Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Operator inference for non-intrusive model reduction with nonlinear
  manifolds   This paper proposes a novel approach for learning a data-driven quadratic
manifold from high-dimensional data, then employing the quadratic manifold to
derive efficient physics-based reduced-order models. The key ingredient of the
approach is a polynomial mapping between high-dimensional states and a
low-dimensional embedding. This mapping comprises two parts: a representation
in a linear subspace (computed in this work using the proper orthogonal
decomposition) and a quadratic component. The approach can be viewed as a form
of data-driven closure modeling, since the quadratic component introduces
directions into the approximation that lie in the orthogonal complement of the
linear subspace, but without introducing any additional degrees of freedom to
the low-dimensional representation. Combining the quadratic manifold
approximation with the operator inference method for projection-based model
reduction leads to a scalable non-intrusive approach for learning reduced-order
models of dynamical systems. Applying the new approach to transport-dominated
systems of partial differential equations illustrates the gains in efficiency
that can be achieved over approximation in a linear subspace.

36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga