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Rogue waves, which are defined as waves with a wave height, or alternatively a crest height, exceeding the significant wave height by a certain factor, continue to endanger ships and offshore infrastructure. Hence, reliable rogue wave forecasting is of utmost importance to increase the safety for maritime operations. While the occurrence of rogue waves is widely acknowledged, their emergence remains unpredictable due to the lack of a well-accepted basis for explaining their occurrence. In fact, two popular mechanisms explaining the formation of rogue waves lead to considerably different conclusions about their predictability. On the one hand, a rogue wave could be formed by a superposition of wave trains with unknown phases. With this generation mechanism, rogue wave prediction is not viable. On the other hand, nonlinear focusing leading to the Benjamin-Feir instability gives rise to slowly developing rogue waves. Hence, this rogue wave formation could be detected with significant advance time. Given this background, there is an imperative need to address the basic question: Are rogue waves predictable? In this article, the authors explore the predictability of rogue waves by constructing and parameterizing neural networks. The networks are trained on available buoy data, which allows not only for an assessment under the most realistic conditions but also for indicating the sufficiency of current ocean measurements for rogue wave prediction. 

Freak waves, waves significantly higher than neighboring waves, are a serious threat to ships and marine infrastructure. Despite significant refinement of operational wave models and recent progress in studying the theoretical foundations of such extreme events, the emergence of these events remains unpredictable. In this work, the authors propose a data-driven wave forecasting approach by combining the essence of common wave models, rapid oscillations, and slowly changing spectrum with data-driven techniques such as recurrent neural networks. A judicious minimization procedure is developed, wherein the sea surface elevation is first decomposed into harmonic functions with varying amplitudes. Then, the amplitude variations are forecasted by fitting universal, black-box models. This approach, which can be used to forecast wave crests and troughs in real time, is tested on available buoy data. Overall, the developed models and fitting strategies outperform simple benchmarks indicating the approach’s potential for operational, real-time wave forecasting. 

Energy localization, which are spatially confined response patterns, have been observed in turbomachinery applications, micro-electromechanical systems, and atomic crystals. While confined energy can reduce a device’s life-span, in sensing and energy harvesting applications, it can be beneficial to steer a system’s response into a localized mode. Building on earlier studies, in this article, the authors extend the research on localization by considering an array of coupled Duffing oscillators arranged in a circle. The system is composed of multiple nonlinear oscillators each connected to two neighboring oscillators via springs. Due to the periodic boundary conditions waves can propagate through the boundaries. These oscillators are hardening in most of the considered cases, and softening in the others. In the studied parameter range, the system is characterized by multi-stable behavior and a localized mode as well as a unison-low-amplitude motion coexist. The possibility that white noise can drive the system response from the localized mode to the low amplitude mode and thus suppresses energy localization is investigated. For different noise levels, the duration needed to stop energy localization as well as the probability to suppress localization within a certain time is numerically studied. In addition, the effects of linear coupling and nonlinear coupling between the oscillators on the strength of localization and the minimum noise addition needed to suppress energy localization are examined in depth. Moreover, modeling of large array dynamics with smaller subsystems is explored and dynamics with non-Gaussian noise is also considered.