Application of Adaptive Multilevel Splitting to High-Dimensional Dynamical Systems

TL;DR

This paper adapts the Trajectory-Adaptive Multilevel Sampling method for high-dimensional stochastic dynamical systems, significantly reducing computational costs and demonstrating its effectiveness on modeling Atlantic Ocean circulation collapse.

Contribution

It introduces a projected time-stepping approach to extend TAMS to high-dimensional systems, enabling efficient probability computations of rapid transitions.

Findings

Reduced computational costs and memory usage.

Successful application to Atlantic Ocean Circulation collapse.

Enhanced capability to analyze high-dimensional stochastic systems.

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.