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Freak or rogue waves are a danger to ships, offshore infrastructure, and other maritime equipment. Reliable rogue wave forecasts could mitigate this risk for operations at sea. While the occurrence of oceanic rogue waves at sea is generally acknowledged, reliable rogue wave forecasts are unavailable. In this paper, the authors seek to overcome this shortcoming by demonstrating how rogue waves can be predicted from field measurements. An extensive buoy data set consisting of billions of waves is utilized to parameterize neural networks. This network is trained to distinguish waves prior to an extreme wave from waves which are not followed by an extreme wave. With this approach, three out of four rogue waves are correctly predicted 1 min ahead of time. When the advance warning time is extended to 5 min, it is found that the ratio of accurate predictions is reduced to seven out of ten rogue waves. Another strength of the trained neural networks is their capabilities to extrapolate. This aspect is verified by obtaining forecasts for a buoy location that is not included in the networks’ training set. Furthermore, the performance of the trained neural network carries over to realistic scenarios where rogue waves are extremely rare.

 

Extreme waves, also known as ‘rogue waves’, have posed considerable challenges to maritime traffic over some time. Efforts have been directed at investigating the mechanisms governing these extreme energy localizations in oceanic environments. Modulational instability, also known as sideband instability, is one such mechanism that has been proposed to explain the occurrence of such phenomena in the framework of non-linear theory. The current work is aimed at better understanding the effects of sideband modulations on the propagation of unidirectional waves. To achieve this, a numerical wave tank (NWT) has been constructed using Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) to investigate the different parameters associated with the generation and propagation of plane, modulated waves. General Process Graphics Computing Unit (GPGPU) computing has been utilized to accelerate the computational process and improve the computational efficiency. The chosen numerical scheme has been validated by carrying out irregular waves focusing simulations to compare with available experimental data. Additionally, a Peregrine-type breather experiment has also been performed as part of the validation studies to look at energy localization within the NWT. The effects of the different parameters associated with the modulations to a plane propagating wave have been investigated using a blend of surface elevation data, eigenvalue, and frequency spectra. The effect of water depth on the perturbations to plane waves has been also investigated. The observations from these experiments can help shed light into the effects of modulations in the propagation of plane waves and help in the study of oceanic energy localization studies in future. 

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. 

In the present effort, a data-driven modeling approach is undertaken to forecast aperiodic responses of non-autonomous systems. As a representative non-autonomous system, a harmonically forced Duffing oscillator is considered. Along with it, an experimental prototype of a Duffing oscillator is studied. Data corresponding to chaotic motions are obtained through simulations of forced oscillators with hardening and softening characteristics and experiments with a bistable oscillator. Portions of these datasets are used to train a neural machine and make response predictions and forecasts for motions on the corresponding attractors. The neural machine is constructed by using a deep recurrent neural network architecture. The experiments conducted with the different numerical and experimental chaotic time-series data confirm the effectiveness of the constructed neural network for the forecasting of non-autonomous system responses. 

Generation and propagation of waves in a numerical wave tank constructed using Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) are considered here. Numerical wave tank simulations have been carried out with implementations of different Wendland kernels in conjunction with different numerical dissipation schemes. The simulations were accelerated by using General Process Graphics Processing Unit (GPGPU) computing to utilize the massively parallel nature of the simulations and thus improve process efficiency. Numerical experiments with short domains have been carried out to validate the dissipation schemes used. The wave tank experiments consist of piston-type wavemakers and appropriate passive absorption arrangements to facilitate comparisons with theoretical predictions. The comparative performance of the different numerical wave tank experiments was carried out on the basis of the hydrostatic pressure and wave surface elevations. The effect of numerical dissipation with the different kernel functions was also studied on the basis of energy analysis. Finally, the observations and results were used to arrive at the best possible numerical set up for simulation of waves at medium and long distances of propagation, which can play a significant role in the study of extreme waves and energy localizations observed in oceans through such numerical wave tank simulations. 

Saliency methods are used extensively to highlight the importance of input features in model predictions. These methods are mostly used in vision and language tasks, and their applications to time series data is relatively unexplored. In this paper, we set out to extensively compare the performance of various saliency-based interpretability methods across diverse neural architectures, including Recurrent Neural Network, Temporal Convolutional Networks, and Transformers in a new benchmark † of synthetic time series data. We propose and report multiple metrics to empirically evaluate the performance of saliency methods for detecting feature importance over time using both precision (i.e., whether identified features contain meaningful signals) and recall (i.e., the number of features with signal identified as important). Through several experiments, we show that (i) in general, network architectures and saliency methods fail to reliably and accurately identify feature importance over time in time series data, (ii) this failure is mainly due to the conflation of time and feature domains, and (iii) the quality of saliency maps can be improved substantially by using our proposed two-step temporal saliency rescaling (TSR) approach that first calculates the importance of each time step before calculating the importance of each feature at a time step.