基于信息几何的计算机代码不确定性量化中鲁棒性分析方法
An information geometry approach for robustness analysis in uncertainty quantification of computer codes
AI总结：
本文提出基于信息几何的鲁棒性分析方法，利用Fisher距离和常微分方程计算扰动密度，用于评估计算机代码在不确定性下的鲁棒性。
摘要：
鲁棒性分析是不确定性量化领域中新兴的一个研究方向。它涉及分析具有不确定输入的计算机模型对输入分布扰动的响应。因此，一种实用的鲁棒性分析方法应依赖于对分布扰动的合理定义。本文针对这一问题，提出了一种严谨的密度扰动方法。该方法基于概率分布流形上的Fisher距离。本文还提出了一种计算扰动密度的数值方法。该方法来源于拉格朗日力学，包括求解常微分方程组。这种扰动定义随后用于计算以分位数为导向的鲁棒性指数。所得到的基于扰动法的灵敏度指数（PLI）在多个数值模型上进行了示例说明。该方法还应用于一个工业研究（核反应堆冷却剂损失事故模拟），其中模型的多个物理参数不确定，且对其分布了解有限。
英文摘要：
Robustness analysis is an emerging field in the domain of uncertainty quantification. It consists of analysing the response of a computer model with uncertain inputs to the perturbation of one or several of its input distributions. Thus, a practical robustness analysis methodology should rely on a coherent definition of a distribution perturbation. This paper addresses this issue by exposing a rigorous way of perturbing densities. The proposed methodology is based the Fisher distance on manifolds of probability distributions. A numerical method to calculate perturbed densities in practice is presented. This method comes from Lagrangian mechanics and consists of solving an ordinary differential equations system. This perturbation definition is then used to compute quantile-oriented robustness indices. The resulting Perturbed-Law based sensitivity Indices (PLI) are illustrated on several numerical models. This methodology is also applied to an industrial study (simulation of a loss of coolant accident in a nuclear reactor), where several tens of the model physical parameters are uncertain with limited knowledge concerning their distributions.
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