Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic self-similar blow up profile for 3-D Euler via
  physics-informed neural networks   We develop a new numerical framework, employing physics-informed neural
networks, to find a smooth self-similar solution for the Boussinesq equations.
The solution in addition corresponds to an asymptotic self-similar profile for
the 3-dimensional Euler equations in the presence of a cylindrical boundary. In
particular, the solution represents a precise description of the Luo-Hou
blow-up scenario [G. Luo, T. Hou, Proc. Natl. Acad. Sci. 111(36): 12968-12973,
2014] for 3-dimensional Euler. To the best of the authors' knowledge, the
solution is the first truly multi-dimensional smooth backwards self-similar
profile found for an equation from fluid mechanics. The new numerical framework
is shown to be both robust and readily adaptable to other equations.

4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an