Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Augmented Variational Superposed Gaussian Approximation for Langevin
  Equations with Rational Polynomial Functions   Reliable methods for obtaining time-dependent solutions of Langevin equations
are in high demand in the field of non-equilibrium theory. In this paper, we
present a new method based on variational superposed Gaussian approximation
(VSGA) and Pad\'e approximant. The VSGA obtains time-dependent probability
density functions as a superposition of multiple Gaussian distributions.
However, a limitation of the VSGA is that the expectation of the drift term
with respect to the Gaussian distribution should be calculated analytically,
which is typically satisfied when the drift term is a polynomial function. When
this condition is not met, the VSGA must rely on the numerical integration of
the expectation at each step, resulting in huge computational cost. We propose
an augmented VSGA (A-VSGA) method that effectively overcomes the limitation of
the VSGA by approximating non-linear functions with the Pad\'e approximant. We
apply the A-VSGA to two systems driven by chaotic input signals, a stochastic
genetic regulatory system and a soft bistable system, whose drift terms are a
rational polynomial function and a hyperbolic tangent function, respectively.
The numerical calculations show that the proposed method can provide accurate
results with less temporal cost than that required for Monte Carlo simulation.

26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga