AI finds formula to predict monster waves

Stories of monstrous waves, called rogue waves, have been part of sailors’ lore for centuries. But when a rogue wave 26 meters high slammed into the Norwegian oil rig Draupner in 1995, digital instruments were there to capture and measure the North Sea monster. It was the first time a rogue had been measured and provided scientific evidence that abnormal ocean waves actually exist.

Since then, these extreme waves have been the subject of numerous studies. And now, researchers at the Niels Bohr Institute at the University of Copenhagen have used AI methods to discover a mathematical model that provides a recipe for how – and especially when – rogue waves can occur.

Using huge amounts of data on ocean movements, researchers can predict the likelihood of being hit by a monster wave at sea at any given time.

“Basically, it’s just very bad luck when one of these giant waves hits. They are caused by a combination of many factors that, until now, have not been combined into a single risk estimate “In the study, we mapped the causal variables that create rogue waves and used artificial intelligence to bring them together into a model that can calculate the probability of rogue waves forming,” explains Dion Häfner.

Häfner is a former doctoral student at the Niels Bohr Institute and first author of the scientific study which has just been published in the journal Proceedings of the National Academy of Sciences (PNAS).

Rogue waves happen every day

In their model, the researchers combined available data on ocean movements and sea states, as well as water depths and bathymetric information. Most importantly, the wave data was collected from buoys located in 158 different locations around the U.S. coasts and overseas territories, which collect data 24 hours a day. When combined, these Data – from more than a billion waves – contains information on wave height and sea state over 700 years.

Researchers analyzed many types of data to find the causes of rogue waves, defined as waves at least twice as high as surrounding waves, including extreme rogue waves that can reach more than 20 meters high. Using machine learning, they turned it all into an algorithm that was then applied to their dataset.

“Our analysis demonstrates that freak waves occur all the time. In fact, we recorded 100,000 waves in our dataset that can be defined as rogue waves. This equates to approximately 1 monster wave occurring every day at n “any random place in the ocean. However, they are not all monstrous waves of extreme size,” explains Johannes Gemmrich, the second author of the study.

Artificial intelligence as a scientist

In this study, the researchers were helped by artificial intelligence. They used several AI methods, including symbolic regression which gives an equation as output, rather than simply returning a single prediction as traditional AI methods do.

Looking at more than a billion waves, the researchers’ algorithm analyzed its own method for finding the causes of rogue waves and condensed it into an equation describing the recipe for a rogue wave. The AI ​​learns the causality of the problem and communicates it to humans in the form of an equation that researchers can analyze and incorporate into their future research.

“For decades, Tycho Brahe collected astronomical observations from which Kepler, after much trial and error, was able to extract Kepler’s laws. Dion used machines to do with waves what Kepler did with planets . For me it is still shocking that something like this is possible,” says Markus Jochum.

Phenomenon known since the 1700s

The new study also breaks with the common perception of what causes rogue waves. Until now, the most common cause of a rogue wave was thought to be when one wave briefly combined with another and stole its energy, causing a large wave to move.

However, researchers establish that the most dominant factor in the materialization of these anomalous waves is what is called “linear superposition”. This phenomenon, known since the 1700s, occurs when two wave systems intersect and reinforce each other for a brief period of time.

“If two wave systems meet at sea in a way that increases the chances of generating high crests followed by deep troughs, the risk of extremely large waves arises. This is knowledge that has been around for 300 years and which we support now through data,” says Dion Häfner.

Safer shipping

The researchers’ algorithm is good news for the shipping industry, which has about 50,000 cargo ships sailing around the planet at any given time. Indeed, thanks to the algorithm, it will be possible to predict when this “perfect” combination of factors will be present to increase the risk of a monster wave which could constitute a danger for anyone at sea.

“As shipping companies plan their routes well in advance, they can use our algorithm to assess risk and determine whether there is a risk of encountering dangerous rogue waves along the way. alternative routes,” explains Dion Häfner. .

The algorithm and research are publicly available, as are the weather and wave data deployed by the researchers. Dion Häfner says that interested parties, such as public authorities and meteorological services, can easily start calculating the probability of rogue waves. And unlike many other models created using artificial intelligence, all intermediate calculations in the researchers’ algorithm are transparent.

“AI and machine learning are typically black boxes that do not enhance human understanding. But in this study, Dion used AI methods to transform a huge database of wave observations into one new probability equation for rogue waves, which can be easily understood by humans and linked to the laws of physics”, concludes Professor Markus Jochum, Dion’s thesis supervisor and co-author.