Adaptive design of experiments methodology for noise resistance with unreplicated experiments

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.