  Gaussian process regression is a popular Bayesian framework for surrogate
modeling of expensive data sources. As part of a broader effort in scientific
machine learning, many recent works have incorporated physical constraints or
other a priori information within Gaussian process regression to supplement
limited data and regularize the behavior of the model. We provide an overview
and survey of several classes of Gaussian process constraints, including
positivity or bound constraints, monotonicity and convexity constraints,
differential equation constraints provided by linear PDEs, and boundary
condition constraints. We compare the strategies behind each approach as well
as the differences in implementation, concluding with a discussion of the
computational challenges introduced by constraints.
