Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adaptive-Sparse Polynomial Dimensional Decomposition Methods for
  High-Dimensional Stochastic Computing   This article presents two novel adaptive-sparse polynomial dimensional
decomposition (PDD) methods for solving high-dimensional uncertainty
quantification problems in computational science and engineering. The methods
entail global sensitivity analysis for retaining important PDD component
functions, and a full- or sparse-grid dimension-reduction integration or quasi
Monte Carlo simulation for estimating the PDD expansion coefficients. A unified
algorithm, endowed with two distinct ranking schemes for grading component
functions, was created for their numerical implementation. The fully
adaptive-sparse PDD method is comprehensive and rigorous, leading to the
second-moment statistics of a stochastic response that converges to the exact
solution when the tolerances vanish. A partially adaptive-sparse PDD method,
obtained through regulated adaptivity and sparsity, is economical and is,
therefore, expected to solve practical problems with numerous variables.
Compared with past developments, the adaptive-sparse PDD methods do not require
its truncation parameter(s) to be assigned \emph{a priori} or arbitrarily. The
numerical results reveal that an adaptive-sparse PDD method achieves a desired
level of accuracy with considerably fewer coefficients compared with existing
PDD approximations. For a required accuracy in calculating the probabilistic
response characteristics, the new bivariate adaptive-sparse PDD method is more
efficient than the existing bivariately truncated PDD method by almost an order
of magnitude. Finally, stochastic dynamic analysis of a disk brake system was
performed, demonstrating the ability of the new methods to tackle practical
engineering problems.

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The categories of this paper are: patt-sol
16
The categories of this paper are: stat
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The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat