Uncertainty Quantification of High Energy Density Material Models using Bayesian Analysis

The development of accurate material models in the high energy density regime is of considerable interest in a variety of fields, including the study of astrophysical impacts and inertial confinement fusion.  While plasma driven ramp compression, such as is now readily performed at the National Ignition Facility (NIF) and OMEGA Laser Facility, provides a powerful tool for probing this regime, the highly integrated nature of these experiments, together with the limitations on data quantity inherent in using such shared facilities, make it difficult to extract reliable model constraints valid across the entire range of relevant pressures (≤10 Mbar), temperatures (≤10⁴ K), and strain rates (≤10⁸ s^-1).  By performing large ensembles of hydrodynamic simulations, we leverage existing data on tantalum strength up to 8 Mbar, to systematically constrain the parameters of a variety of analytical strength models.  Through Bayesian techniques, we obtain quantitative estimates of these parameters and their uncertainties and propagate these values to estimates and uncertainties in the material strength itself.  Moreover, by explicitly constraining the model parameter space, this method allows us to clearly identify those relatively unconstrained dimensions, thereby pointing the way to future experiments with the greatest potential for producing further improvements in our material models.