities of EOS are accuracy, consistency, robustness, and predictive ability outside the domain where they have been fitted. A much less recognized criterion for choosing an EOS is the influence of the uncertainty from the relevant data. These data have associated uncertainties arising from the measurements and simulations, and how the EOS model incorporates the values provide an exciting challenge. Current approaches to the EOS model construction do not capture these data uncertainties, potentially underestimating the total uncertainty in extrapolation regions while overfitting the data in interpolation regions.



Gaussian Processes (GPs) are a class of kernel methods that can provide a potential alternative to the current approach that does not contain data uncertainty in the model. GPs come equipped with the possibility to obtain a predictive variance (i.e., error bars, confidence intervals) for each prediction. Unfortunately, the GP formulation assumes no noise in the inputs, only in the observations. In this work, we will formulate an Errors-in-Variables GP EOS model that explores the processes of propagating input and output uncertainties to model uncertainty in EOS table generation. We will demonstrate the approach using experimental and simulation data for gold and explore the robustness of uncertainty propagation in the resulting EOS due to data sparsity, experiment and simulation noises, and extrapolation from available data.