Uncertainty propagation in equation-of-state modeling with Gaussian processes*

High-fidelity equation of state (EOS) models is critical in understanding material properties under varying temperatures and pressures. Current approaches to EOS modeling struggle to capture uncertainties from data, leading to potential underestimations in extrapolation regions and over-fitting in interpolation regions. Gaussian Processes (GPs) offer a solution, as they can provide a predictive variance for each prediction and account for uncertainties in both input and output variables.

The application of GPs in EOS modeling has the potential to be a valuable tool for EOS generation, allowing for more informed decisions based on a better understanding of the uncertainty in the EOS tables. In this work, we present a new approach to EOS modeling using Errors-in-Variables GP, allowing for a more accurate representation of the total uncertainty in the model. Using experimental and simulation data for gold, we demonstrate the robustness of uncertainty propagation in the resulting EOS and examine how it is affected by factors such as data sparsity, experiment and simulation noises, and extrapolation.