Sensitivity analysis of high-dimensional models with correlated inputs

IF 3.7 3区 计算机科学 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Juraj Kardoš , Wouter Edeling , Diana Suleimenova , Derek Groen , Olaf Schenk
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引用次数: 0

Abstract

Sensitivity analysis is an important tool used in many domains of computational science to either gain insight into the mathematical model and interaction of its parameters or study the uncertainty propagation through the input–output interactions. In many applications, the inputs are stochastically dependent, which violates one of the essential assumptions in the state-of-the-art sensitivity analysis methods. Consequently, the results obtained ignoring the correlations provide values which do not reflect the true contributions of the input parameters. This study proposes an approach to address the parameter correlations using a polynomial chaos expansion method and Rosenblatt and Cholesky transformations to reflect the parameter dependencies. Treatment of the correlated variables is discussed in context of variance and derivative-based sensitivity analysis. We demonstrate that the sensitivity of the correlated parameters can not only differ in magnitude, but even the sign of the derivative-based index can be inverted, thus significantly altering the model behavior compared to the prediction of the analysis disregarding the correlations. Numerous experiments are conducted using workflow automation tools within the VECMA toolkit.
具有相关输入的高维模型敏感性分析
灵敏度分析在计算科学的许多领域中是一种重要的工具,用于深入了解数学模型及其参数的相互作用,或研究通过输入-输出相互作用的不确定性传播。在许多应用中,输入是随机依赖的,这违反了最先进的灵敏度分析方法中的一个基本假设。因此,忽略相关性获得的结果提供的值不能反映输入参数的真实贡献。本文提出了一种利用多项式混沌展开方法和Rosenblatt和Cholesky变换来反映参数依赖性的方法来处理参数相关性。在方差和基于导数的敏感性分析的背景下讨论了相关变量的处理。我们证明了相关参数的敏感性不仅可以在量级上不同,甚至基于导数的指数的符号也可以反转,从而与忽略相关性的分析预测相比,显著改变了模型行为。使用VECMA工具包中的工作流自动化工具进行了大量实验。
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来源期刊
Journal of Computational Science
Journal of Computational Science COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS-COMPUTER SCIENCE, THEORY & METHODS
CiteScore
5.50
自引率
3.00%
发文量
227
审稿时长
41 days
期刊介绍: Computational Science is a rapidly growing multi- and interdisciplinary field that uses advanced computing and data analysis to understand and solve complex problems. It has reached a level of predictive capability that now firmly complements the traditional pillars of experimentation and theory. The recent advances in experimental techniques such as detectors, on-line sensor networks and high-resolution imaging techniques, have opened up new windows into physical and biological processes at many levels of detail. The resulting data explosion allows for detailed data driven modeling and simulation. This new discipline in science combines computational thinking, modern computational methods, devices and collateral technologies to address problems far beyond the scope of traditional numerical methods. Computational science typically unifies three distinct elements: • Modeling, Algorithms and Simulations (e.g. numerical and non-numerical, discrete and continuous); • Software developed to solve science (e.g., biological, physical, and social), engineering, medicine, and humanities problems; • Computer and information science that develops and optimizes the advanced system hardware, software, networking, and data management components (e.g. problem solving environments).
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