Maximizing Regional Sensitivity Analysis indices to find sensitive model behaviors

IF 1.5 4区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY

International Journal for Uncertainty Quantification Pub Date : 2024-04-01 DOI:10.1615/int.j.uncertaintyquantification.2024051424

Sebastien Roux, Patrice Loisel, Samuel Buis

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Abstract

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.

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最大化区域敏感性分析指数，找到敏感的模型行为

我们使用区域敏感性分析（RSA）来解决任何维度模型输出的敏感性分析问题。经典的区域灵敏度分析计算的是模型输入变化对模型输出空间目标区域出现情况影响的灵敏度指数。在这项工作中，我们将这一观点向前推进了一步，提出针对给定的模型输入，找到其出现最能解释该输入变化的区域。当该区域存在时，可将其视为对所研究的模型输入变化特别敏感的模型行为。我们将这种方法命名为 mRSA（最大化 RSA）。mRSA 被正式表述为一个使用基于区域的敏感性指数的优化问题。我们研究了两种公式，一种是理论公式，另一种是使用专用算法的数值公式。通过使用一个二维测试模型和一个产生时间序列的环境模型，我们证明了 mRSA 作为一种新的模型探索工具，可以为不同维度模型输出的敏感性提供可解释的见解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal for Uncertainty Quantification ENGINEERING, MULTIDISCIPLINARY-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

3.60

自引率

5.90%

发文量

期刊介绍： The International Journal for Uncertainty Quantification disseminates information of permanent interest in the areas of analysis, modeling, design and control of complex systems in the presence of uncertainty. The journal seeks to emphasize methods that cross stochastic analysis, statistical modeling and scientific computing. Systems of interest are governed by differential equations possibly with multiscale features. Topics of particular interest include representation of uncertainty, propagation of uncertainty across scales, resolving the curse of dimensionality, long-time integration for stochastic PDEs, data-driven approaches for constructing stochastic models, validation, verification and uncertainty quantification for predictive computational science, and visualization of uncertainty in high-dimensional spaces. Bayesian computation and machine learning techniques are also of interest for example in the context of stochastic multiscale systems, for model selection/classification, and decision making. Reports addressing the dynamic coupling of modern experiments and modeling approaches towards predictive science are particularly encouraged. Applications of uncertainty quantification in all areas of physical and biological sciences are appropriate.