@Article{IJNAM-4-368,
author = {J. Burkardt, Max D. Gunzburger and C. Webster},
title = {Reduced Order Modeling of Some Nonlinear Stochastic Partial Differential Equations},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2007},
volume = {4},
number = {3-4},
pages = {368--391},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/867.html}
}