LARGE DEVIATION THEORY AND RARE EVENT COMPUTATION

Rare events may be crucial in many natural systems, either because they have a huge impact (climate extremes, high risk situations, ...) or because even if they occur very rarely they completely change the nature of the system (phase transitions in physics, conformation change of molecules, abrupt climate changes, and so on). They are however often extremely difficult to study, because they are so rare. From a computational science point of view, one would have to make extremely long numerical simulations, which are either impossible or have a prohibitive cost. It is therefore necessary to develop specific algorithms aimed at computing rare events. We are developing such rare event algorithms, based on large deviation theory or importance sampling, and apply them in complex dynamical systems like turbulence dynamics, climate dynamics or phase transitions.

Rare event algorithms

a) The adaptive multilevel splitting algorithm to compute transition paths and transition rates arXiv:1507.05577, [.pdf]
b) Computing rare events for deterministic systems using cloning algorithms, arXiv:1511.02703, [.pdf]
c) Population dynamics method with a multi-canonical feedback control in order to compute Donsker--Varadhan (large time) large deviations arXiv:1601.06648, [.pdf]

Applications of rare event computations to complex dynamical systems

a) Transition paths and transition rates for first order phase transitions beyond Freidlin--Wentzell regime: the 1D Allen-Cahn equation arXiv:1507.05577, [.pdf]
b) Probability of extreme heat waves (project in collaboration with J. Wouters and F. Ragone, funded by AXA).
c) Probability of abrupt climate change : the example of Jupiter.

Research topics

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