Surrogate models are commonly used in place of computationally expensive simulations in engineering design and optimization, and the predictive performance of surrogate models is usually influenced by the quality of design of experiments (DoE). One way to eliminate the effect of the randomness of DoE is to average multiple prediction accuracies over multiple DoEs. However, how many DoEs are needed to obtain stable prediction results for problems with different dimensionalities remains a challenging issue. Mathematical test functions have been employed in a large body of literatures to identify the predictive performance of surrogate models. In this work, 30 test functions ranging from 1 dimension to 16 dimensions are selected to investigate the relationship between the number of DoEs needed for a stable prediction accuracy and the number of sample points. A convergence condition is used to determine whether a reliable model accuracy has been obtained. In this paper, the number of DoEs required for estimating the model accuracy is provided as a suggestion for those who develop surrogate models and select test functions to validate the performance of models.

代理模型通常用于代替工程设计和优化中计算量大的模拟，并且代理模型的预测性能通常受实验设计质量 (DoE) 的影响。消除 DoE 随机性影响的一种方法是在多个 DoE 上平均多个预测精度。然而，对于不同维度的问题，需要多少 DoE 才能获得稳定的预测结果仍然是一个具有挑战性的问题。大量文献中使用了数学测试函数来确定代理模型的预测性能。在这项工作中，选择了从 1 维到 16 维的 30 个测试函数来研究稳定预测精度所需的 DoE 数量与样本点数量之间的关系。收敛条件用于确定是否已获得可靠的模型精度。在本文中，为那些开发代理模型和选择测试函数来验证模型性能的人提供了估计模型准确性所需的 DoE 数量作为建议。