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.

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]

Rare event algorithms

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

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.