Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: emgr - The Empirical Gramian Framework   System Gramian matrices are a well-known encoding for properties of
input-output systems such as controllability, observability or minimality.
These so-called system Gramians were developed in linear system theory for
applications such as model order reduction of control systems. Empirical
Gramian are an extension to the system Gramians for parametric and nonlinear
systems as well as a data-driven method of computation. The empirical Gramian
framework - emgr - implements the empirical Gramians in a uniform and
configurable manner, with applications such as Gramian-based (nonlinear) model
reduction, decentralized control, sensitivity analysis, parameter
identification and combined state and parameter reduction.

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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph