MIT Engineers Use Artificial Intelligence To Capture the Complexity of Breaking Waves

MIT engineers have discovered a technique to predict how waves break using machine learning and data from wave tank tests. "You could mimic waves with this to help build structures better, more efficiently, and without enormous safety considerations," Themis Sapsis adds.

The predictions of the new model should aid researchers in improving ocean climate models and fine-tuning offshore structure design.

When waves reach a certain height, they break, cresting and shattering into a spray of droplets and bubbles. These waves can range in size from a surfer's point break to a soft ripple coming to shore. For decades, scientists have been unable to anticipate how and when a wave will break due to the complexity of the dynamics involved.

MIT researchers have developed a novel way for simulating how waves break. Using machine learning and data from wave-tank testing, the researchers altered equations that had previously been used to predict wave behavior. Such equations are commonly used by engineers to aid in the construction of stable offshore platforms and structures. The equations, however, have not been able to reflect the intricacy of breaking waves until recently.

The researchers observed that the improved model was more accurate in predicting how and when waves would break. The model, for example, was more accurate than standard wave equations in determining a wave's steepness immediately before breaking, as well as its energy and frequency after breaking.

Their findings, which were recently published in the journal Nature Communications, will aid scientists in better understanding how a breaking wave impacts the water in its vicinity. Understanding how these waves interact can aid in the development of offshore constructions. It can also help forecast how the water interacts with the environment. Scientists may use improved predictions of how waves break to anticipate how much carbon dioxide and other atmospheric gases the ocean can absorb, for example.

“Wave breaking is what puts air into the ocean,” explains research author Themis Sapsis, an associate professor of mechanical and ocean engineering at MIT and an affiliate of the Institute for Data, Systems, and Society. “It may sound like a detail, but if you multiply its effect over the area of the entire ocean, wave breaking starts becoming fundamentally important to climate prediction.”

Lead author and MIT postdoc Debbie Eeltink collaborated on the project with Aix-Marseille University's Hubert Branger and Christopher Luneau, Kyoto University's Amin Chabchoub, University of Geneva's Jerome Kasparian, and Delft University of Technology's T.S. van den Bremer.

Learning tank

Scientists often use one of two ways to forecast the dynamics of a breaking wave: either they try to exactly recreate the wave at the size of individual water and air molecules, or they undertake experiments to try to describe waves using real observations. The first is computationally expensive and difficult to model even across a small region, while the second takes a long time to execute enough experiments to provide statistically significant findings.

Instead, the MIT researchers used elements from both methodologies to create a machine-learning-based model that is more economical and accurate. The researchers began with a set of equations that are commonly used to describe wave behavior. They wanted to enhance the model by "training" it on data from actual trials of breaking waves.

“We had a simple model that doesn’t capture wave breaking, and then we had the truth,” Eeltink continues, referring to trials that included wave breaking. “Then we wanted to use machine learning to learn the difference between the two.”
Experiments in a 40-meter-long tank provided the researchers with wave breaking data. A paddle was attached to one end of the tank, which the team used to start each wave. The paddle was positioned to create a breaking wave in the tank's centre. As waves traveled down the tank, gauges along the length of the tank monitored the water's height.
“It takes a lot of time to run these experiments,” Eeltink explains. “Between each experiment, you have to wait for the water to completely calm down before you launch the next experiment, otherwise they influence each other.” 

Safe harbor

In total, the researchers conducted around 250 trials, using the data to train a neural network, a form of machine-learning technique. The algorithm is taught to compare the real waves in trials with the anticipated waves in the basic model, and then tweak the model to suit reality depending on any disparities between the two.

After training the system with their experimental data, the researchers fed it completely fresh data — this time, measurements from two separate tests conducted in different wave tanks with various diameters. In these experiments, they discovered that the updated model generated more accurate predictions than the simple, untrained model, such as better estimations of the steepness of a breaking wave.

The "downshift," in which a wave's frequency is changed to a lower value, was also represented by the new model, which is an important feature of breaking waves. The frequency of a wave determines its speed. Lower frequencies travel quicker than higher frequencies in ocean waves. As a result, the wave will accelerate following the downshift. The new model forecasts the shift in frequency before and after each breaking wave, which might be useful in coastal storm preparation.

“When you want to forecast when high waves of a swell would reach a harbor, and you want to leave the harbor before those waves arrive, then if you get the wave frequency wrong, then the speed at which the waves are approaching is wrong,” Eeltink adds. 

The team's modified wave model is available as open-source code, which others may be able to use in climate simulations of the ocean's ability to absorb carbon dioxide and other atmospheric gases, for example. Simulated testing of offshore platforms and coastal constructions can also use the code.

“The number one purpose of this model is to predict what a wave will do,” Sapsis explains.  “If you don’t model wave breaking right, it would have tremendous implications for how structures behave. With this, you could simulate waves to help design structures better, more efficiently, and without huge safety factors.” 
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