Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Online adaptive basis refinement and compression for reduced-order
  models via vector-space sieving   In many applications, projection-based reduced-order models (ROMs) have
demonstrated the ability to provide rapid approximate solutions to
high-fidelity full-order models (FOMs). However, there is no a priori assurance
that these approximate solutions are accurate; their accuracy depends on the
ability of the low-dimensional trial basis to represent the FOM solution. As a
result, ROMs can generate inaccurate approximate solutions, e.g., when the FOM
solution at the online prediction point is not well represented by training
data used to construct the trial basis. To address this fundamental deficiency
of standard model-reduction approaches, this work proposes a novel
online-adaptive mechanism for efficiently enriching the trial basis in a manner
that ensures convergence of the ROM to the FOM, yet does not incur any FOM
solves. The mechanism is based on the previously proposed adaptive
$h$-refinement method for ROMs [12], but improves upon this work in two crucial
ways. First, the proposed method enables basis refinement with respect to any
orthogonal basis (not just the Kronecker basis), thereby generalizing the
refinement mechanism and enabling it to be tailored to the physics
characterizing the problem at hand. Second, the proposed method provides a fast
online algorithm for periodically compressing the enriched basis via an
efficient proper orthogonal decomposition (POD) method, which does not incur
any operations that scale with the FOM dimension. These two features allow the
proposed method to serve as (1) a failsafe mechanism for ROMs, as the method
enables the ROM to satisfy any prescribed error tolerance online (even in the
case of inadequate training), and (2) an efficient online basis-adaptation
mechanism, as the combination of basis enrichment and compression enables the
basis to adapt online while controlling its dimension.

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The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
2
The categories of this paper are: math
23
The categories of this paper are: solv-int
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The categories of this paper are: supr-con
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
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The categories of this paper are: adap-org