Within the framework of best-estimate-plus-uncertainty approaches, the assessment of model parameter uncertainties, associated with numerical simulators, is a key element in safety analysis. The results (or outputs) of the simulation must be compared and validated against experimental values, when such data are available. This validation step, as part of the broader verification, validation, and uncertainty quantification process, is required to ensure a reliable use of the simulator for modeling and prediction. This work aims to define quantitative criteria to support this validation for multivariate outputs, while taking into account modeling uncertainties (uncertain input parameters) and experimental uncertainties (measurement uncertainties). For this purpose, different statistical indicators, based on likelihood or statistical depths, are investigated and extended to the multidimensional case. First, the properties of the criteria are studied, either analytically or by simulation, for some specific cases (Gaussian distribution for experimental uncertainties, identical distributions of experiments and simulations, particular discrepancies). Then, some natural extensions to multivariate outputs are proposed, with guidelines for practical use depending on the objectives of the validation (strict/hard or average validation). From this, transformed criteria are proposed to make them more comparable and less sensitive to the dimension of the output. It is shown that these transformations allow for a fairer and more relevant comparison and interpretation of the different criteria. Finally, these criteria are applied to a code dedicated to nuclear material behavior simulation. The need to reduce the uncertainty of the model parameters is thus highlighted, as well as the outputs on which to focus.

中文翻译：

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用于将仿真结果与实验数据进行比较的基于可能性和深度的标准，以支持数值仿真器的验证

在最佳估计加不确定性方法的框架内，与数值模拟器相关的模型参数不确定性的评估是安全分析的关键要素。当数据可用时，必须将模拟结果（或输出）与实验值进行比较和验证。该验证步骤作为更广泛的验证、验证和不确定性量化过程的一部分，需要确保可靠地使用模拟器进行建模和预测。这项工作旨在定义定量标准以支持多变量输出的验证，同时考虑建模不确定性（不确定的输入参数）和实验不确定性（测量不确定性）。为此，根据可能性或统计深度，研究不同的统计指标并将其扩展到多维情况。首先，针对某些特定情况（实验不确定性的高斯分布、实验和模拟的相同分布、特定差异），通过分析或模拟研究标准的属性。然后，提出了对多变量输出的一些自然扩展，并根据验证的目标（严格/硬或平均验证）提供实际使用指南。由此，提出了变换后的标准，使它们更具可比性并且对输出的维度不太敏感。结果表明，这些转变可以对不同标准进行更公平、更相关的比较和解释。最后，这些标准应用于专用于核材料行为模拟的代码。因此，强调了减少模型参数不确定性的必要性，以及需要关注的输出。