  A new gradient-based adaptive sampling method is proposed for design of
experiments applications which balances space filling, local refinement, and
error minimization objectives while reducing reliance on delicate tuning
parameters. High order local maximum entropy approximants are used for
metamodelling, which take advantage of boundary-corrected kernel density
estimation to increase accuracy and robustness on highly clumped datasets, as
well as conferring the resulting metamodel with some robustness against data
noise in the common case of unreplicated experiments. Two-dimensional test
cases are analyzed against full factorial and latin hypercube designs and
compare favourably. The proposed method is then applied in a unique manner to
the problem of adaptive spatial resolution in time-varying non-linear
functions, opening up the possibility to adapt the method to solve partial
differential equations.
