Related papers: On the predictability of rogue events
Ocean dynamics constitute a source of incertitude in determining the ocean's role in complex climatic phenomena. Current observation systems have limitations in achieving sufficiently statistical precision for three-dimensional oceanic…
Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…
Advances in machine learning have revolutionized capabilities in applications ranging from natural language processing to marketing to health care. Here, we demonstrate the efficacy of machine learning in predicting chaotic behavior in…
Two numerical methods are proposed for detection of coupling between multiple time series generated by deterministic nonlinear systems. The first detects interdependence or the existence of coupling between time series. The second…
The identification of complex periodic windows in the two-dimensional parameter space of certain dynamical systems has recently attracted considerable interest. While for discrete systems, a discrimination between periodic and chaotic…
This work proposes a robust data-driven predictive control approach for unknown nonlinear systems in the presence of bounded process and measurement noise. Data-driven reachable sets are employed for the controller design instead of using…
The occurrence of extreme (rogue) waves in the ocean is for the most part still shrouded in mystery, as the rare nature of these events makes them difficult to analyze with traditional methods. Modern data mining and machine learning…
We present a theoretical study of extreme events occurring in phononic lattices. In particular, we focus on the formation of rogue or freak waves, which are characterized by their localization in both spatial and temporal domains. We…
In this brief report we study numerically the spontaneous emergence of rogue waves in (i) modulationally unstable plane wave at its long-time statistically stationary state and (ii) bound-state multi-soliton solutions representing the…
Extreme events, or rogue waves, are high-amplitude, rare occurrences that emerge across diverse physical systems and often defy conventional statistical predictions. While optical systems provide a controlled setting for studying these…
A central area of research in nonlinear science is the study of instabilities that drive the emergence of extreme events. Unfortunately, experimental techniques for measuring such phenomena often provide only partial characterization. For…
Spatiotemporal chaotic systems are difficult to characterize in a model-free manner because of their high dimensionality, strong nonlinearity, and sensitivity to initial conditions. Coupled map lattices, as a representative class of…
In multi-component systems, several rogue waves can be simultaneously excited using simple initial conditions in the form of a plane wave with a small amplitude single-peak perturbation. This is in drastic contrast with the case of…
Numerical simulations of the recently derived fully nonlinear equations of motion for weakly three-dimensional water waves [V.P. Ruban, Phys. Rev. E {\bf 71}, 055303(R) (2005)] with quasi-random initial conditions are reported, which show…
Rogue waves are intense and unexpected wavepackets ubiquitous in complex systems. In optics, they are promising as robust and noise-resistant beams for probing and manipulating the underlying material. Localizing large optical power is…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…
Rogue waves are extreme ocean events characterized by the sudden formation of anomalously large crests, and remain an important subject of investigation in oceanography and mathematics. A central problem is to quantify the probability of…
Although deterministic chaos has been predicted to occur in the triply resonant optical parametric oscillator (TROPO) fifteen years ago, experimental evidence of chaotic behavior in this system has been lacking so far, in marked contrast…
Extreme-event predictability in turbulence is strongly state dependent, yet event-by-event predictability horizons are difficult to quantify without access to governing equations or costly perturbation ensembles. Here we train an…
We present a general framework to predict precursors to extreme events in turbulent dynamical systems. The approach combines phase-space reconstruction techniques with recurrence matrices and convolutional neural networks to identify…