论文标题
以目标为导向的A-Tostori估计模型误差作为参数估计的帮助
Goal-Oriented A-Posteriori Estimation of Model Error as an Aid to Parameter Estimation
论文作者
论文摘要
在这项工作中，提出了一个贝叶斯模型校准框架，该框架利用了面向目标的A形级误差估计值（QOI）（QOIS），用于以PDE为特征的高保真模型类别。结果表明，对于大量的计算模型，当低效率（替代）模型的参数以可接受的精确率知道时，可以开发一个计算廉价的程序，以校准物理事件的高保真模型的参数。与未校准的较高保真度模型相比，建议使用所谓的低忠诚度模型计算出的QOIS中的QOIS中的主要成分是面向目标的A-posterii误差估计值。 QOI中误差的估计值用于定义贝叶斯反转分析中的可能性函数。采用标准的贝叶斯方法来计算高保真模型模型参数的后验分布。作为应用，使用二阶线性椭圆BVP校准了准线性二阶椭圆形边界值问题（BVP）中的参数。在第二次应用中，使用具有已知参数值的较低保真度线性肿瘤生长模型对涉及非线性时间依赖性PDE的肿瘤生长模型的参数进行校准。
In this work, a Bayesian model calibration framework is presented that utilizes goal-oriented a-posterior error estimates in quantities of interest (QoIs) for classes of high-fidelity models characterized by PDEs. It is shown that for a large class of computational models, it is possible to develop a computationally inexpensive procedure for calibrating parameters of high-fidelity models of physical events when the parameters of low-fidelity (surrogate) models are known with acceptable accuracy. The main ingredients in the proposed model calibration scheme are goal-oriented a-posteriori estimates of error in QoIs computed using a so-called lower fidelity model compared to those of an uncalibrated higher fidelity model. The estimates of error in QoIs are used to define likelihood functions in Bayesian inversion analysis. A standard Bayesian approach is employed to compute the posterior distribution of model parameters of high-fidelity models. As applications, parameters in a quasi-linear second-order elliptic boundary-value problem (BVP) are calibrated using a second-order linear elliptic BVP. In a second application, parameters of a tumor growth model involving nonlinear time-dependent PDEs are calibrated using a lower fidelity linear tumor growth model with known parameter values.
