Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Flow-driven spectral chaos (FSC) method for simulating long-time
  dynamics of arbitrary-order non-linear stochastic dynamical systems   Uncertainty quantification techniques such as the time-dependent generalized
polynomial chaos (TD-gPC) use an adaptive orthogonal basis to better represent
the stochastic part of the solution space (aka random function space) in time.
However, because the random function space is constructed using tensor
products, TD-gPC-based methods are known to suffer from the curse of
dimensionality. In this paper, we introduce a new numerical method called the
'flow-driven spectral chaos' (FSC) which overcomes this curse of dimensionality
at the random-function-space level. The proposed method is not only
computationally more efficient than existing TD-gPC-based methods but is also
far more accurate. The FSC method uses the concept of 'enriched stochastic flow
maps' to track the evolution of a finite-dimensional random function space
efficiently in time. To transfer the probability information from one random
function space to another, two approaches are developed and studied herein. In
the first approach, the probability information is transferred in the
mean-square sense, whereas in the second approach the transfer is done exactly
using a new theorem that was developed for this purpose. The FSC method can
quantify uncertainties with high fidelity, especially for the long-time
response of stochastic dynamical systems governed by ODEs of arbitrary order.
Six representative numerical examples, including a nonlinear problem (the
Van-der-Pol oscillator), are presented to demonstrate the performance of the
FSC method and corroborate the claims of its superior numerical properties.
Finally, a parametric, high-dimensional stochastic problem is used to
demonstrate that when the FSC method is used in conjunction with Monte Carlo
integration, the curse of dimensionality can be overcome altogether.

11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci