Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recurrent neural networks and Koopman-based frameworks for temporal
  predictions in a low-order model of turbulence   The capabilities of recurrent neural networks and Koopman-based frameworks
are assessed in the prediction of temporal dynamics of the low-order model of
near-wall turbulence by Moehlis et al. (New J. Phys. 6, 56, 2004). Our results
show that it is possible to obtain excellent reproductions of the long-term
statistics and the dynamic behavior of the chaotic system with properly trained
long-short-term memory (LSTM) networks, leading to relative errors in the mean
and the fluctuations below $1\%$. Besides, a newly developed Koopman-based
framework, called Koopman with nonlinear forcing (KNF), leads to the same level
of accuracy in the statistics at a significantly lower computational expense.
Furthermore, the KNF framework outperforms the LSTM network when it comes to
short-term predictions. We also observe that using a loss function based only
on the instantaneous predictions of the chaotic system can lead to suboptimal
reproductions in terms of long-term statistics. Thus, we propose a
model-selection criterion based on the computed statistics which allows to
achieve excellent statistical reconstruction even on small datasets, with
minimal loss of accuracy in the instantaneous predictions.

31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio