Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Learning Transient Partial Differential Equations with Local Neural
  Operators   In decades, enormous computational resources are poured into solving the
transient partial differential equations for multifarious physical fields. The
latest artificial intelligence has shown great potential in accelerating these
computations, but its road to wide applications is hindered by the variety of
computational domains and boundary conditions. Here, we overcome this obstacle
by constructing a learning framework capable of purely representing the
transient PDEs with local neural operators (LNOs). This framework is
demonstrated in learning several transient PDEs, especially the Navier-Stokes
equations, and successfully applied to solve problems with quite different
domains and boundaries, including the internal flow, the external flow, and
remarkably, the flow across the cascade of airfoils. In these applications, our
LNOs are faster than the conventional numerical solver by over 1000 times,
which could be significant for scientific computations and engineering
simulations.

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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex