  Modern advanced manufacturing and advanced materials design often require
searches of relatively high-dimensional process control parameter spaces for
settings that result in optimal structure, property, and performance
parameters. The mapping from the former to the latter must be determined from
noisy experiments or from expensive simulations. We abstract this problem to a
mathematical framework in which an unknown function from a control space to a
design space must be ascertained by means of expensive noisy measurements,
which locate optimal control settings generating desired design features within
specified tolerances, with quantified uncertainty. We describe targeted
adaptive design (TAD), a new algorithm that performs this sampling task
efficiently. TAD creates a Gaussian process surrogate model of the unknown
mapping at each iterative stage, proposing a new batch of control settings to
sample experimentally and optimizing the updated log-predictive likelihood of
the target design. TAD either stops upon locating a solution with uncertainties
that fit inside the tolerance box or uses a measure of expected future
information to determine that the search space has been exhausted with no
solution. TAD thus embodies the exploration-exploitation tension in a manner
that recalls, but is essentially different from, Bayesian optimization and
optimal experimental design.
