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国际不确定性的量化期刊

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ISSN 打印: 2152-5080

ISSN 在线: 2152-5099

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

卷 10, 册 6, 2020, pp. 595-622
DOI: 10.1615/Int.J.UncertaintyQuantification.2020032978
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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 heterogeneous 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.

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对本文的引用
  1. Gorodetsky A. A., Jakeman J. D., Geraci G., MFNets: data efficient all-at-once learning of multifidelity surrogates as directed networks of information sources, Computational Mechanics, 68, 4, 2021. Crossref

  2. Li Kunpeng, Fu Tao, Zhang Tianci, Song Xueguan, CMS: a novel surrogate model with hierarchical structure based on correlation mapping, Engineering with Computers, 2022. Crossref

  3. Dhulipala Somayajulu L.N., Shields Michael D., Spencer Benjamin W., Bolisetti Chandrakanth, Slaughter Andrew E., Labouré Vincent M., Chakroborty Promit, Active learning with multifidelity modeling for efficient rare event simulation, Journal of Computational Physics, 468, 2022. Crossref

  4. Xiao Chaohao, Zhu Xiaoqian, Cao Xiaoqun, Yin Fukang, Nie Jun, Hu Fujia, PA_CasualLSTM: A new time series prediction network with the physical constraint and adjusted Fourier neural operator for the time-dependent partial differential equation, Frontiers in Physics, 10, 2022. Crossref

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