We address the question of sensitivity analysis for model outputs of any dimension using Regional Sensitivity Analysis (RSA). Classical RSA computes sensitivity indices related to the impact of model inputs variations on the occurrence of a target region of the model output space. In this work, we put this perspective one step further by proposing to find, for a given model input, the region whose occurrence is best explained by the variations of this input. When it exists, this region can be seen as a model behavior which is particularly sensitive to the variations of the model input under study. We name this method mRSA (for maximized RSA). mRSA is formalized as an optimization problem using region-based sensitivity indices. Two formulations are studied, one theoretically and one numerically using a dedicated algorithm. Using a 2D test model and an environmental model producing time series, we show that mRSA, as a new model exploration tool, can provide interpretable insights on the sensitivity of model outputs of various dimensions.

中文翻译：

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最大化区域敏感性分析指数以查找敏感模型行为

我们使用区域敏感性分析（RSA）解决任何维度的模型输出的敏感性分析问题。经典 RSA 计算与模型输入变化对模型输出空间目标区域的影响相关的敏感度指数。在这项工作中，我们将这一观点更进一步，提出对于给定的模型输入，找到最能由该输入的变化来解释其出现的区域。当它存在时，该区域可以被视为对所研究的模型输入的变化特别敏感的模型行为。我们将此方法命名为 mRSA（最大化 RSA）。 mRSA 被形式化为使用基于区域的敏感性指数的优化问题。研究了两种公式，一种是理论上的，一种是使用专用算法进行数值计算的。使用 2D 测试模型和生成时间序列的环境模型，我们表明 mRSA 作为一种新的模型探索工具，可以提供有关各种维度模型输出敏感性的可解释的见解。