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Forecasting and understanding the behavior of complex systems such as turbulence, climate and finance is a challenging task. To tackle this problem, various tools have been developed using dynamical systems theory, statistical mechanics or stochastic fits to the data using e.g. Auto Regressive Moving Average (ARMA) processes. Such approaches are however limited by the presence of multiple metastable states, that can trap the system in non-equilibrium quasi-steady state, or attract the trajectories in the phase space.
Examples of such meta-stable states are blocked and zonal flows in the mid-latitude atmospheric dynamics, crises and period of growth in economy and finance. At present time, there is no general theory that allows the prediction of the plausibility of, time-life of or dynamics around such meta-stable states. Improved description of the system dynamics of the trajectories in the presence of metastable states have been recently obtained by splitting the original time-series in short subsamples that obey basic ARMA processes [1,2,3]. In those papers, several indicators have been derived to analyze the data. They provide information about the number of degrees of freedom active in the systems and the probability of jumps towards other metastable states.
The goal of this PhD study is to go one step further, and use this method to forecast the behavior of complex systems. The PhD candidate will construct stochastic generators of plausible turbulent, climate and financial fields by including the underlying dynamical properties as derived by the previous indicators. She/he will assess the quality of the generated fields by comparing the results on real data. During the PhD thesis, the candidate will acquire competences in statistics, fundamental physics, climate dynamics and finance. She/he will develop numerical tools and models with the analysis of time-series.
The Phd Thesis require a good knowledge of stochastic processes and therefore a background on applied statistics or theoretical physics. The candidate should know how to use statistical analysis software as R, Matlab and/or Python. She/he should have a good level of understanding of English language, to work in an international environment.
[1] Davide Faranda, Gabriele Messori and Pascal Yiou. Dynamical proxies of North Atlantic predictability and extremes. Accepted for publication in Scientific Reports, 2017.
[2] Guillaume Nevo, Nikki Vercauteren, Amandine Kaiser, Berengere Dubrulle, Davide Faranda. A statistical-mechanical approach to study the hydrodynamic stability of stably stratified atmospheric boundary layer. Submitted, 2017.
[3] Davide Faranda and Dimitri Defrance: A wavelet-based-approach to detect climate change on the coherent and turbulent component of the atmospheric circulation. Earth System Dynamics, 7 517-523, 2016.