空间填充设计的若干方法与性质研究

Space-filling designs are commonly used for computer experiments whose outputs have no random error. In this project, we shall study methodologies to design computer experiments and properties of some space-filling designs, which include: optimization techniques for multi-fidelity computer experiments, sampling properties of some space-filling designs, and constructive algorithms for distance based space-filling designs. .Low fidelity experiments have low cost and high fidelity experiments have low error and thus by using multi fidelity experiments we can reach preciser model than that from single fidelity experiments. For computer experiments with tunable accuracy, we will derive criteria to select input values and accuracy levels. We will use multi fidelity experiments to reach preciser optimum with lower cost. .We shall study asymptotic distributions of the mean output from some space-filling designs including nested Latin hypercube designs and sliced Latin hypercube designs. Such results are necessary for making confidence statement, numerical integration, stochastic optimization, sensitivity analysis and other investigations. .We shall expand the methodology to generate asymptotic optimum distance-based designs which have been studied by mathematicians to develop a practical algorithm to generate nearly optimum distance-based space-filling designs. Such designs shall be constructed without mass computation or constraint on the number of design points and be efficient for model fitting.

由于输出没有随机误差，计算机实验一般采用空间填充设计。本项目拟研究某些空间填充设计的方法及性质，包括：多精度计算机实验的优化设计方法，某些空间填充设计的采样性质，以及基于距离准则的构造性设计方法。.低精度实验成本低，高精度实验误差小，结合使用建模预测精度优于单精度实验。针对精度可调节的计算机实验，我们拟研究针对计算机实验的参数选取优良性准则和精度选取准则，使用多种精度的实验进行寻优，以节省时间及提高寻优准确度。.我们拟研究嵌套或分层的拉丁超方设计及一些其它设计的均值估计的渐进分布，为置信推断、数值积分、随机优化、敏感性分析等研究提供理论基础。.我们拟将数学领域中渐近意义下基于距离准则最优的设计引入计算机实验设计领域并改进，得到构造性的基于距离准则的最优设计方法，并验证该方法对于次数较多的计算机实验具有生成快速、使用灵活及建模预测精度高的特性。

由于输出没有随机误差，计算机实验一般采用空间填充设计。本项目研究了某些空间填充设计的方法及性质，包括：多精度计算机实验的优化设计方法，某些空间填充设计的采样性质，以及基于距离准则的构造性设计方法。低精度实验成本低，高精度实验误差小，结合使用建模预测精度优于单精度实验。针对精度可调节的计算机实验，我们研究了针对计算机实验的参数选取优良性准则和精度选取准则，使用多种精度的实验进行寻优，以节省时间及提高寻优准确度。我们研究了嵌套或分层的拉丁超方设计及一些其它设计的均值估计的渐进分布，为置信推断、数值积分、随机优化、敏感性分析等研究提供理论基础。我们将数学领域中渐近意义下基于距离准则最优的设计引入计算机实验设计领域并改进，得到了构造性的基于距离准则的最优设计方法，并验证了该方法对于次数较多的计算机实验具有生成快速、使用灵活及建模预测精度高的特性。