MFNets: MULTI-FIDELITY DATA-DRIVEN NETWORKS FOR BAYESIAN LEARNING AND PREDICTION

被引:20
作者
Gorodetsky, Alex A. [1 ]
Jakeman, John D. [1 ]
Geraci, Gianluca [1 ]
Eldred, Michael S. [1 ]
机构
[1] Sandia Natl Labs, Optimizat & Uncertainty Quantificat, Albuquerque, NM 87123 USA
关键词
machine learning; Bayesian network; multifidelity modeling; regression; uncertainty quantification; control-variate Monte Carlo; multilevel Monte Carlo; co-kriging; STOCHASTIC COLLOCATION; OPTIMIZATION; EFFICIENCY; INFERENCE;
D O I
10.1615/Int.J.UncertaintyQuantification.2020032978
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
This paper presents a Bayesian multifidelity uncertainty quantification framework, called MFNets, which can be used to overcome three of the major challenges that arise when data from different sources are used to enhance statistical estimation and prediction with quantified uncertainty. Specifically, we demonstrate that MFNets can (1) fuse hetero-geneous data sources arising from simulations with different parameterizations, e.g., simulation models with different uncertain parameters or data sets collected under different environmental conditions; (2) encode known relationships among data sources to reduce data requirements; and (3) improve the robustness of existing multifidelity approaches to corrupted data. In this paper we use MFNets to construct linear-subspace surrogates and estimate statistics using Monte Carlo sampling. In addition to numerical examples highlighting the efficacy of MFNets we also provide a number of theoretical results. Firstly we provide a mechanism to assess the quality of the posterior mean of a MFNets Monte Carlo estimator as a frequentist estimator. We then use this result to compare MFNets estimators to existing single fidelity, multilevel, and control variate Monte Carlo estimators. In this context, we show that the Monte Carlo- based control variate estimator can be derived entirely from the use of Bayes rule and linear-Gaussian models to our knowledge the first such derivation. Finally, we demonstrate the ability to work with different uncertain parameters across different models.
引用
收藏
页码:595 / 622
页数:28
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