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.

翻译：本文提出了一种新的基于梯度的自适应采样方法，用于实验设计应用，该方法在平衡空间填充、局部细化与误差最小化目标的同时，减少了对精细调参参数的依赖。采用高阶局部最大熵近似进行元建模，通过边界修正的核密度估计提高对高度聚集数据集的精度和鲁棒性，并赋予所得元模型在常见无重复实验情况下对数据噪声的鲁棒性。通过全因子设计与拉丁超立方设计的二维测试案例对比分析，表明该方法具有优越性。最后，将所提方法创新性地应用于时变非线性函数的自适应空间分辨率问题，为将其推广至求解偏微分方程开辟了可能性。