Physical systems of interest to society are extremely complex. For example, the atmosphere and ocean of Earth, relevant for questions of global warming, long time climate estimates or prediction of extreme whether events, consists of a tremendeous number of interacting systems, each with many degrees of freedom. It is impossible to consider the system in its full complexity when trying to make predictions, in particular if the questions concern long-time prediction or rare events.
Indeed, multiscale systems are ubiquitous in nature: the underlying processes relevant to many physical phenomena often happen on vastly different length- or time-scales. This opens up the possibility of coarse-graining and averaging, where fast, fluctuating degrees of freedom can be considered as effective noise on slow degrees of freedom. In particular, this helps to reduce, or coarse-grain, complex physical models into much simpler models that are tractable analytically or numerically to enable prediction and deeper understanding of the involved processes.
Rare events, for example conformational changes of the relevant unknowns, are particularly interesting and rich in such a setup. In stochastic systems, unlikely fluctuations can push the system from its typical state into other, meta-stable configurations with often vastly different properties. Examples are chemical reactions, phase transitions, weather patterns, protein folding, or persistent structures in fluid flow. In such situations, large deviation theory gives precise and rigorous estimates of the probabilities and mechanisms of these conformational changes, by generalising the notion of free energy and entropy to arbitrary stochastic systems.
Obtaining explicit large deviation principles in this multiscale setup is a big challenge, since the associated fluctuations stem from averaging of complex physical processes, and therefore are generally non-linear, non-Gaussian, or even non-Markovian. The computation of large deviation principles in such a setup is of high importance, as it would allow us to estimate transition probabilities on the effective, coarse-grained model, without the need to consider all (fast, unimportant) degrees of freedom, thus making computation feasible.
The proposal concerns itself with the development of theory and numerical algorithms in the above situation, and to make available the developed techniques to applied sciences. The PI will apply these large deviation methods for multiscale systems and coarse-grained models to three concrete problems: (i) Metastability in atmospheric jets, where turbulent fluctuations facilitate the disappearance of planetary jets in atmospheric flow, (ii) magnetically confined fusion experiments, where conformational changes in the boundary layer in plasma reactors prevent efficient confinement, and (iii) fibre-optics communications, where random fluctuations in optical fibres lead to bit-flips in photonic communication.
All theoretical research efforts will result in the development of algorithms or software implementations permitting the re-use by researchers in other fields that are concerned with rare events in multiscale systems.
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