Fixed inducing points online Bayesian calibration for computer models with an application to a scale-resolving CFD simulation

JOURNAL OF COMPUTATIONAL PHYSICS

卷:434

Article

Duan, Yu¹  Eaton, Matthew D.¹  Bluck, Michael J.¹ 

[1] Imperial Coll London, Dept Mech Engn, Rolls Royce Modelling & Analyt M&A Grp, Nucl Engn Grp, London SW7 2BX, England

关键词: Online learning;    Bayesian calibration;    Stochastic variational inference;    Gaussian processes;   

DOI  :  10.1016/j.jcp.2021.110243

来源: Elsevier

【 摘 要 】

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 does not scale well with regard to the number of data points and also it lacks an online learning capability. The proposed FIPO-BC algorithm greatly improves the computational efficiency of the algorithm and, in addition, enables online calibration to be performed 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 (scale adaptive simulation shear-stress transport 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 points in FIFO-BC is sufficiently fine. Given that fewer datapoints are needed in the proposed FIPO-BC algorithm, compared to the STD-BC algorithm, it will be a more computational efficient algorithm. In our demonstration test cases, the proposed 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. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

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