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Abstract 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. 

Abstract A probabilistic approach is needed to address systems with uncertainties arising in natural processes and engineering applications. For computational convenience, however, the stochastic effects are often ignored. Thus, numerical integration routines for stochastic dynamical systems are rudimentary compared to those for the deterministic case. In this work, the authors present a method to carry out stochastic simulations by using methods developed for the deterministic case. Thereby, the well-developed numerical integration routines developed for deterministic systems become available for studies of stochastic systems. The convergence of the developed method is shown and the method's performance is demonstrated through illustrative examples.