Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: DeepSets and their derivative networks for solving symmetric PDEs   Machine learning methods for solving nonlinear partial differential equations
(PDEs) are hot topical issues, and different algorithms proposed in the
literature show efficient numerical approximation in high dimension. In this
paper, we introduce a class of PDEs that are invariant to permutations, and
called symmetric PDEs. Such problems are widespread, ranging from cosmology to
quantum mechanics, and option pricing/hedging in multi-asset market with
exchangeable payoff. Our main application comes actually from the particles
approximation of mean-field control problems. We design deep learning
algorithms based on certain types of neural networks, named PointNet and
DeepSet (and their associated derivative networks), for computing
simultaneously an approximation of the solution and its gradient to symmetric
PDEs. We illustrate the performance and accuracy of the PointNet/DeepSet
networks compared to classical feedforward ones, and provide several numerical
results of our algorithm for the examples of a mean-field systemic risk,
mean-variance problem and a min/max linear quadratic McKean-Vlasov control
problem.

9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom