Development of an uncertainty-aware equation of state for gold

Abstract: This study introduces a framework that employs Gaussian Processes (GPs) to develop high-fidelity equation of state (EOS) tables, essential for modeling material properties across varying temperatures and pressures. GPs offer a robust predictive modeling approach and are especially adept at handling uncertainties systematically. By integrating Error-in-Variables (EIV) into the GP model, we adeptly navigate uncertainties in both input parameters (like temperature and density) and output variables (including pressure and other thermodynamic properties). Our methodology is demonstrated using first-principles density functional theory (DFT) data for gold, observing its properties over maximum density compression (up to 100 g/cc) and extreme temperatures within the warm dense matter region (reaching 300 eV). Furthermore, we assess the resilience of our uncertainty propagation within the resultant EOS tables under various conditions, including data scarcity and the intrinsic noise of experiments and simulations.