Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Schwarz Waveform Relaxation Physics-Informed Neural Networks for Solving
  Advection-Diffusion-Reaction Equations   This paper develops a physics-informed neural network (PINN) based on the
Schwarz waveform relaxation (SWR) method for solving local and nonlocal
advection-diffusion-reaction equations. Specifically, we derive the formulation
by constructing subdomain-dependent local solutions by minimizing local loss
functions, allowing the decomposition of the training process in different
domains in an embarrassingly parallel procedure. Provided the convergence of
PINN, the overall proposed algorithm is convergent. By constructing local
solutions, one can, in particular, adapt the depth of the deep neural networks,
depending on the solution's spectral space and time complexity in each
subdomain. We present some numerical experiments based on classical and
Robin-SWR to illustrate the performance and comment on the convergence of the
proposed method.

16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an