Application of Adaptive Multilevel Splitting to High-Dimensional Dynamical Systems

S. Baars; D. Castellana; F. W. Wubs; H. A. Dijkstra

doi:10.1016/j.jcp.2020.109876

Application of Adaptive Multilevel Splitting to High-Dimensional Dynamical Systems

S. Baars, D. Castellana, F. W. Wubs, H. A. Dijkstra

Research output: Contribution to journal › Article › Academic › peer-review

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.

Original language	English
Article number	109876
Pages (from-to)	1-12
Number of pages	12
Journal	Journal of Computational Physics
Volume	424
DOIs	https://doi.org/10.1016/j.jcp.2020.109876
Publication status	Published - 1 Jan 2021

Bibliographical note

Funding Information:
The authors would like to thank Jeroen Wouters and Daan Crommelin for the useful discussions. We would also like to thank the reviewers for their very helpful and constructive comments, which greatly improved the paper. This work is part of the Mathematics of Planet Earth research program with project number 657.014.007 , which is financed by the Netherlands Organisation for Scientific Research (NWO) (SB and FW), the SMCM project of the Netherlands eScience Center (NLeSC) with project number 027.017.G02 (SB, FW and HD) and the European Union's Horizon 2020 research and innovation program for the ITN CRITICS under Grant Agreement Number 643073 (DC and HD).

Publisher Copyright:
© 2020 Elsevier Inc.

Keywords

Model order reduction
Multilevel splitting
Ocean circulation
Rare transitions
Stochastic dynamical systems

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10.1016/j.jcp.2020.109876

cells-10-00508-v2Final published version, 5.7 MBLicence: Taverne

Cite this

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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. ",

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Application of Adaptive Multilevel Splitting to High-Dimensional Dynamical Systems

Abstract

Bibliographical note

Keywords

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