基于采样的自适应贝叶斯正交法用于概率模型更新

IF 6.9 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY
Jingwen Song , Zhanhua Liang , Pengfei Wei , Michael Beer
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引用次数: 0

摘要

贝叶斯(概率)模型更新是计算科学中的一个基本概念,它允许将先验信念与观测数据相结合,以减少计算机模拟器预测的不确定性。然而,对模型参数的后验概率密度函数(PDF)进行有效评估是一项挑战,尤其是对计算量巨大的模拟器而言。本研究提出了一种基于采样的自适应贝叶斯正交方法来填补这一空白。该方法基于用高斯过程(GP)模型逼近所研究的模拟器,然后引入条件采样程序生成样本路径,从而推断出证据项的概率分布。这种推断出的概率分布确实衡量了证据项的预测不确定性,因此在此基础上提出了一种获取函数,以确定 GP 模型的预测不确定性对证据项的预测不确定性影响最大的位置。所有上述要素最终形成了一种自适应算法,用于更新模型参数的后验 PDF,并预先指定精度容限。通过对数值实例和工程应用的案例研究,验证了所提方法处理多模式问题的能力,并证明了其在估计模型证据和后验 PDF 的计算效率和精度方面的优越性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Sampling-based adaptive Bayesian quadrature for probabilistic model updating
Bayesian (probabilistic) model updating is a fundamental concept in computational science, allowing for the incorporation of prior beliefs with observed data to reduce prediction uncertainty of a computer simulator. However, the efficient evaluation of posterior probability density functions (PDFs) of model parameters poses challenges, particularly for computationally expansive simulators. This work presents a sampling-based adaptive Bayesian quadrature method to fill this gap. The method is based on approximating the simulator under investigation with a Gaussian process (GP) model, and then a conditional sampling procedure is introduced for generating sample paths, this way to infer a probability distribution for the evidence term. This inferred probability distribution indeed measures the prediction uncertainty of the evidence term, and thus based on which, an acquisition function is proposed to identify the site at which the prediction uncertainty of the GP model contributes the most to that of the evidence term. All the above ingredients finally form an adaptive algorithm for updating the posterior PDFs of model parameters with pre-specified accuracy tolerance. Case studies across numerical examples and engineering applications validate the ability of the proposed method to deal with multi-modal problems, and demonstrate its superiority in terms of computational efficiency and precision for estimating model evidence and posterior PDFs.
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来源期刊
CiteScore
12.70
自引率
15.30%
发文量
719
审稿时长
44 days
期刊介绍: Computer Methods in Applied Mechanics and Engineering stands as a cornerstone in the realm of computational science and engineering. With a history spanning over five decades, the journal has been a key platform for disseminating papers on advanced mathematical modeling and numerical solutions. Interdisciplinary in nature, these contributions encompass mechanics, mathematics, computer science, and various scientific disciplines. The journal welcomes a broad range of computational methods addressing the simulation, analysis, and design of complex physical problems, making it a vital resource for researchers in the field.
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