Within the framework of complex system analyses, such as aircraft and launch vehicles, the presence of computationally intensive models (e.g., finite element models and multidisciplinary analyses) coupled with the dependence on discrete and unordered technological design choices results in challenging modeling problems. In this paper, the use of Gaussian process surrogate modeling of mixed continuous/discrete functions and the associated challenges are extensively discussed. A unifying formalism is proposed in order to facilitate the description and comparison between the existing covariance kernels allowing to adapt Gaussian processes to the presence of discrete unordered variables. Furthermore, the modeling performances of these various kernels are tested and compared on a set of analytical and aerospace-engineering-design-related benchmarks with different characteristics and parameterizations. Eventually, general tendencies and recommendations for such types of modeling problem using Gaussian process are highlighted.

在复杂系统分析的框架内，例如飞机和运载火箭，计算密集型模型（例如，有限元模型和多学科分析）的存在以及对离散和无序技术设计选择的依赖导致具有挑战性的建模问题。在本文中，广泛讨论了混合连续/离散函数的高斯过程代理建模的使用以及相关挑战。为了促进现有协方差内核之间的描述和比较，提出了统一形式主义，允许使高斯过程适应离散无序变量的存在。此外，这些不同内核的建模性能在一组具有不同特性和参数化的分析和航空航天工程设计相关基准上进行了测试和比较。最后，强调了使用高斯过程的此类建模问题的一般趋势和建议。