Uncertainty Quantification for a Copper Equation of State

We present a method for creating an uncertainty-aware equation of state (EOS) for copper using a combination of experimental and ab-initio data, in the form of density functional theory (DFT) calculations. We adopt a Bayesian framework to fit a variety of materials models to isobaric, isothermal, isentropic, shock, melt, and other data. Using a Bayesian approach, we compute an ensemble of possible model parameters with associated uncertainties, allowing us to create an ensemble of EOSs and associated probabilities. The method we present provides a robust approach for incorporating new experimental data and updating model parameters and the uncertainty assessment when new data becomes available. We also discuss systematic uncertainty in ab-initio data, with comparisons of the electronic free energy computed using average atom DFT, plane-wave DFT, and Thomas-Fermi, as well as how the different approaches affect the parameter distributions and calculated uncertainty. We also discuss possible future extensions of this work, for example by using free energy perturbation theory to calculate phase boundaries using DFT.