Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomial meta-models with canonical low-rank approximations: numerical
  insights and comparison to sparse polynomial chaos expansions   The growing need for uncertainty analysis of complex computational models has
led to an expanding use of meta-models across engineering and sciences. The
efficiency of meta-modeling techniques relies on their ability to provide
statistically-equivalent analytical representations based on relatively few
evaluations of the original model. Polynomial chaos expansions (PCE) have
proven a powerful tool for developing meta-models in a wide range of
applications; the key idea thereof is to expand the model response onto a basis
made of multivariate polynomials obtained as tensor products of appropriate
univariate polynomials. The classical PCE approach nevertheless faces the
"curse of dimensionality", namely the exponential increase of the basis size
with increasing input dimension. To address this limitation, the sparse PCE
technique has been proposed, in which the expansion is carried out on only a
few relevant basis terms that are automatically selected by a suitable
algorithm. An alternative for developing meta-models with polynomial functions
in high-dimensional problems is offered by the newly emerged low-rank
approximations (LRA) approach. By exploiting the tensor-product structure of
the multivariate basis, LRA can provide polynomial representations in highly
compressed formats. Through extensive numerical investigations, we herein first
shed light on issues relating to the construction of canonical LRA with a
particular greedy algorithm involving a sequential updating of the polynomial
coefficients along separate dimensions. Canonical LRA exhibit smaller errors
than sparse PCE in cases when the number of available model evaluations is
small with respect to the input dimension. By introducing the conditional
generalization error, we further demonstrate that canonical LRA tend to
outperform sparse PCE in the prediction of extreme model responses.

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The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol