Year: 2007
International Journal of Numerical Analysis and Modeling, Vol. 4 (2007), Iss. 3-4 : pp. 368–391
Abstract
Determining accurate statistical information about outputs from ensembles of realizations is not generally possible whenever the input-output map involves the (computational) solution of systems of nonlinear partial differential equations (PDEs). This is due to the high cost of effecting each realization. Recently, in applications such as control and optimization that also require multiple solutions of PDEs, there has been much interest in reduced-order models (ROMs) that greatly reduce the cost of determining approximate solutions. We explore the use of ROMs for determining outputs that depend on solutions of stochastic PDEs. One is then able to cheaply determine much larger ensembles, but this increase in sample size is countered by the lower fidelity of the ROM used to approximate the state. In the contexts of proper orthogonal decomposition-based ROMs, we explore these counteracting effects on the accuracy of statistical information about outputs determined from ensembles of solutions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2007-IJNAM-867
International Journal of Numerical Analysis and Modeling, Vol. 4 (2007), Iss. 3-4 : pp. 368–391
Published online: 2007-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: reduced order modeling stochastic differential equations Brownian motion Monte Carlo methods finite element methods.