Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Enabling equation-free modeling via diffusion maps   Equation-free modeling aims at extracting low-dimensional macroscopic
dynamics from complex high-dimensional systems that govern the evolution of
microscopic states. This algorithm relies on lifting and restriction operators
that map macroscopic states to microscopic states and vice versa. Combined with
simulations of the microscopic state, this algorithm can be used to apply
Newton solvers to the implicitly defined low-dimensional macroscopic system or
solve it more efficiently using direct numerical simulations. The key challenge
is the construction of the lifting and restrictions operators that usually
require a priori insight into the underlying application. In this paper, we
design an application-independent algorithm that uses diffusion maps to
construct these operators from simulation data. Code is available at
https://doi.org/10.5281/zenodo.5793299.

4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex