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.
翻译:在这项工作中,提出了贝叶西亚模型校准框架,对以PDEs为特征的高不忠模型类别使用目标导向的、具有兴趣数量的意外误差估计值(QIs),显示对于大量计算模型类别,可以开发计算成本低廉的程序,校准高不忠物理事件模型的参数,因为低不忠(surogate)模型的参数是可以接受的准确的。拟议模型校准方案的主要成分是:对使用所谓的低忠诚模型对高不忠模型类别进行计算时,对QIs的误差进行目标导向的意外误差估计值(QoIs)。对于大量计算模型,可以开发一个计算成本低费用的程序,用于校准高不忠模型(surogate)模型的外表层分布。由于应用了准线性二级地等离心边界值参数(BVPP),使用已知的直线性直线性直线性直线性直径直径模型进行校准。