Skip to main content
Log in

Swimming strategy of settling elongated micro-swimmers by reinforcement learning

  • Article
  • Published:
Science China Physics, Mechanics & Astronomy Aims and scope Submit manuscript

Abstract

Particular types of plankton in aquatic ecosystems can coordinate their motion depending on the local flow environment to reach regions conducive to their growth or reproduction. Investigating their swimming strategies with regard to the local environment is important to obtain in-depth understanding of their behavior in the aquatic environment. In the present research, to examine an impact of the shape and gravity on a swimming strategy, plankton is considered as settling swimming particles of ellipsoidal shape. The Q-learning approach is adopted to obtain swimming strategies for smart particles with a goal of efficiently moving upwards in a two-dimensional steady flow. Strategies obtained from reinforcement learning are compared to those of naive gyrotactic particles that are modeled considering the behavior of realistic plankton. It is found that the elongation of particles improves the performance of upward swimming by facilitating particles resistance to the perturbation of vortex. In the case when the settling velocity is included, the strategy obtained by reinforcement learning has similar performance to that of the naive gyrotactic one, and they both align swimmers in upward direction. The similarity between the strategy obtained from machine learning and the biological gyrotactic strategy indicates the relationship between the aspherical shape and settling effect of realistic plankton and their gyrotactic feature.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. D. F. Blair, Annu. Rev. Microbiol. 49, 489 (1995).

    Article  Google Scholar 

  2. K. Drescher, K. C. Leptos, Tuval. Tuval, T. Ishikawa, T. J. Pedley, and R. E. Goldstein, Phys. Rev. Lett. 102, 168101 (2009), arXiv: 0901.2087.

    Article  ADS  Google Scholar 

  3. J. O. Kessler, J. Fluid Mech. 173, 191 (1986).

    Article  ADS  Google Scholar 

  4. T. J. Pedley, and J. O. Kessler, Proc. R. Soc. Lond. B 231, 47 (1987).

    Article  ADS  Google Scholar 

  5. R. N. Bearon, A. L. Hazel, and G. J. Thorn, J. Fluid Mech. 680, 602 (2011).

    Article  ADS  MathSciNet  Google Scholar 

  6. W. M. Durham, J. O. Kessler, and Stocker. Stocker, Science 323, 1067 (2009).

    Article  ADS  Google Scholar 

  7. W. M. Durham, Climent. Climent, and Stocker. Stocker, Phys. Rev. Lett. 106, 238102 (2011).

    Article  ADS  Google Scholar 

  8. J. O. Kessler, Nature 313, 218 (1985).

    Article  ADS  Google Scholar 

  9. G. J. Thorn, and R. N. Bearon, Phys. Fluids 22, 041902 (2010).

    Article  ADS  Google Scholar 

  10. O. A. Croze, Sardina. Sardina, M. Ahmed, M. A. Bees, and Brandt. Brandt, J. R. Soc. Interface 10, 20121041 (2013).

    Article  Google Scholar 

  11. F. De Lillo, Cencini. Cencini, W. M. Durham, Barry. Barry, R. Stocker, Climent. Climent, and Boffetta. Boffetta, Phys. Rev. Lett. 112, 44502 (2014), arXiv: 1310.1270.

    Article  Google Scholar 

  12. F. Santamaria, F. De Lillo, Cencini. Cencini, and Boffetta. Boffetta, Phys. Fluids 26, 111901 (2014), arXiv: 1410.1671.

    Article  ADS  Google Scholar 

  13. C. Zhan, Sardina. Sardina, E. Lushi, and Brandt. Brandt, J. Fluid Mech. 739, 22 (2014), arXiv: 1311.3185.

    Article  ADS  MathSciNet  Google Scholar 

  14. K. Tawada, and Miyamoto. Miyamoto, J. Eukaryot. Microbiol. 20, 289 (1973).

  15. K. L. Poff, and Skokut. Skokut, Proc. Natl. Acad. Sci. 74, 2007 (1977).

    Article  ADS  Google Scholar 

  16. J.-O. Kessler, Prog. Phycol. Res. 4, 258 (1986).

    Google Scholar 

  17. X. Garcia, S. Rafaï, and Peyla. Peyla, Phys. Rev. Lett. 110, 138106 (2013), arXiv: 1301.2431.

    Article  ADS  Google Scholar 

  18. H. L. Fuchs, E. J. Hunter, E. L. Schmitt, and R. A. Guazzo, J. Exp. Biol. 216, 1458 (2013).

    Article  Google Scholar 

  19. H. L. Fuchs, G. P. Gerbi, E. J. Hunter, A. J. Christman, and F. J. Diez, J. Exp. Biol. 218, 1419 (2015).

    Article  Google Scholar 

  20. A. Sengupta, Carrara. Carrara, and Stocker. Stocker, Nature 543, 555 (2017).

    Article  ADS  Google Scholar 

  21. G. Novati, Verma. Verma, D. Alexeev, Rossinelli. Rossinelli, W. M. van Rees, and Koumoutsakos. Koumoutsakos, Bioinspir. Biomim. 12, 036001 (2017), arXiv: 1610.04248.

    Article  ADS  Google Scholar 

  22. M. Gazzola, A. A. Tchieu, Alexeev. Alexeev, A. de Brauer, and P. Kou-moutsakos, J. Fluid Mech. 789, 726 (2016), arXiv: 1509.04605.

    Article  ADS  MathSciNet  Google Scholar 

  23. G. Reddy, Celani. Celani, T. J. Sejnowski, and Vergassola. Vergassola, Proc. Natl. Acad. Sci. 113, E4877 (2016).

    Article  ADS  Google Scholar 

  24. S. Colabrese, Gustavsson. Gustavsson, A. Celani, and Biferale. Biferale, Phys. Rev. Lett. 118, 158004 (2017), arXiv: 1701.08848.

    Article  ADS  Google Scholar 

  25. S. Colabrese, Gustavsson. Gustavsson, A. Celani, and Biferale. Biferale, Phys. Rev. Fluids 3, 84301 (2018), arXiv: 1711.05853.

    Article  Google Scholar 

  26. K. Gustavsson, Biferale. Biferale, A. Celani, and Colabrese. Colabrese, Eur. Phys. J. E 40, 110 (2017).

    Article  Google Scholar 

  27. N. R. Challabotla, Zhao. Zhao, and H. I. Andersson, Phys. Fluids 27, 061703 (2015).

    Article  ADS  Google Scholar 

  28. D. Kamykowski, R.-E. Reed, and G.-J. Kirkpatrick, Mar. Biol. 113, 319 (1992).

    Google Scholar 

  29. W. Lampert, Funct. Ecol. 3, 21 (1989).

    Article  Google Scholar 

  30. H. Yamazaki, and Squires. Squires, Mar. Ecol. Prog. Ser. 144, 299 (1996).

    Article  ADS  Google Scholar 

  31. R. Schuech, and S. Menden-Deuer, Limnol. Oceanogr. 4, 1 (2014).

    Article  Google Scholar 

  32. K. A. Miklasz, and M. W. Denny, Limnol. Oceanogr. 55, 2513 (2010).

    Article  ADS  Google Scholar 

  33. M. N. Ardekani, Sardina. Sardina, L. Brandt, L. Karp-Boss, R. N. Bearon, and E. A. Variano, J. Fluid Mech. 831, 655 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  34. J. Qiu, Marchioli. Marchioli, H. I. Andersson, and Zhao. Zhao, Int. J. Multiphas. Flow 118, 173 (2019).

    Article  Google Scholar 

  35. C. Siewert, R. P. J. Kunnen, Meinke. Meinke, and W. Schröder, Atmos. Res. 142, 45 (2014).

    Article  Google Scholar 

  36. C. J. C. H. Watkins, and Dayan. Dayan, Mach. Learn. 8, 279 (1992).

    Google Scholar 

  37. R. S. Sutton, and A. G. Barto, Reinforcement Learning: An Introduction (Adaptive Computation and Machine Learning) (MIT Press, Cambridge, 1998).

    Google Scholar 

  38. M. Tan, Multi-Agent Reinforcement Learning: Independent vs. Cooperative Agents, Machine Learning Proceedings 1993 (Morgan Kaufmann, San Francisco, 1993), pp. 330–337.

    Google Scholar 

  39. K. Gustavsson, Berglund. Berglund, P. R. Jonsson, and Mehlig. Mehlig, Phys. Rev. Lett. 116, 108104 (2016), arXiv: 1501.02386.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to LiHao Zhao.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11911530141, 11772172, and 91752205). JingRan Qiu, WeiXi Huang and LiHao Zhao acknowledge the support from the Institute for Guo Qiang of Tsinghua University (Grant No. 2019GQG1012).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qiu, J., Huang, W., Xu, C. et al. Swimming strategy of settling elongated micro-swimmers by reinforcement learning. Sci. China Phys. Mech. Astron. 63, 284711 (2020). https://doi.org/10.1007/s11433-019-1502-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11433-019-1502-2

Keywords

Navigation