论文标题
固定诱导点在线贝叶斯校准计算机模型，并应用于秤的CFD模拟
Fixed Inducing Points Online Bayesian Calibration for Computer Models with an Application to a Scale-Resolving CFD Simulation
论文作者
论文摘要
本文提出了一种新颖的固定诱导点在线贝叶斯校准（FIPO-BC）算法，以使用基准数据库有效地学习模型参数。标准的贝叶斯校准（STD-BC）算法提供了一种统计方法来校准计算昂贵模型的参数。但是，STD-BC算法随着数据点的数量而非常糟糕，并且缺乏在线学习能力。提出的FIPO-BC算法大大提高了计算效率，并通过在一组预定义的诱导点上执行校准来实现在线校准。 为了证明FIPO-BC算法的过程，进行了两次测试，找到最佳值并探索1）简单函数中参数的后验分布，以及2）在尺度分辨率解决的湍流模型（SAS-SST）中的高波数阻尼因子（SAS-SST）。将具有不同诱导点的FIPO-BC的结果（例如校准模型参数及其后分布）与STD-BC的结果进行了比较。发现一旦FIPO-BC的预定义诱导点足够细，FIPO-BC和STD-BC可以提供非常相似的结果。但是，FIPO-BC算法至少比STD-BC算法快十倍。同时，FIPO-BC的在线功能允许连续更新校准输出，并有可能减少生成数据库时的工作量。
This paper proposes a novel fixed inducing points online Bayesian calibration (FIPO-BC) algorithm to efficiently learn the model parameters using a benchmark database. The standard Bayesian calibration (STD-BC) algorithm provides a statistical method to calibrate the parameters of computationally expensive models. However, the STD-BC algorithm scales very badly with the number of data points and lacks online learning capability. The proposed FIPO-BC algorithm greatly improves the computational efficiency and enables the online calibration by executing the calibration on a set of predefined inducing points. To demonstrate the procedure of the FIPO-BC algorithm, two tests are performed, finding the optimal value and exploring the posterior distribution of 1) the parameter in a simple function, and 2) the high-wave number damping factor in a scale-resolving turbulence model (SAS-SST). The results (such as the calibrated model parameter and its posterior distribution) of FIPO-BC with different inducing points are compared to those of STD-BC. It is found that FIPO-BC and STD-BC can provide very similar results, once the predefined set of inducing point in FIPO-BC is sufficiently fine. But, the FIPO-BC algorithm is at least ten times faster than the STD-BC algorithm. Meanwhile, the online feature of the FIPO-BC allows continuous updating of the calibration outputs and potentially reduces the workload on generating the database.
