Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient Approximation of Solutions of Parametric Linear Transport
  Equations by ReLU DNNs   We demonstrate that deep neural networks with the ReLU activation function
can efficiently approximate the solutions of various types of parametric linear
transport equations. For non-smooth initial conditions, the solutions of these
PDEs are high-dimensional and non-smooth. Therefore, approximation of these
functions suffers from a curse of dimension. We demonstrate that through their
inherent compositionality deep neural networks can resolve the characteristic
flow underlying the transport equations and thereby allow approximation rates
independent of the parameter dimension.

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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
21
The categories of this paper are: adap-org