Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Neural Networks Enforcing Physical Symmetries in Nonlinear Dynamical
  Lattices: The Case Example of the Ablowitz-Ladik Model   In this work we introduce symmetry-preserving, physics-informed neural
networks (S-PINNs) motivated by symmetries that are ubiquitous to solutions of
nonlinear dynamical lattices. Although the use of PINNs have recently attracted
much attention in data-driven discovery of solutions chiefly to partial
differential equations, we demonstrate that they fail at enforcing important
physical laws including symmetries of solutions and conservation laws. Through
the correlation of parity symmetries in both space and time of solutions to
differential equations with their group equivariant representation, we
construct group-equivariant NNs which respect spatio-temporal parity symmetry.
Moreover, we adapt the proposed architecture to enforce different types of
periodicity (or localization) of solutions to nonlinear dynamical lattices. We
do so by applying S-PINNs to the completely integrable Ablowitz-Ladik model,
and performing numerical experiments with a special focus on waveforms that are
related to rogue structures. These include the Kuznetsov-Ma soliton, and
Akhmediev breather as well as the Peregrine soliton. Our numerical results
demonstrate the superiority and robustness of the proposed architecture over
standard PINNs.

31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess