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Swimming in schools gives fish an energy boost

Swimming in schools give fish an energetic advantage, a new study shows.

Scientists developed a highly detailed simulation of the complex interplay between swimming fish and their flow environment. Previous research had only studied fish schooling with very simplified models that didn’t account accurately for fluid dynamics, researchers say.

Using the supercomputer “Piz Daint” at the Swiss National Supercomputing Centre (CSCS) allowed, for the first time, state-of-the-art computationally intensive simulations without simplifications.

fish schooling simulation
Two leading fish generate a way that a follower uses to increase its swimming-efficiency. (Credit: CSElab/ETH Zurich)

Scientists were also able to combine the realistic flow simulations with reinforcement learning, a potent machine learning algorithm. This kind of learning algorithm has been used in games such as “Go,” enabling the computer to outperform humans. Deploying reinforcement learning on complex physical systems, however, has never been done before, as the algorithm requires thousands of iterations.

Pavlov’s dog

The algorithm is reminiscent of Pavlov’s dog, scientists say. The agents learn an optimal strategy for achieving a goal by receiving a reward.

“We created the mathematical conditions and gave the fish the single goal of swimming as efficiently as possible.”

For the current study, researchers used it to train the fish for optimal swimming behavior and to let them decide independently how to most efficiently react to the unsteady flow fields of their fellow swimmers.



Into the vortex

In their simulation, the researchers observed the swimming behavior of up to three fish, both in 2D and 3D, in various configurations. No flow simulation has ever included more than one swimmer in three dimensions. They analyzed every detail of each individual flow vortex to understand the behavior of the fish.


Verma and Novati conducted the study, which appears in the Proceedings of the National Academy of Sciences, under the leadership of Petros Koumoutsakos, a professor at ETH Zurich.

The fish swam most energetically when they swam not one after the other, as previously suggested, but at an offset from the swimming direction of the leader. At such locations they harnessed the vortices that the leader generated by intercepting them with their head, splitting the vortex into fragments that they then guided down their bodies. The progress of these fragmented vortices supplies the fish with thrust without robbing the leader of energy.


Verma emphasizes that the simulations didn’t examine every aspect involved in the efficient swimming behavior of fish, but the algorithms they developed and the physics they learned more about could be useful for autonomously swimming or flying robots.

Robot submarine flaps its fins to swim without power

An autonomous robot swimmer or flyer could handle unexpected flow situations—for example, when flying between buildings in high winds to deliver goods, or during search and rescue operations in stormy conditions.

“The possibility of letting airplanes with similar destinations fly in formation along certain routes to save fuel is also being considered. The algorithms developed in our work could also be put to use here,” says Novati.

Source: Simone Ulmer for ETH Zurich