Forecasting with Lyapunov vectors

Advanced Study Group 2018/2019

The goal of this advanced study group is to debate methodologies that might be helpful to solve current problems related to the use of (covariant) Lyapunov vectors to forecast extreme and rare events in distinct areas.
Traditionally, the ability to predict the future based on past and present data is of high relevance in areas like climate changes, stock markets, critical transitions, ocean waves, extreme weathers, among others. The fundamental principles behind the mechanism of predicting rare and extreme events is of special interest. Specially, the principle behind the anticipation of peaks in 3D chaotic systems might be the alignment of invariant manifolds in the tangent space, which leads to the alignment of Lyapunov vectors preceding
the peaks. Although the method of Lyapunov vectors is restricted to a linear analysis around trajectories, signatures of their alignment should be observed at larger scales. The main purpose of the present advanced study group is to search for principles which allow Lyapunov vectors (and nonlinear extensions) to anticipate extreme and rare events in high dimensional complex systems, breeding ensembles for weather forecast, location of Coherent Lagrangian Structures, which correspond in geophysical flows to frontal regions,
among others.