Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adaptive $h$-refinement for reduced-order models   This work presents a method to adaptively refine reduced-order models \emph{a
posteriori} without requiring additional full-order-model solves. The technique
is analogous to mesh-adaptive $h$-refinement: it enriches the reduced-basis
space online by `splitting' a given basis vector into several vectors with
disjoint support. The splitting scheme is defined by a tree structure
constructed offline via recursive $k$-means clustering of the state variables
using snapshot data. The method identifies the vectors to split online using a
dual-weighted-residual approach that aims to reduce error in an output quantity
of interest. The resulting method generates a hierarchy of subspaces online
without requiring large-scale operations or full-order-model solves. Further,
it enables the reduced-order model to satisfy \emph{any prescribed error
tolerance} regardless of its original fidelity, as a completely refined
reduced-order model is mathematically equivalent to the original full-order
model. Experiments on a parameterized inviscid Burgers equation highlight the
ability of the method to capture phenomena (e.g., moving shocks) not contained
in the span of the original reduced basis.

7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex