Numerical predictions of quantities of interest measured within physical systems rely on the use of mathematical models that should be validated, or at best, not invalidated. Model validation usually involves the comparison of experimental data (outputs from the system of interest) and model predictions, both obtained at a specific validation scenario. The design of this validation experiment should be directly relevant to the objective of the model, that of predicting a quantity of interest at a prediction scenario. In this paper, we address two specific issues arising when designing validation experiments. The first issue consists in determining an appropriate validation scenario in cases where the prediction scenario cannot be carried out in a controlled environment. The second issue concerns the selection of observations when the quantity of interest cannot be readily observed. The proposed methodology involves the computation of influence matrices that characterize the response surface of given model functionals. Minimization of the distance between influence matrices allow one for selecting a validation experiment most representative of the prediction scenario. We illustrate our approach on two numerical examples. The first example considers the validation of a simple model based on an ordinary differential equation governing an object in free fall to put in evidence the importance of the choice of the validation experiment. The second numerical experiment focuses on the transport of a pollutant and demonstrates the impact that the choice of the quantity of interest has on the validation experiment to be performed.

翻译：物理系统中关注量的数值预测依赖于使用应被验证（或至少未被证伪）的数学模型。模型验证通常涉及将特定验证场景下的实验数据（待研究系统的输出）与模型预测结果进行比较。该验证实验的设计应直接服务于模型的根本目标——即在预测场景下对关注量进行预测。本文针对验证实验设计中的两个具体问题展开研究。第一个问题在于：当预测场景无法在受控环境中进行时，如何确定合适的验证场景。第二个问题关注的是：当关注量无法直接观测时如何选择观测数据。所提出的方法通过计算表征给定模型泛函响应面的影响矩阵来实现。通过最小化影响矩阵间的距离，可选出最能代表预测场景的验证实验。我们通过两个数值算例对所提方法进行阐释。第一个算例验证了基于控制自由落体物体运动的常微分方程的简单模型，揭示了验证实验选择的重要性。第二个数值实验聚焦污染物输运问题，展示了关注量选择对所需执行的验证实验的影响。