AI Discovers Formula for Anticipating Giant Waves


Researchers have utilized artificial intelligence to address the challenge of predicting Rogue Waves, also known as giant waves, which have been difficult to forecast. Analyzing data from over a billion ocean waves, the AI system identified potential triggering factors. By comparing this information with existing physical models, the system formulated a predictive formula for such Rogue Waves. This development holds the potential to assist the maritime industry in enhancing the prediction of these waves, thus mitigating associated risks.

Rogue Waves, also referred to as Freak Waves, emerge seemingly out of nowhere on the open sea, towering more than twice the height of the surrounding waves. In 1995, for instance, a 25-meter-high Rogue Wave struck the Draupner oil platform in the North Sea, and numerous vessels succumbed to these “killer waves.” The origin of these waves and the ability to forecast them have been elusive.

While scientists can recreate Rogue Waves in laboratory settings and computer models, and some contributing factors are understood, a comprehensive prediction of Rogue Waves has remained elusive until now.

Data From One Billion Waves

Now, artificial intelligence could provide a solution. Researchers from the Niels Bohr Institute in Copenhagen under the direction of Dion Häfner have looked into whether coupled neural networks can recognize the causes of rogue waves and derive a predictive formula. They fed the AI systems with data from buoys in various oceans, recording parameters such as wave speed and frequency, wave height, wave steepness, and direction. Additionally, factors like water depth, seafloor topography, and other variables were taken into account.

The dataset comprised data for over a billion waves, encompassing both normal and rogue waves. “Our analysis demonstrated that abnormal waves occur all the time. In fact, we registered 100,000 waves in our dataset that can be defined as rogue waves,” reports co-author Johannes Gemmrich from the University of Victoria in Canada. “This means that every day, somewhere in the ocean, there is roughly one monster wave—though not all of them have an extreme height.”

What factors are decisive for a giant wave?

For their study, the researchers initially had multiple AI systems analyze the entire dataset or only specific segments. These segments included, for example, summer or winter data, shallow water, or deep water waves. The goal was to identify potential causal factors. Subsequently, the researchers examined the factors on which the neural networks agreed independently of the dataset used. Following additional tests and training sessions, Häfner and his team selected a specific AI model to continue their work.

A crucial next step involved using the method of symbolic regression, common in computer science and mathematics. This method was employed to generate an equation from the results of the AI system. The artificial intelligence evaluates how well different formulas and models fed into it represent the causal relationships and derive a suitable equation. Häfner’s colleague Markus Jochum explains, “The result ia new equation for the probability of rogue waves, which can be easily understood by people and related to the laws of physics.”

Overlap, steepness, and crest-trough height

The outcome confirms some of the previous assumptions and findings but also provides new insights. Giant waves can form when normal waves intersect at a specific angle and overlap. Whether this results in a monster wave also depends on the steepness and height difference between the wave trough and crest. Häfner clarifies, “If two wave systems meet at sea in a way that increases the chance to generate high crests followed by deep troughs, the risk of extremely large waves arises.”

It was also observed that giant waves in shallow and deep open-sea waters follow slightly different laws. They are influenced to varying degrees by the topography of the seafloor, and the favorable wave form differs. The researchers report, “In deeper water, the risk of Rogue Waves increases with the steepness of the wave. In shallow water, it is exactly the opposite: here, we find a clear negative correlation with wave steepness.

Better than common forecasting models

The effectiveness of the AI-generated formula in predicting Rogue Waves was tested by Häfner and his colleagues using previously unincorporated measurement data. The results of several existing models were compared with those of their neural networks, and the prognosis formula was derived using symbolic regression.

The outcome: “Our models predict the frequency of Rogue Waves better in all different test cases than the common methods,” write Häfner and his colleagues. The forecast using the neural network was slightly more accurate than the formula derived through symbolic regression. However, both aligned better with actual Rogue Wave events than all other formulas and models, as reported by the team.

Assistance for navigation

According to the researchers, their model opens new possibilities for better predicting the risk of Rogue Waves in the future. It could be used, for example, to identify potentially hazardous weather and sea conditions in specific maritime areas. Häfner suggests, “As shipping companies plan their routes well in advance, they can use our algorithm to get a risk assessment of whether there is a chance of encountering dangerous rogue waves along the way. Based on this, they can choose alternative routes.”

The team has made their data and algorithm publicly available for use and testing by interested parties. Simultaneously, they are working on refining the model to make particularly powerful Rogue Waves more predictably identifiable.

Source: National Academy of Sciences, 2023; doi: 10.1073/pnas.2306275120)