针对具有复杂特性计算机模型的试验设计

The increasing system complexity and computational load has made many computer simulation experiments very time-consuming. The development of computer surrogate models (or metamodels) and experimental design theories for computer experiments has greatly mitigated the situation. However, most research work in this area has been developed exclusively for computer experiments with continuous inputs and deterministic single response. They cannot be applied to computer experiments with complex characteristics such as multiple-response and stochasticity, which are frequently seen in research and practice. This project aims to develop experimental design schemes for computer experiments with complex characteristics to expand the applicability of surrogate models. Two types of typical computer models will be considered, namely models with mixed-type inputs and stochastic models. Characteristics of these two types of models will be analyzed, and design principles for traditional computer experiments will be modified and extended. The proposed experimental design schemes will be developed specifically according to the special characteristics of those models. Statistical sampling properties of the proposed designs will be analyzed; extensive simulation experiments and real examples will also be conducted to demonstrate their superior properties. The success of this project will greatly enhance the application of surrogate models in broader areas of research and practice.

日益增长的系统复杂度和运算量使得很多基于计算机模型的仿真试验变得异常耗时。计算机代理模型以及相关试验设计理论为之提供了一个有效解决方案。然而，该领域绝大部分研究仅针对具有连续输入变量和单输出响应的确定性计算机模型，对于科研和实践中常见的一些具有多输出响应以及随机性等复杂特性的模型却无能为力。 本课题拟针对具有复杂特性的计算机模型进行试验设计，以拓展代理模型的应用范围。本课题将主要关注两类具有代表性的常见计算机模型：含有混合型输入变量的模型和随机性模型。分析基于这些模型的计算机试验的特性，对传统的计算机试验设计理论进行扩展和修正，提出充分针对它们特点的新型试验设计方案。本课题将对提出的试验设计方案进行统计采样性能分析，并且通过大量的仿真和计算机模型实例来验证它们所带来的性能提升。本项目的成功将为计算机代理模型在科研与实践中更广泛的应用起到积极的推广作用。

本课题的主要研究内容为针对具有复杂特性的计算机模型提供试验设计方案，并主要研究含有混合型输入变量的计算机仿真模型和随机型计算机仿真模型这两类目前比较常见的情况。经过本课题项目组成员的努力，目前已经针对这两类具有复杂特性的仿真模型各自提出了新型的优化解决方案。对于含有混合型输入变量的仿真模型，基于传统的切片设计，我们提出了性能更加完善的双向切片设计的试验方案；对于随机型计算机仿真模型，我们提出了包含先导试验的序贯设计方案。我们针对本课题提出的试验方案进行了大量仿真验证和与已有方法的对比，证实了其优越性。相关课题成果已发表在相关领域的高质量国际期刊和会议论文集上。这些最新成果将会有效推动具有复杂特性的计算机代理模型在科研与实践中的进一步广泛应用。