Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Learning reduced order models from data for hyperbolic PDEs   Given a set of solution snapshots of a hyperbolic PDE, we are interested in
learning a reduced order model (ROM). To this end, we propose a novel decompose
then learn approach. We decompose the solution by expressing it as a
composition of a transformed solution and a de-transformer. Our idea is to
learn a ROM for both these objects, which, unlike the solution, are well
approximable in a linear reduced space. A ROM for the (untransformed) solution
is then recovered via a recomposition. The transformed solution results from
composing the solution with a spatial transform that aligns the spatial
discontinuities. Furthermore, the de-transformer is the inverse of the spatial
transform and lets us recover a ROM for the solution. We consider an image
registration technique to compute the spatial transform, and to learn a ROM, we
resort to the dynamic mode decomposition (DMD) methodology. Several benchmark
problems demonstrate the effectiveness our method in representing the data and
as a predictive tool.

28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex