  Bayesian hybrid models fuse physics-based insights with machine learning
constructs to correct for systematic bias. In this paper, we compare Bayesian
hybrid models against physics-based glass-box and Gaussian process black-box
surrogate models. We consider ballistic firing as an illustrative case study
for a Bayesian decision-making workflow. First, Bayesian calibration is
performed to estimate model parameters. We then use the posterior distribution
from Bayesian analysis to compute optimal firing conditions to hit a target via
a single-stage stochastic program. The case study demonstrates the ability of
Bayesian hybrid models to overcome systematic bias from missing physics with
less data than the pure machine learning approach. Ultimately, we argue
Bayesian hybrid models are an emerging paradigm for data-informed
decision-making under parametric and epistemic uncertainty.
