Uncertainty Propagation in Errors-in-Variables Equation-of-State Model

High-fidelity equation of state (EOS) models are essential in the modelling of a wide range of material properties under the influence of temperature and pressure.  Desired quantities of EOS are accuracy, consistency, robustness, and predictive ability outside of the domain where they have been fitted. A much less recognized criterion for the choice of an EOS is the influence of the uncertainty from the fitting data. These data have associated uncertainties arising from the measurements and simulations and how the EOS model incorporates the values provide an interesting 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 usually assumes that there is 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 both input and output uncertainties to model uncertainty in EOS table generation. We will demonstrate the approach using experimental and simulation data for Boron Carbide and explore the robustness of uncertainty propagation in the resulting EOS due to data sparsity, experiment and simulation noises and extrapolation away from available data.