Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sparse approximation of data-driven Polynomial Chaos expansions: an
  induced sampling approach   One of the open problems in the field of forward uncertainty quantification
(UQ) is the ability to form accurate assessments of uncertainty having only
incomplete information about the distribution of random inputs. Another
challenge is to efficiently make use of limited training data for UQ
predictions of complex engineering problems, particularly with high dimensional
random parameters. We address these challenges by combining data-driven
polynomial chaos expansions with a recently developed preconditioned sparse
approximation approach for UQ problems. The first task in this two-step process
is to employ the procedure developed in (Ahlfeld et al. 2016) to construct an
"arbitrary" polynomial chaos expansion basis using a finite number of
statistical moments of the random inputs. The second step is a novel procedure
to effect sparse approximation via $\ell^1$ minimization in order to quantify
the forward uncertainty. To enhance the performance of the preconditioned
$\ell^1$ minimization problem, we sample from the so-called induced
distribution, instead of using Monte Carlo (MC) sampling from the original,
unknown probability measure. We demonstrate on test problems that induced
sampling is a competitive and often better choice compared with sampling from
asymptotically optimal measures (such as the equilibrium measure) when we have
incomplete information about the distribution. We demonstrate the capacity of
the proposed induced sampling algorithm via sparse representation with limited
data on test functions, and on a Kirchoff plating bending problem with random
Young's modulus.

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The categories of this paper are: stat
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat