Adaptive multilevel splitting: Historical perspective and recent results

Cérou, Frédéric; Guyader, Arnaud; Rousset, Mathias

doi:10.1063/1.5082247

Cited by 42 publications

(42 citation statements)

References 42 publications

(57 reference statements)

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“…Another method that has been successfully applied to problems of interest for the geophysical and climate community is the Adaptive Multilevel Splitting (AMS) algorithm [39,53]. This method is particularly well suited to study rare transitions between two metastable states or attractors A and B.…”

Section: Rare Event Sampling Algorithms Based On Large Deviation Theorymentioning

confidence: 99%

Applications of large deviation theory in geophysical fluid dynamics and climate science

et al. 2021

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The climate is a complex, chaotic system with many degrees of freedom. Attaining a deeper level of understanding of climate dynamics is an urgent scientific challenge, given the evolving climate crisis. In statistical physics, many-particle systems are studied using Large Deviation Theory (LDT). A great potential exists for applying LDT to problems in geophysical fluid dynamics and climate science. In particular, LDT allows for understanding the properties of persistent deviations of climatic fields from long-term averages and for associating them to low-frequency, large-scale patterns. Additionally, LDT can be used in conjunction with rare event algorithms to explore rarely visited regions of the phase space. These applications are of key importance to improve our understanding of high-impact weather and climate events. Furthermore, LDT provides tools for evaluating the probability of noise-induced transitions between metastable climate states. This is, in turn, essential for understanding the global stability properties of the system. The goal of this review is manifold. First, we provide an introduction to LDT. We then present the existing literature. Finally, we propose possible lines of future investigations. We hope that this paper will prepare the ground for studies applying LDT to solve problems encountered in climate science and geophysical fluid dynamics.

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Section: Rare Event Sampling Algorithms Based On Large Deviation Theorymentioning

confidence: 99%

Applications of large deviation theory in geophysical fluid dynamics and climate science

et al. 2021

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“…Obtaining this eigenvalue is not always an easy -or even possible -task, and often one needs to resort to numerical methods. Methods to overcome this difficulty often include techniques based on population dynamics, namely cloning or splitting [8][9][10][11], and importance sampling [12][13][14][15][16] which provide information about the configurations frequently visited by the rare events. Notice that even if one manages to diagonalise the tilted generator (or the Markov matrix), the generation of rare trajectories is non-trivial: while rare trajectories are "generated" by the tilted operator, this is not a proper stochastic operator and these trajectories cannot be directly sampled.…”

Section: Introductionmentioning

confidence: 99%

Optimal sampling of dynamical large deviations via matrix product states

2021

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The large deviation (LD) statistics of dynamical observables is encoded in the spectral properties of deformed Markov generators. Recent works have shown that tensor network methods are well suited to compute the relevant leading eigenvalues and eigenvectors accurately. However, the efficient generation of the corresponding rare trajectories is a harder task. Here we show how to exploit the MPS approximation of the dominant eigenvector to implement an efficient sampling scheme which closely resembles the optimal (so-called "Doob") dynamics that realises the rare events. We demonstrate our approach on three well-studied lattice models, the Fredrickson-Andersen and East kinetically constrained models (KCMs), and the symmetric simple exclusion process (SSEP). We discuss how to generalise our approach to higher dimensions.

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“…More recently it has been applied to rare events in stochastic models of wall turbulence (Rolland 2018) and atmospheric dynamics (Bouchet, Rolland & Simonnet 2019). A review of the AMS algorithm, its history and applications is also available in Cérou, Guyader & Rousset (2019).…”

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confidence: 99%