MIT engineers use artificial intelligence to capture the complexity of breaking waves
The new model’s predictions should help researchers improve ocean climate simulations and refine the design of offshore structures.
The waves break once they reach a critical height, before peaking and crashing into a shower of droplets and bubbles. These waves can be as big as a surfer’s point break and as small as a slight ripple rolling towards the shore. For decades, the dynamics of how and when a wave breaks has been too complex for scientists to predict.
Now, MIT engineers have found a new way to model how waves break. Researchers tweaked equations that were previously used to predict wave behavior using machine learning and wave reservoir test data. Engineers frequently use such equations to help them design robust offshore platforms and structures. But so far, the equations have not been able to capture the complexity of breaking waves.
The researchers found that the modified model predicted how and when the waves would break more accurately. The model, for example, estimated the slope of a wave shortly before breaking, and its energy and frequency after breaking, more accurately than traditional wave equations.
Their results, recently published in the journal Nature Communication, will help scientists understand how a breaking wave affects the water around it. Knowing precisely how these waves interact can help refine the design of offshore structures. It can also improve predictions of how the ocean interacts with the atmosphere. Having better estimates of how waves break can help scientists predict, for example, how much carbon dioxide and other atmospheric gases the ocean can absorb.
“Wave breaking is what puts air in the ocean,” says study author Themis Sapsis, an associate professor of mechanical and ocean engineering and an affiliate at the Institute for Data, Systems, and Society of MIT. “It may seem like a detail, but if you multiply its effect over the area of the whole ocean, wave breaking starts to become fundamentally important for climate prediction.”
Co-authors of the study include lead author and post-doctoral fellow at MIT Debbie Eeltink, Hubert Branger and Christopher Luneau from the University of Aix-Marseille, Amin Chabchoub from Kyoto University, Jerome Kasparian from l University of Geneva and TS van den Bremer from Delft University of Technology. .
To predict the dynamics of a breaking wave, scientists typically take one of two approaches: either they attempt to precisely simulate the wave at the scale of individual molecules of water and air, or they conduct experiments to try to characterize the waves with real measurements. The first approach is computationally expensive and difficult to simulate even on a small area; the second requires an enormous amount of time to run enough experiments to produce statistically significant results.
Instead, the MIT team borrowed elements from both approaches to develop a more efficient and accurate model using machine learning. The researchers started with a set of equations that is considered the standard description of wave behavior. They aimed to improve the model by “training” the model on breaking wave data from real experiments.
“We had a simple model that doesn’t capture wave breaking, and then we had the truth, that is, experiments that involve wave breaking,” says Eeltink. “Then we wanted to use machine learning to learn the difference between the two.”
The researchers obtained data on wave breaking by carrying out experiments in a 40-meter-long tank. The tank was fitted at one end with a paddle that the team used to initiate each wave. The team tuned the paddle to produce a breaking wave in the middle of the tank. Gauges running the length of the reservoir measured the height of the water as the waves propagated through the reservoir.
“It takes a long time to conduct these experiments,” says Eeltink. “Between each experiment, you have to wait for the water to completely calm down before starting the next experiment, otherwise they will influence each other.”
In total, the team conducted around 250 experiments, the data from which was used to train a type of machine learning algorithm known as a neural network. Specifically, the algorithm is trained to compare the actual waves in the experiments with the predicted waves in the simple model, and based on any difference between the two, the algorithm adjusts the model to fit reality.
After training the algorithm on their experimental data, the team exposed the model to entirely new data — in this case, measurements from two independent experiments, each run in separate wave tanks with different dimensions. In these tests, they found that the updated model made more accurate predictions than the simple, untrained model, such as making better estimates of the slope of a breaking wave.
The new model also captured an essential property of breaking waves known as “retrogradation”, in which the frequency of a wave is shifted to a lower value. The speed of a wave depends on its frequency. For ocean waves, low frequencies travel faster than high frequencies. Therefore, after the downshift, the wave will move faster. The new model predicts the change in frequency, before and after each breaking wave, which could be particularly relevant for preparing for coastal storms.
“When you want to forecast when high waves of a swell would hit a port, and you want to leave the port before those waves arrive, then if you are wrong about the frequency of the waves, then the speed at which the waves are approaching is wrong,” says Eeltink.
The team’s updated wave model comes as open-source code that others could potentially use, for example in climate simulations of the ocean’s potential to absorb carbon dioxide and d other atmospheric gases. The code can also be incorporated into simulated testing of offshore platforms and coastal structures.
“The number one goal of this model is to predict what a wave will do,” says Sapsis. “If you don’t model wave breaking correctly, it would have huge implications for the behavior of structures. With this you can simulate waves to help design structures better, more efficiently and without huge safety factors.
Reference: “Nonlinear wave evolution with data-driven breaking” by D. Eeltink, H. Branger, C. Luneau, Y. He, A. Chabchoub, J. Kasparian, TS van den Bremer & TP Sapsis, April 29, 2022, Nature Communication.
This research is supported, in part, by the Swiss National Science Foundation and the US Office of Naval Research.