Adaptive design of experiments methodology for noise resistance with unreplicated experiments

TL;DR

This paper introduces a gradient-based adaptive sampling method for experimental design that enhances noise robustness and accuracy, especially in unreplicated experiments, by using high-order local approximants and boundary-corrected kernel density estimation.

Contribution

It presents a novel adaptive sampling approach that balances multiple objectives and improves robustness against noise in unreplicated experiments, with potential applications to PDEs.

Findings

Method compares favorably with factorial and Latin hypercube designs.

Enhanced robustness against data noise in highly clumped datasets.

Potential for adaptive spatial resolution in nonlinear, time-varying functions.

Abstract

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.