Breakthroughs, discoveries, and DIY tips sent every weekday. Much like mermaids, the kraken, or the hafgufa, rogue waves have been regarded as a maritime myth. These waves do not always leave a lot of data behind, making it feel as if they spring up from the depths out of nowhere. However, one monster wave did leave data behind for scientists. On January 1, 1995, a monstrous 80-foot wave slammed into the Draupner oil platform in the North Sea.

Big data and large-scale machine learning have had a profound impact on science and engineering, particularly in fields focused on forecasting and prediction. Yet, it is still not clear how we can use the superior pattern matching abilities of machine learning models for scientific discovery. This is because the goals of machine learning and science are generally not aligned. In addition to being accurate, scientific theories must also be causally consistent with the underlying physical process and allow for human analysis, reasoning, and manipulation to advance the field. In this paper, we present a case study on discovering a new symbolic model for oceanic rogue waves from data using causal analysis, deep learning, parsimony-guided model selection, and symbolic regression. We train an artificial neural network on causal features from an extensive dataset of observations from wave buoys, while selecting for predictive performance and causal invariance. We apply symbolic regression to distill this black-box model into a mathematical equation that retains the neural network's predictive capabilities, while allowing for interpretation in the context of existing wave theory. The resulting model reproduces known behavior, generates well-calibrated probabilities, and achieves better predictive scores on unseen data than current theory. This showcases how machine learning can facilitate inductive scientific discovery, and paves the way for more accurate rogue wave forecasting.

In this paper, we study data-driven localized wave solutions and parameter discovery in the massive Thirring (MT) model via the deep learning in the framework of physics-informed neural networks (PINNs) algorithm. Abundant data-driven solutions including soliton of bright/dark type, breather and rogue wave are simulated accurately and analyzed contrastively with relative and absolute errors. For higher-order localized wave solutions, we employ the extended PINNs (XPINNs) with domain decomposition to capture the complete pictures of dynamic behaviors such as soliton collisions, breather oscillations and rogue-wave superposition. In particular, we modify the interface line in domain decomposition of XPINNs into a small interface zone and introduce the pseudo initial, residual and gradient conditions as interface conditions linked adjacently with individual neural networks. Then this modified approach is applied successfully to various solutions ranging from bright-bright soliton, dark-dark soliton, dark-antidark soliton, general breather, Kuznetsov-Ma breather and second-order rogue wave. Experimental results show that this improved version of XPINNs reduce the complexity of computation with faster convergence rate and keep the quality of learned solutions with smoother stitching performance as well. For the inverse problems, the unknown coefficient parameters of linear and nonlinear terms in the MT model are identified accurately with and without noise by using the classical PINNs algorithm.

A team of researchers has developed a new framework which utilizes advanced machine learning and statistical algorithms to predict rare events without the need for large data sets. Scientists can use a combination of advanced machine learning and sequential sampling techniques to predict extreme events without the need for large data sets, according to researchers from Brown and MIT. When it comes to predicting disasters brought on by extreme events (think earthquakes, pandemics, or "rogue waves" that could destroy coastal structures), computational modeling faces an almost insurmountable challenge: Statistically speaking, these events are so rare that there's just not enough data on them to use predictive models to accurately forecast when they'll happen next. However, a group of scientists from Brown University and Massachusetts Institute of Technology suggests that it doesn't have to be that way. In a study published in Nature Computational Science, the researchers explain how they utilized statistical algorithms which require less data for accurate predictions, in combination with a powerful machine learning technique developed at Brown University.

A 15-foot tall racing exoskeleton that could soon be tearing across the Nevada desert has been presented at the International Consumer Electronics Show (CES) at Las Vegas this year. Creators say their creation'Prosthesis' can hit a top speed of roughly 20 miles per hour (32kmh) – and despite its imposing size it is nearly silent when it moves. They now want to create a'X1 Mech Racing League' where mechanical exoskeletons go head-to-head. The 8,000lb (3,600kg) 'anti-robot' is controlled by a human pilot who stands at the centre of the mechanical exoskeleton, using arm movements to drive it forward at terrifying speeds. The 8,000lb (3,600kg) 'anti-robot' is controlled by a human pilot who stands at the centre of the mechanical exoskeleton, using arm movements to drive it forward at terrifying speeds.

Using AI and data science, an MIT team was able to accurately predict rogue waves coming out of the blue in the middle of the ocean, in near real time, to help sailors change their navigation path and avoid destruction and death. Rogue waves, while rare, are unpredictable, tall (up to 100 feet) and devastating. The physical mechanism producing these waves is well understood, and is typically modeled using rotating elements. Out of curiosity, I produced a video a few years ago, with rotating elements - this was a pure mathematical simulation just for fun - and it turns out that it models pretty well the mechanism that turns regular waves into rogue waves. The intent was to have some mathematical fun: indeed I called my video "belly dancing mathematics" as it also models that process quite well.

Using AI and data science, an MIT team was able to accurately predict rogue waves coming out of the blue in the middle of the ocean, in near real time, to help sailors change their navigation path and avoid destruction and death. Rogue waves, while rare, are unpredictable, tall (up to 100 feet) and devastating. The physical mechanism producing these waves is well understood, and is typically modeled using rotating elements. Out of curiosity, I produced a video a few years ago, with rotating elements - this was a pure mathematical simulation just for fun - and it turns out that it models pretty well the mechanism that turns regular waves into rogue waves. The intent was to have some mathematical fun: indeed I called my video "belly dancing mathematics" as it also models that process quite well.