Application of Adaptive Multilevel Splitting to High-Dimensional Dynamical Systems
Data Analysis, Statistics and Probability
2020-11-12 v1 Numerical Analysis
Numerical Analysis
Computational Physics
Fluid Dynamics
Geophysics
Abstract
Stochastic nonlinear dynamical systems can undergo rapid transitions relative to the change in their forcing, for example due to the occurrence of multiple equilibrium solutions for a specific interval of parameters. In this paper, we modify one of the methods developed to compute probabilities of such transitions, Trajectory-Adaptive Multilevel Sampling (TAMS), to be able to apply it to high-dimensional systems. The key innovation is a projected time-stepping approach, which leads to a strong reduction in computational costs, in particular memory usage. The performance of this new implementation of TAMS is studied through an example of the collapse of the Atlantic Ocean Circulation.
Cite
@article{arxiv.2011.05745,
title = {Application of Adaptive Multilevel Splitting to High-Dimensional Dynamical Systems},
author = {S. Baars and D. Castellana and F. W. Wubs and H. A. Dijkstra},
journal= {arXiv preprint arXiv:2011.05745},
year = {2020}
}