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International Journal for Uncertainty Quantification
インパクトファクター: 4.911 5年インパクトファクター: 3.179 SJR: 1.008 SNIP: 0.983 CiteScore™: 5.2

ISSN 印刷: 2152-5080
ISSN オンライン: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2020031957
Forthcoming Article

A multi-fidelity neural network surrogate sampling method for uncertainty quantification

Mohammad Motamed
University of New Mexico

要約

We propose a multi-fidelity neural network surrogate sampling method for the uncertainty quantification of physical/biological systems described by ordinary or partial differential equations. We first generate a set of low/high-fidelity data by low/high-fidelity computational models, e.g. using coarser/finer discretizations of the governing differential equations. We then construct a two-level neural network, where a large set of low-fidelity data are utilized in order to accelerate the construction of a high-fidelity surrogate model with a small set of high-fidelity data. We then embed the constructed high-fidelity surrogate model in the framework of Monte Carlo sampling. The proposed algorithm combines the approximation power of neural networks with the advantages of Monte Carlo sampling within a multi-fidelity framework. We present two numerical examples to demonstrate the accuracy and efficiency of the proposed method. We show that dramatic savings in computational cost may be achieved when the output predictions are desired to be accurate within small tolerances.