Space-filling experimental designs are widely used in engineering computer experiments, where only a limited number of expensive model evaluations can be afforded. Distance-based designs such as Maximin or Minimax ensure global space-filling, while Latin hypercube sampling enforces uniform one-dimensional projections, yet neither guarantees uniformity in lowdimensional subspaces. Maximum Projection (MaxPro) designs were introduced to improve uniformity in low-dimensional subspaces, yet their original formulation relies on the Euclidean distance and may induce systematic density distortions in bounded domains. We demonstrate that the standard MaxPro criterion leads to statistically non-uniform sampling, resulting in undersampling of corner regions and biased Monte Carlo estimates. To remedy this issue, we introduce a periodic variant of the criterion, termed Uniform Maximum Projection (uMaxPro), in which the Euclidean metric is replaced by a periodic distance based on the minimum image convention. The proposed uMaxPro designs preserve the projection-aware structure of MaxPro while achieving statistical uniformity of the design-generation mechanism. Numerical experiments show unbiased Monte Carlo integration with reduced variance, excellent subspace projection performance, and competitive discrepancy properties. The methodology is further validated on benchmark engineering problems, including a meso-scale finite element model of concrete, demonstrating improved accuracy in surrogate modeling and probabilistic estimation. The resulting criterion provides a simple and computationally efficient modification of MaxPro that enhances its robustness for nonadaptive computer experiments. The construction algorithm, open-source implementation, and reproducible optimized designs are provided to facilitate practical adoption of the method.

翻译：空间填充实验设计广泛应用于工程计算机实验中，此类实验仅能承担有限次昂贵模型评估的代价。基于距离的设计（如最大最小距离或最小最大距离）可确保全局空间填充，拉丁超立方采样则能保证一维投影的均匀性，但两者均无法保障低维子空间的均匀性。最大投影（MaxPro）设计旨在改善低维子空间的均匀性，但其原始公式依赖欧几里得距离，可能导致有界域内系统性的密度畸变。我们证明标准MaxPro准则会导致统计非均匀采样，造成角区域采样不足及蒙特卡洛估计有偏。为解决此问题，我们引入该准则的周期变体——均匀最大投影（uMaxPro），其中欧几里得度量被基于最小镜像约定的周期距离替代。所提出的uMaxPro设计在保留MaxPro投影感知结构的同时，实现了设计生成机制的统计均匀性。数值实验显示，该方法可实现无偏蒙特卡洛积分且方差降低，具备优异的子空间投影性能及竞争力强的差异度量性质。该方法的有效性进一步通过基准工程问题（包括混凝土细观有限元模型）得到验证，展示了在代理建模与概率估计中精度的提升。最终准则为MaxPro提供了简单且计算高效的改进方案，增强了其在非自适应计算机实验中的稳健性。为促进该方法的实际应用，我们提供了构建算法、开源实现及可复现的优化设计。