Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Model Reduction with MapReduce-enabled Tall-and-Skinny Singular Value
  Decomposition   We present a method for computing reduced-order models of parameterized
partial differential equation solutions. The key analytical tool is the
singular value expansion of the parameterized solution, which we approximate
with a singular value decomposition of a parameter snapshot matrix. To evaluate
the reduced-order model at a new parameter, we interpolate a subset of the
right singular vectors to generate the reduced-order model's coefficients. We
employ a novel method to select this subset that uses the parameter gradient of
the right singular vectors to split the terms in the expansion yielding a mean
prediction and a prediction covariance---similar to a Gaussian process
approximation. The covariance serves as a confidence measure for the reduce
order model. We demonstrate the efficacy of the reduced-order model using a
parameter study of heat transfer in random media. The high-fidelity simulations
produce more than 4TB of data; we compute the singular value decomposition and
evaluate the reduced-order model using scalable MapReduce/Hadoop
implementations. We compare the accuracy of our method with a scalar response
surface on a set of temperature profile measurements and find that our model
better captures sharp, local features in the parameter space.

9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
3
The categories of this paper are: physics
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The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga