Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some observations on high-dimensional partial differential equations
  with Barron data   We use explicit representation formulas to show that solutions to certain
partial differential equations lie in Barron spaces or multilayer spaces if the
PDE data lie in such function spaces. Consequently, these solutions can be
represented efficiently using artificial neural networks, even in high
dimension. Conversely, we present examples in which the solution fails to lie
in the function space associated to a neural network under consideration.

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The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
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The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph