Data-driven prediction and prevention of extreme events in a spatially extended excitable system

Abstract

Extreme events occur in many spatially extended dynamical systems, often devastatingly affecting human life which makes their reliable prediction and efficient prevention highly desirable. We study the prediction and prevention of extreme events in a spatially extended system, a system of coupled FitzHugh-Nagumo units, in which extreme events occur in a spatially and temporally irregular way. Mimicking typical constraints faced in field studies, we assume not to know the governing equations of motion and to be able to observe only a subset of all phase-space variables for a limited period of time. Based on reconstructing the local dynamics from data and despite being challenged by the rareness of events, we are able to predict extreme events remarkably well. With small, rare, and spatiotemporally localized perturbations which are guided by our predictions, we are able to completely suppress extreme events in this system.

Dynamical indicators for the prediction of bursting phenomena in high-dimensional systems

“…We numerically integrate the Kolmogorov equation (14) and its associated OTD equations (19). To evaluate the right hand sides of the equations, we use a standard pseudo-spectral scheme with 2/3 dealiasing [44].…”

“…We solve the Kolmogorov equation (14) from 17 separate initial conditions which are random in phase and have exponentially decaying energy spectra. For each of the 17 simulations, we simultaneously solve the coupled OTD equations (19) with the initial conditions (21). The solutions of the Kolmogorov equation and the associated OTD equations are evolved for 1100 time units and saved to the disk every 0.2 time unit.…”

“…We solve the MNLS (29) equation and its associated OTD equation (19) where ·, · now denotes the standard L 2 inner product on complex valued functions,…”

“…[15,16]) which is comparable with Mean Square Models (models based on carefully tuned Langevin equations [17]). Since rare extreme events are associated with strong nonlinearities and intermittently positive Lyapunov exponents (i.e., high sensitivity to perturbations), their prediction from a finite set of observations is challenging and remains an active area of research (see, e.g., Giannakis and Majda [18], Bialonski et al [19]). …”

Alignment of Lyapunov Vectors: A Quantitative Criterion to Predict Catastrophes?

“…Considerable work was done in the last years to understand the mechanisms behind the emergence of large-amplitude pulses3. An idea of the intense activity concerning outliers in several distinct lasers, in nanophotonic devices and media, in excitable systems, and in other key applications may be obtained by perusing a small selection of representative papers published in the last two years456789101112131415.…”