Life and death of a virtual copepod in turbulence

Project Information

C0PEP0D

Grant agreement ID: 834238

DOI

10.3030/834238

Project closed

EC signature date 24 May 2019

Start date 1 September 2019

End date 31 August 2025

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 2 215 794,00

EU contribution

€ 2 215 794,00

Coordinated by

ECOLE CENTRALE DE MARSEILLE EGIM
France

Periodic Reporting for period 4 - C0PEP0D (Life and death of a virtual copepod in turbulence)

Reporting period: 2024-03-01 to 2025-08-31

Summary of the context and overall objectives of the project

C0PEP0D was aimed at deciphering how planktonic copepods exploit hydrodynamic and chemical sensing to detect and track targets in turbulent flows.

Copepods are millimetric crustaceans that play a crucial role in marine ecosystems. They live in all seas and oceans and are thought to be the most abundant multicellular organisms on the planet. Yet, copepods are blind. To detect prey, predators, and mates, copepods use highly developed hydrodynamic and chemical sensing. How are they able to distinguish a meaningful signal in oceanic turbulence? Copepods, being one of the greatest success stories of marine evolution, likely evolved smart algorithms to process this sensing information. But today, these algorithms are poorly understood.

The objective of C0PEP0D was to address three questions:
Q1: Mating. How do male copepods follow the pheromone trail left by females?
Q2: Finding. How do copepods use hydrodynamic signals to “see”?
Q3: Feeding. What are the best feeding strategies in turbulent flow?

We hypothesized that reinforcement learning can help reverse-engineer the algorithms used by copepods. To test this hypothesis, we built a virtual environment where copepods are trained: virtual copepods sense flow velocity and chemical concentration, and this sensing information is processed by a neural network trained by reinforcement learning. This theoretical and numerical approach is complemented by experiments on real copepods to measure how copepods react in turbulent flow.

With this project, we have discovered how hydrodynamic and chemical signalling help plankton to perceive their environment. This research opens new avenues in marine ecology, fluid mechanics, and data processing in robotics.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

The C0PEP0D project lasted six years, from September 2019 to August 2025. During this period, three PhD students, three postdocs, and one research engineer have worked on the project.

Among the main achievements, three open-source codes have been developed and made available on github.com/C0PEP0D:
- sheld0n: A code that enables advection of active particles in flows.
- otto: A Python package to visualize, evaluate and learn strategies for odor-based searches.
- RLfl0w: A reinforcement learning code to optimize the trajectories of active particles in complex flows

Nine publications have been published, and two are currently under review. These publications are all freely available on arXiv.org (see also the webpage of the project C0PEP0D.github.io). The main results are the following.

- Surfing on turbulence: We showed that plankton can exploit flow information to "surf" on turbulence. Using this strategy, they can potentially move up and down the water column during daily vertical migration by increasing their swimming speed by up to a factor of two. We collaborated with Michelle DiBenedetto (Princeton, USA) to show that some larvae exhibit the surfing strategy conjectured

- Odor source tracking in turbulence: Searching for the source of an odor stirred by a turbulent flow is a difficult problem. We proposed an idealized benchmark for this problem and solved it with a reinforcement learning algorithm. We also proposed a heuristic strategy, called space-aware infotaxis, which is quasi-optimal for this problem.

- Robust strategy for flow sensing detection:We proposed a new approach to hydrodynamic sensing that exploits stereoscopy to improve prey detection. Our findings demonstrate that stereoscopic sensing is an efficient and robust method for planktonic organisms to detect targets from their hydrodynamic signatures (Redaelli et al., in preparation).

- Theory of flow sensing in plankton: We developed a theoretical approach to understand which components of the flow information can be sensed by a ciliated organism.

- Inverse design problem for soft particles: We generalized Stokes mobility theory from rigid to deformable bodies to model the direct problem: how a soft particle deforms and moves in flow. We then showed how to use automatic differentiation and reinforcement learning to solve the inverse problem: finding the optimal particle design that achieves a passive behavior in response to flow.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

The project has developed an interdisciplinary approach to plankton navigation, which combines fluid mechanics, machine learning, and marine ecology. This original approach allowed us to significantly advance the current state of the art, providing a solid mathematical basis for problems inspired by plankton behaviors in flows. Besides, by sharing our numerical codes, we provided open-source simulations and benchmarks that can be used by a wider community.

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