Journal
PHYSICAL REVIEW E
Volume 91, Issue 3, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.91.032915
Keywords
-
Categories
Funding
- ONR MURI [N00014-12-1-0912]
- ONR DRI [N00014-14-1-0150]
- ONR [N00014-13-1-0797]
- NSF [DMS-1317919]
Ask authors/readers for more resources
This paper presents a nonparametric modeling approach for forecasting stochastic dynamical systems on low-dimensional manifolds. The key idea is to represent the discrete shift maps on a smooth basis which can be obtained by the diffusion maps algorithm. In the limit of large data, this approach converges to a Galerkin projection of the semigroup solution to the underlying dynamics on a basis adapted to the invariant measure. This approach allows one to quantify uncertainties (in fact, evolve the probability distribution) for nontrivial dynamical systems with equation-free modeling. We verify our approach on various examples, ranging from an inhomogeneous anisotropic stochastic differential equation on a torus, the chaotic Lorenz three-dimensional model, and the Nino-3.4 data set which is used as a proxy of the El Nino Southern Oscillation.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available