Estimating Physics Models and Quantifying Their Uncertainty Using Optimization With a Bayesian Objective Function

Abstract

This paper reports a verification study for a method that fits functions to sets of data from several experiments simultaneously. The method finds a maximum a posteriori probability estimate of a function subject to constraints (e.g., convexity in the study), uncertainty about the estimate, and a quantitative characterization of how data from each experiment constrains that uncertainty. While this work focuses on a model of the equation of state (EOS) of gasses produced by detonating a high explosive, the method can be applied to a wide range of physics processes with either parametric or semiparametric models. As a verification exercise, a reference EOS is used and artificial experimental data sets are created using numerical integration of ordinary differential equations and pseudo-random noise. The method yields an estimate of the EOS that is close to the reference and identifies how each experiment most constrains the result.