Abstract

A computer model can be used for predicting an output only after specifying the values of some unknown physical constants known as calibration parameters. The unknown calibration parameters can be estimated from real data by conducting physical experiments. This paper presents an approach to optimally design such a physical experiment. The problem of optimally designing a physical experiment, using a computer model, is similar to the problem of finding an optimal design for fitting nonlinear models. However, the problem is more challenging than the existing work on nonlinear optimal design because of the possibility of model discrepancy, that is, the computer model may not be an accurate representation of the true underlying model. Therefore, we propose an optimal design approach that is robust to potential model discrepancies. We show that our designs are better than the commonly used physical experimental designs that do not make use of the information contained in the computer model and other nonlinear optimal designs that ignore potential model discrepancies. We illustrate our approach using a toy example and a real example from industry.

摘要

只有在指定一些称为校准参数的未知物理常数的值后，计算机模型才能用于预测输出。未知的校准参数可以通过进行物理实验从真实数据中估计出来。本文提出了一种优化设计这种物理实验的方法。使用计算机模型优化设计物理实验的问题类似于寻找拟合非线性模型的最佳设计的问题。然而，由于存在模型差异的可能性，该问题比现有的非线性优化设计工作更具挑战性，也就是说，计算机模型可能不是真实基础模型的准确表示。因此，我们提出了一种对潜在模型差异具有鲁棒性的最优设计方法。我们表明，我们的设计优于不利用计算机模型中包含的信息的常用物理实验设计和其他忽略潜在模型差异的非线性优化设计。我们使用一个玩具示例和一个来自行业的真实示例来说明我们的方法。