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Learning to school in the presence of hydrodynamic interactions

  • M. Gazzola (a1), A. A. Tchieu (a2), D. Alexeev (a3), A. de Brauer (a4) and P. Koumoutsakos (a3)...
Abstract

Schooling, an archetype of collective behaviour, emerges from the interactions of fish responding to sensory information mediated by their aqueous environment. A fundamental and largely unexplored question in fish schooling concerns the role of hydrodynamics. Here, we investigate this question by modelling swimmers as vortex dipoles whose interactions are governed by the Biot–Savart law. When we enhance these dipoles with behavioural rules from classical agent-based models, we find that they do not lead robustly to schooling because of flow-mediated interactions. We therefore propose to use swimmers equipped with adaptive decision-making that adjust their gaits through a reinforcement learning algorithm in response to nonlinearly varying hydrodynamic loads. We demonstrate that these swimmers can maintain their relative position within a formation by adapting their strength and school in a variety of prescribed geometrical arrangements. Furthermore, we identify schooling patterns that minimize the individual and collective swimming effort, through an evolutionary optimization. The present work suggests that the adaptive response of individual swimmers to flow-mediated interactions is critical in fish schooling.

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Corresponding author
Email address for correspondence: petros@ethz.ch
References
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Abrahams M. V. & Colgan P. W. 1987 Fish schools and their hydrodynamic function: a reanalysis. Environ. Biol. Fishes 20 (1), 7980.
Aditi Simha R. & Ramaswamy S. 2002 Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles. Phys. Rev. Lett. 89 (5), 058101.
Aoki I. 1982 A simulation study on the schooling mechanism in fish. Bull. Japan. Soc. Sci. Fisheries 48 (8), 10811088.
Aref H., Newton P., Stremler M. A., Tokieda T. & Vainchtein D. 2003 Vortex crystals. Adv. Appl. Mech. 39, 179.
Barnes R. S. K. & Hughes R. N. 1988 An Introduction to Marine Ecology. Blackwell.
Boschitsch B. M., Dewey P. A. & Smits A. J. 2014 Propulsive performance of unsteady tandem hydrofoils in an in-line configuration. Phys. Fluids 26 (5), 051901.
Brady J. F. & Bossis G. 1988 Stokesian dynamics. Annu. Rev. Fluid Mech. 20, 111157.
Brady J. F., Phillips R. J., Lester J. C. & Bossis G. 1988 Dynamic simulation of hydrodynamically interacting suspensions. J. Fluid Mech. 195 (1), 257280.
Breder C. M. 1965 Vortices and fish schools. Zool. New York 50 (2), 97114.
Chate H., Ginelli F., Gregoire G., Peruani F. & Raynaud F. 2008 Modeling collective motion: variations on the Vicsek model. Eur. Phys. J. B 64 (3–4), 451456.
Couzin I. D., Krause J., Franks N. R. & Levin S. A. 2005 Effective leadership and decision-making in animal groups on the move. Nature 433 (7025), 513516.
Couzin I. D., Krause J., James R., Ruxton G. D. & Franks N. R. 2002 Collective memory and spatial sorting in animal groups. J. Theoret. Biol. 218 (1), 111.
Cullen J. M., Shaw E. & Baldwin H. A. 1965 Methods for measuring the three-dimensional structure of fish schools. Animal Behaviour 13 (4), 534543.
Dewey P. A., Quinn D. B., Boschitsch B. M. & Smits A. J. 2014 Propulsive performance of unsteady tandem hydrofoils in a side-by-side configuration. Phys. Fluids 26 (4), 041903.
Gazzola M.2013 Simulation, optimization and learning of artificial swimmers. PhD thesis, ETH Zurich.
Gazzola M., Burckhardt C. J., Bayati B., Engelke M., Greber U. F. & Koumoutsakos P. 2009 A stochastic model for microtubule motors describes the in vivo cytoplasmic transport of human adenovirus. PLoS Comput. Biol. 5 (12), e1000623.
Gazzola M., Chatelain P., van Rees W. M. & Koumoutsakos P. 2011a Simulations of single and multiple swimmers with non-divergence free deforming geometries. J. Comput. Phys. 230 (19), 70937114.
Gazzola M., Hejazialhosseini B. & Koumoutsakos P. 2014 Reinforcement learning and wavelet adapted vortex methods for simulations of self-propelled swimmers. SIAM J. Sci. Comput. 36 (3), B622B639.
Gazzola M., Mimeau C., Tchieu A. A. & Koumoutsakos P. 2012a Flow mediated interactions between two cylinders at finite Re numbers. Phys. Fluids 24 (4), 043103.
Gazzola M., van Rees W. M. & Koumoutsakos P. 2012b C-start: optimal start of larval fish. J. Fluid Mech. 698, 518.
Gazzola M., Vasilyev O. V. & Koumoutsakos P. 2011b Shape optimization for drag reduction in linked bodies using evolution strategies. Comput. Struct. 89 (11–12), 12241231.
Goto Y. & Tanaka H. 2015 Purely hydrodynamic ordering of rotating disks at a finite Reynolds number. Nat. Commun. 6.
Hansen N., Muller S. D. & Koumoutsakos P. 2003 Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evol. Comput. 11 (1), 118.
Hatwalne Y., Ramaswamy S., Rao M. & Simha R. A. 2004 Rheology of active-particle suspensions. Phys. Rev. Lett. 92 (11), 118101.
Hubbard S., Babak P., Sigurdsson S. T. & Magnusson K. G. 2004 A model of the formation of fish schools and migrations of fish. Ecol. Model. 174 (4), 359374.
Huth A. & Wissel C. 1992 The simulation of the movement of fish schools. J. Theoret. Biol. 156 (3), 365385.
Ishikawa T., Simmonds M. P. & Pedley T. J. 2006 Hydrodynamic interaction of two swimming model micro-organisms. J. Fluid Mech. 568, 119160.
Jiang H. S., Osborn T. R. & Meneveau C. 2002 The flow field around a freely swimming copepod in steady motion. Part I. Theoretical analysis. J. Plankton Res. 24 (3), 167189.
Kanso E. & Newton P. N. 2009 Passive locomotion via normal-mode coupling in a submerged spring–mass system. J. Fluid Mech. 641, 205215.
Kern S. & Koumoutsakos P. 2006 Simulations of optimized anguilliform swimming. J. Expl Biol. 209 (24), 48414857.
Koch D. L. & Subramanian G. 2011 Collective hydrodynamics of swimming microorganisms: living fluids. Annu. Rev. Fluid Mech. 43, 637659.
Landeau L. & Terborgh J. 1986 Oddity and the ‘confusion effect’ in predation. Animal Behaviour 34 (5), 13721380.
Liao J. C., Beal D. N., Lauder G. V. & Triantafyllou M. S. 2003 Fish exploiting vortices decrease muscle activity. Science 302 (5650), 15661569.
Lin Z., Thiffeault J.-L. & Childress S. 2011 Stirring by squirmers. J. Fluid Mech. 669, 167177.
Major P. F. 1978 Predator–prey interactions in two schooling fishes, Caranx ignobilis and Stolephorus purpureus . Animal Behaviour 26 (0), 760777.
Misund O. A., Aglen A. & Fronaes E. 1995 Mapping the shape, size, and density of fish schools by echo integration and a high-resolution sonar. ICES J. Marine Sci. 52 (1), 1120.
Nair S. & Kanso E. 2007 Hydrodynamically coupled rigid bodies. J. Fluid Mech. 592, 393411.
Niwa H. S. 1994 Self-organizing dynamic-model of fish schooling. J. Theoret. Biol. 171 (2), 123136.
Paoletti P. & Mahadevan L. 2011 Planar controlled gliding, tumbling and descent. J. Fluid Mech. 689, 489516.
Park H., Noca F. & Koumoutsakos P.2005 Vortex-generating microscopic robots would move in swarms. Tech. Rep., NASA Jet Propulsion Laboratory.
Parrish J. K., Viscido S. V. & Grünbaum D. 2002 Self-organized fish schools: an examination of emergent properties. Biol. Bull. 202 (3), 296305.
Partridge B. L. 1982 The structure and function of fish schools. Sci. Am. 246 (6), 114123.
Partridge B. L., Pitcher T., Cullen J. M. & Wilson J. 1980 The three-dimensional structure of fish schools. Behav. Ecol. Sociobiol. 6 (4), 277288.
Pitcher T. J., Magurran A. E. & Winfield I. J. 1982 Fish in larger shoals find food faster. Behav. Ecol. Sociobiol. 10 (2), 149151.
van Rees W. M., Gazzola M. & Koumoutsakos P. 2013 Optimal shapes for anguilliform swimmers at intermediate reynolds numbers. J. Fluid Mech. 722, R3.
van Rees W. M., Gazzola M. & Koumoutsakos P. 2015 Optimal morphokinematics for undulatory swimmers at intermediate Reynolds numbers. J. Fluid Mech. 775, 178188.
Reynolds C. W. 1987 Flocks, herds and schools: a distributed behavioural model. In SIGGRAPH’87: Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques, pp. 7187.
Ristroph L. & Zhang J. 2008 Anomalous hydrodynamic drafting of interacting flapping flags. Phys. Rev. Lett. 101 (19), 194502.
Rossinelli D., Chatagny L. & Koumoutsakos P. 2011 Evolutionary optimization of scalar transport in cylinder arrays on multiGPU/multicore architectures. In Evolutionary and Deterministic Methods for Design, Optimization and Control, pp. 773784. Proc. Euro-Gen.
Saffman P. G. 1967 The self-propulsion of a deformable body in a perfect fluid. J. Fluid Mech. 28, 385389.
Shaw E. 1978 Schooling fishes. Am. Sci. 66 (2), 166175.
Sutton S. R. & Barto A. G. 1998 Reinforcement Learning: An Introduction. MIT Press.
Taylor G. I. 1952 Analysis of the swimming of long and narrow animals. Proc. R. Soc. Lond. A 214, 158183.
Tchieu A. A., Crowdy D. & Leonard A. 2010 Fluid-structure interaction of two bodies in an inviscid fluid. Phys. Fluids 22 (10), 107101.
Tchieu A. A., Kanso E. & Newton P. K. 2012 The finite-dipole dynamical system. Proc. R. Soc. Lond. A 468, 30063026.
Wu T. Y. 1971 Hydrodynamics of swimming fish and cetaceans. Adv. Appl. Maths 11, 163.
Tsang A. C. H. & Kanso E. 2013 Dipole interactions in doubly periodic domains. J. Nonlinear Sci. 23 (6), 971991.
Vicsek T., Czirok A., Benjacob E., Cohen I. & Shochet O. 1995 Novel type of phase-transition in a system of self-driven particles. Phys. Rev. Lett. 75 (6), 12261229.
Viscido S. V., Parrish J. K. & Grunbaum D. 2005 The effect of population size and number of influential neighbors on the emergent properties of fish schools. Ecol. Model. 183 (2–3), 347363.
Watkins C. & Dayan P. 1992 Q-learning. Mach. Learn. 8 (3–4), 279292.
Weihs D. 1973 Hydromechanics of fish schooling. Nature 241 (5387), 290291.
Weihs D. 2004 The hydrodynamics of dolphin drafting. J. Biol. 3 (2), 8.
Whittlesey R., Liska S. & Dabiri J. 2010 Fish schooling as a basis for vertical axis wind turbine farm design. Bioinspir. Biomim. 5 (3), 035005.
Wolfgang M. J., Anderson J. M., Grosenbaugh M. A., Yue D. K. & Triantafyllou M. S. 1999 Near-body flow dynamics in swimming fish. J. Exp. Biol. 202 (17), 23032327.
Zhu L., Lauga E. & Brandt L. 2012 Self-propulsion in viscoelastic fluids: pushers vs. pullers. Phys. Fluids 24, 051902.
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