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Machine learning for active matter


The availability of large datasets has boosted the application of machine learning in many fields and is now starting to shape active-matter research as well. Machine learning techniques have already been successfully applied to active-matter data—for example, deep neural networks to analyse images and track objects, and recurrent nets and random forests to analyse time series. Yet machine learning can also help to disentangle the complexity of biological active matter, helping, for example, to establish a relation between genetic code and emergent bacterial behaviour, to find navigation strategies in complex environments, and to map physical cues to animal behaviours. In this Review, we highlight the current state of the art in the application of machine learning to active matter and discuss opportunities and challenges that are emerging. We also emphasize how active matter and machine learning can work together for mutual benefit.

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Fig. 1: Active-matter systems and phenomena.
Fig. 2: Data acquisition and analysis.
Fig. 3: Data-driven models.
Fig. 4: Navigation and search strategies.
Fig. 5: Collective dynamics in interacting populations.


  1. 1.

    Mehta, P. et al. A high-bias, low-variance introduction to machine learning for physicists. Phys. Rep. 810, 1–124 (2019).

    MathSciNet  Google Scholar 

  2. 2.

    Das Sarma, S., Deng, D. L. & Duan, L. M. Machine learning meets quantum physics. Phys. Today 72, 48–54 (2019).

    Google Scholar 

  3. 3.

    Waller, L. & Tian, L. Machine learning for 3D microscopy. Nature 523, 416–417 (2015).

    Google Scholar 

  4. 4.

    Barbastathis, G., Ozcan, A. & Situ, G. On the use of deep learning for computational imaging. Optica 6, 921–943 (2019).

    Google Scholar 

  5. 5.

    Brunton, S. L., Noack, B. R. & Koumoutsakos, P. Machine learning for fluid mechanics. Annu. Rev. Fluid Mech. 52, 477–508 (2020).

    Google Scholar 

  6. 6.

    Webb, S. Deep learning for biology. Nature 554, 555–557 (2018).

    Google Scholar 

  7. 7.

    Bechinger, C. et al. Active particles in complex and crowded environments. Rev. Mod. Phys. 88, 045006 (2016).

    MathSciNet  Google Scholar 

  8. 8.

    Ruelle, D. Chance and Chaos (Princeton Univ. Press, 1991).

  9. 9.

    Gustavsson, K., Berglund, F., Jonsson, P. & Mehlig, B. Preferential sampling and small-scale clustering of gyrotactic microswimmers in turbulence. Phys. Rev. Lett. 116, 108104 (2016).

    Google Scholar 

  10. 10.

    Sengupta, A., Carrara, F. & Stocker, R. Phytoplankton can actively diversify their migration strategy in response to turbulent cues. Nature 543, 555–558 (2017).

    Google Scholar 

  11. 11.

    Durham, W. M., Kessler, J. O. & Stocker, R. Disruption of vertical motility by shear triggers formation of thin phytoplankton layers. Science 323, 1067–1070 (2009).

    MATH  Google Scholar 

  12. 12.

    Durham, W. M. et al. Turbulence drives microscale patches of motile phytoplankton. Nat. Commun. 4, 2148 (2013).

    Google Scholar 

  13. 13.

    Yeomans, J. M. Nature’s engines: active matter. Europhys. News 48, 21–25 (2017).

    Google Scholar 

  14. 14.

    Urzay, J., Doostmohammadi, A. & Yeomans, J. M. Multi-scale statistics of turbulence motorized by active matter. J. Fluid Mech. 822, 762–773 (2017).

    MathSciNet  MATH  Google Scholar 

  15. 15.

    Doostmohammadi, A., Ignés-Mullol, J., Yeomans, J. M. & Sagués, F. Active nematics. Nat. Commun. 9, 3246 (2018).

    Google Scholar 

  16. 16.

    Palacci, J., Sacanna, S., Steinberg, A. P., Pine, D. J. & Chaikin, P. M. Living crystals of light-activated colloidal surfers. Science 339, 936–940 (2013).

    Google Scholar 

  17. 17.

    Buttinoni, I. et al. Dynamical clustering and phase separation in suspensions of self-propelled colloidal particles. Phys. Rev. Lett. 110, 238301 (2013).

    Google Scholar 

  18. 18.

    Charlesworth, H. J. & Turner, M. S. Intrinsically motivated collective motion. Proc. Natl Acad. Sci. USA 116, 15362–15367 (2019).

    Google Scholar 

  19. 19.

    Strandburg-Peshkin, A. et al. Visual sensory networks and effective information transfer in animal groups. Curr. Biol. 23, R709–R711 (2013).

    Google Scholar 

  20. 20.

    Attanasi, A. et al. Information transfer and behavioural inertia in starling flocks. Nat. Phys. 10, 691–696 (2014).

    Google Scholar 

  21. 21.

    Trianni, V. Evolutionary Swarm Robotics (Springer, 2008).

  22. 22.

    Doncieux, S., Bredeche, N., Mouret, J.-B. & Eiben, A. E. G. Evolutionary robotics: what, why, and where to. Front. Robot. AI (2015).

  23. 23.

    Bayındır, L. A review of swarm robotics tasks. Neurocomputing 172, 292–321 (2016).

    Google Scholar 

  24. 24.

    Khadka, U., Holubec, V., Yang, H. & Cichos, F. Active particles bound by information flows. Nat. Commun. 9, 3864 (2018).

    Google Scholar 

  25. 25.

    Marchetti, M. C. et al. Hydrodynamics of soft active matter. Rev. Mod. Phys. 85, 1143–1189 (2013).

    Google Scholar 

  26. 26.

    Falasco, G., Pfaller, R., Bregulla, A. P., Cichos, F. & Kroy, K. Exact symmetries in the velocity fluctuations of a hot brownian swimmer. Phys. Rev. E 94, 030602 (2016).

    Google Scholar 

  27. 27.

    Frenkel, D. & Smit, B. Understanding Molecular Simulation: From Algorithms to Applications (Elsevier, 2001).

  28. 28.

    Rosenbluth, M. N. Genesis of the Monte Carlo algorithm for statistical mechanics. AIP Conf. Proc. 690, 22–30 (2003).

    Google Scholar 

  29. 29.

    Wolfram, S. Cellular automata as models of complexity. Nature 311, 419–424 (1984).

    Google Scholar 

  30. 30.

    Lauga, E. & Powers, T. R. The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72, 096601 (2009).

    MathSciNet  Google Scholar 

  31. 31.

    Floreano, D. & Mattiussi, C. Bio-inspired Artificial Intelligence: Theories, Methods, and Technologies (MIT Press, 2008).

  32. 32.

    LeCun, Y., Bengio, Y. & Hinton, G. Deep learning. Nature 521, 436–444 (2015).

    Google Scholar 

  33. 33.

    Rabault, J., Kolaas, J. & Jensen, A. Performing particle image velocimetry using artificial neural networks: a proof-of-concept. Meas. Sci. Tech. 28, 125301 (2017).

    Google Scholar 

  34. 34.

    Hannel, M. D., Abdulali, A., O’Brien, M. & Grier, D. G. Machine-learning techniques for fast and accurate feature localization in holograms of colloidal particles. Opt. Express 26, 15221–15231 (2018).

    Google Scholar 

  35. 35.

    Boenisch, F. et al. Tracking all members of a honey bee colony over their lifetime using learned models of correspondence. Front. Robot. AI 5 (2018).

  36. 36.

    Newby, J. M., Schaefer, A. M., Lee, P. T., Forest, M. G. & Lai, S. K. Convolutional neural networks automate detection for tracking of submicron-scale particles in 2D and 3D. Proc. Natl Acad. Sci. USA 115, 9026–9031 (2018).

    Google Scholar 

  37. 37.

    Helgadottir, S., Argun, A. & Volpe, G. Digital video microscopy enhanced by deep learning. Optica 6, 506–513 (2019).

    Google Scholar 

  38. 38.

    Mehlig, B. Artificial neural networks. Preprint at (2019).

  39. 39.

    Rivenson, Y. et al. Deep learning microscopy. Optica 4, 1437–1443 (2017).

    Google Scholar 

  40. 40.

    Wu, Y. et al. Extended depth-of-field in holographic imaging using deep-learning-based autofocusing and phase recovery. Optica 5, 704–710 (2018).

    Google Scholar 

  41. 41.

    Pinkard, H., Phillips, Z., Babakhani, A., Fletcher, D. A. & Waller, L. Deep learning for single-shot autofocus microscopy. Optica 6, 794–797 (2019).

    Google Scholar 

  42. 42.

    Ling, H. et al. Behavioural plasticity and the transition to order in jackdaw flocks. Nat. Commun. 10, 5174 (2019).

    Google Scholar 

  43. 43.

    Ouellette, N. T. Flowing crowds. Science 363, 27–28 (2019).

    Google Scholar 

  44. 44.

    Jeckel, H. et al. Learning the space-time phase diagram of bacterial swarm expansion. Proc. Natl Acad. Sci. USA 116, 1489–1494 (2019).

    Google Scholar 

  45. 45.

    Regev, A. et al. The human cell atlas. eLife 6, e27041 (2017).

    Google Scholar 

  46. 46.

    Pathak, J., Hunt, B., Girvan, M., Lu, Z. & Ott, E. Model-free prediction of large spatiotemporally chaotic systems from data: A reservoir computing approach. Phys. Rev. Lett. 120, 024102 (2018).

    Google Scholar 

  47. 47.

    Bo, S., Schmidt, F., Eichhorn, R. & Volpe, G. Measurement of anomalous diffusion using recurrent neural networks. Phys. Rev. E 100, 010102(R) (2019).

    Google Scholar 

  48. 48.

    Muñoz-Gil, G., Garcia-March, M. A., Manzo, C., Martín-Guerrero, J. D. & Lewenstein, M. Single trajectory characterization via machine learning. New J. Phys. 22, 013010 (2020).

    Google Scholar 

  49. 49.

    Dehkharghani, A., Waisbord, N., Dunkel, J. & Guasto, J. S. Bacterial scattering in microfluidic crystal flows reveals giant active Taylor–Aris dispersion. Proc. Natl Acad. Sci. USA 116, 11119–11124 (2019).

    Google Scholar 

  50. 50.

    Borgnino, M. et al. Alignment of nonspherical active particles in chaotic flows. Phys. Rev. Lett. 123, 138003 (2019).

    MathSciNet  Google Scholar 

  51. 51.

    Schmidt, M. & Lipson, H. Distilling free-form natural laws from experimental data. Science 324, 81–85 (2009).

    Google Scholar 

  52. 52.

    Brunton, S. L., Proctor, J. L. & Kutz, J. N. Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proc. Natl Acad. Sci. USA 113, 3932–3937 (2016).

    MathSciNet  MATH  Google Scholar 

  53. 53.

    Rudy, S. H., Brunton, S. L., Proctor, J. L. & Kutz, J. N. Data-driven discovery of partial differential equations. Sci. Adv. 3, e1602614 (2017).

    Google Scholar 

  54. 54.

    Cvitanović, P. Recurrent flows: the clockwork behind turbulence. J. Fluid Mech. 726, 1–4 (2013).

    MathSciNet  MATH  Google Scholar 

  55. 55.

    Fonda, E., Pandey, A., Schumacher, J. & Sreenivasan, K. R. Deep learning in turbulent convection networks. Proc. Natl Acad. Sci. USA 116, 8667–8672 (2019).

    MathSciNet  Google Scholar 

  56. 56.

    Weinreb, C., Wolock, S., Tusi, B. K., Socolovsky, M. & Klein, A. M. Fundamental limits on dynamic inference from single-cell snapshots. Proc. Natl Acad. Sci. USA 115, E2467–E2476 (2018).

    Google Scholar 

  57. 57.

    Pearce, P. et al. Learning dynamical information from static protein and sequencing data. Nat. Commun. 10, 5368 (2019).

    Google Scholar 

  58. 58.

    Viswanathan, G. M., Da Luz, M. G. E., Raposo, E. P. & Stanley, H. E. The Physics of Foraging: An Introduction to Random Searches and Biological Encounters (Cambridge Univ. Press, 2011).

  59. 59.

    Volpe, G. & Volpe, G. The topography of the environment alters the optimal search strategy for active particles. Proc. Natl Acad. Sci. USA 114, 11350–11355 (2017).

    Google Scholar 

  60. 60.

    Muiños-Landin, S., Ghazi-Zahedi, K. & Cichos, F. Reinforcement learning of artificial microswimmers. Preprint at (2018).

  61. 61.

    Kiørboe, T. A Mechanistic Approach to Plankton Ecology (Princeton Univ. Press, 2008).

  62. 62.

    Colabrese, S., Gustavsson, K., Celani, A. & Biferale, L. Flow navigation by smart microswimmers via reinforcement learning. Phys. Rev. Lett. 118, 158004 (2017).

    Google Scholar 

  63. 63.

    Yoo, B. & Kim, J. Path optimization for marine vehicles in ocean currents using reinforcement learning. J. Mar. Sci. Tech. 21, 334–343 (2015).

    Google Scholar 

  64. 64.

    Biferale, L., Bonaccorso, F., Buzzicotti, M., Leoni, P. C. D. & Gustavsson, K. Zermelo’s problem: optimal point-to-point navigation in 2D turbulent flows using reinforcement learning. Chaos 29, 103138 (2019).

    MathSciNet  Google Scholar 

  65. 65.

    Schneider, E. & Stark, H. Optimal steering of a smart active particle. Europhys. Lett. 127, 34003 (2019).

    Google Scholar 

  66. 66.

    Reddy, G., Celani, A., Sejnowski, T. J. & Vergassola, M. Learning to soar in turbulent environments. Proc. Natl Acad. Sci. USA 113, E4877–E4884 (2016).

    Google Scholar 

  67. 67.

    Reddy, G., Wong-Ng, J., Celani, A., Sejnowski, T. J. & Vergassola, M. Glider soaring via reinforcement learning in the field. Nature 562, 236–239 (2018).

    Google Scholar 

  68. 68.

    Vicsek, T. & Zafeiris, A. Collective motion. Phys. Rep. 517, 71–140 (2012).

    Google Scholar 

  69. 69.

    Berdahl, A. M. et al. Collective animal navigation and migratory culture: from theoretical models to empirical evidence. Phil. Trans. R. Soc. B 373, 20170009 (2018).

    Google Scholar 

  70. 70.

    Mijalkov, M., McDaniel, A., Wehr, J. & Volpe, G. Engineering sensorial delay to control phototaxis and emergent collective behaviors. Phys. Rev. X 6, 011008 (2016).

    Google Scholar 

  71. 71.

    Leyman, M., Ogemark, F., Wehr, J. & Volpe, G. Tuning phototactic robots with sensorial delays. Phys. Rev. E 98, 052606 (2018).

    Google Scholar 

  72. 72.

    Volpe, G. & Wehr, J. Effective drifts in dynamical systems with multiplicative noise: a review of recent progress. Rep. Prog. Phys. 79, 053901 (2016).

    Google Scholar 

  73. 73.

    Palmer, G. & Yaida, S. Optimizing collective fieldtaxis of swarming agents through reinforcement learning. Preprint at (2017).

  74. 74.

    Gazzola, M., Tchieu, A. A., Alexeev, D., de Brauer, A. & Koumoutsakos, P. Learning to school in the presence of hydrodynamic interactions. J. Fluid Mech. 789, 726–749 (2016).

    MathSciNet  Google Scholar 

  75. 75.

    Verma, S., Novati, G. & Koumoutsakos, P. Efficient collective swimming by harnessing vortices through deep reinforcement learning. Proc. Natl Acad. Sci. USA 115, 5849–5854 (2018).

    Google Scholar 

  76. 76.

    Donahue, J. et al. Long-term recurrent convolutional networks for visual recognition and description. In Proc. IEEE Conf. Computer Vision and Pattern Recognition 2625–2634 (IEEE, 2015).

  77. 77.

    Bierbach, D. et al. Insights into the social behavior of surface and cave-dwelling fish (Poecilia mexicana) in light and darkness through the use of a biomimetic robot. Front. Robot. AI 5, 3 (2018).

    Google Scholar 

  78. 78.

    Hüttenrauch, M., Šošić, A. & Neumann, G. Deep reinforcement learning for swarm systems. J. Mach. Learn. Res. 20, 1–31 (2019).

    MathSciNet  MATH  Google Scholar 

  79. 79.

    Jones, S., Winfield, A. F., Hauert, S. & Studley, M. Onboard evolution of understandable swarm behaviors. Adv. Intell. Sys. 1, 1900031 (2019).

    Google Scholar 

  80. 80.

    Li, W., Gauci, M. & Groß, R. Turing learning: a metric-free approach to inferring behavior and its application to swarms. Swarm Intell. 10, 211–243 (2016).

    Google Scholar 

  81. 81.

    Halloy, J. et al. Social integration of robots into groups of cockroaches to control self-organized choices. Science 318, 1155–1158 (2007).

    Google Scholar 

  82. 82.

    Rubenstein, M., Cornejo, A. & Nagpal, R. Programmable self-assembly in a thousand-robot swarm. Science 345, 795–799 (2014).

    Google Scholar 

  83. 83.

    Palmer, S. E., Marre, O., Berry, M. J. & Bialek, W. Predictive information in a sensory population. Proc. Natl Acad. Sci. USA 112, 6908–6913 (2015).

    Google Scholar 

  84. 84.

    R., S. & J. R., S. Ecology and physics of bacterial chemotaxis in the ocean. Microbiol. Mol. Biol. Rev. 76, 792–812 (2012).

    Google Scholar 

  85. 85.

    Zahedi, K. & Ay, N. Quantifying morphological computation. Entropy 15, 1887–1915 (2013).

    MATH  Google Scholar 

  86. 86.

    Bray, D. Protein molecules as computational elements in living cells. Nature 376, 307–312 (1995).

    Google Scholar 

  87. 87.

    Qian, L., Winfree, E. & Bruck, J. Neural network computation with dna strand displacement cascades. Nature 475, 368–372 (2011).

    Google Scholar 

  88. 88.

    Kirkpatrick, J. et al. Overcoming catastrophic forgetting in neural networks. Proc. Natl Acad. Sci. USA 114, 3521–3526 (2017).

    MathSciNet  MATH  Google Scholar 

  89. 89.

    Abbe, E. & Sandon, C. Provable limitations of deep learning. Preprint at (2019).

  90. 90.

    Lakshminarayanan, B., Pritzel, A. & Blundell, C. Simple and scalable predictive uncertainty estimation using deep ensembles. In Proc. 31st Int. Conf. Advances in Neural Information Processing Systems 6402–6413 (NIPS, 2017).

  91. 91.

    Rudin, C. Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead. Nat. Mach. Intell. 1, 206–215 (2019).

    Google Scholar 

  92. 92.

    Jakobi, N., Husbands, P. & Harvey, I. In Advances in Artificial Life (eds Morán, F. et al.) 704–720 (Springer, 1995).

  93. 93.

    Birattari, M. et al. Automatic off-line design of robot swarms: a manifesto. Front. Robot. AI (2019).

  94. 94.

    Domingos, P. A few useful things to know about machine learning. Commun. ACM 55, 78 (2012).

    Google Scholar 

  95. 95.

    Chicco, D. Ten quick tips for machine learning in computational biology. BioData Min. 10, 35 (2017).

    Google Scholar 

  96. 96.

    Nichols, J. A., Chan, H. W. H. & Baker, M. A. B. Machine learning: applications of artificial intelligence to imaging and diagnosis. Biophys. Rev. 11, 111–118 (2019).

    Google Scholar 

  97. 97.

    Hand, D. J. Classifier technology and the illusion of progress. Stat. Sci. 21, 1–14 (2006).

    MathSciNet  MATH  Google Scholar 

  98. 98.

    Smith, G. The AI Delusion (Oxford Univ. Press, 2018).

  99. 99.

    Goodfellow, I., Bengio, Y. & Courville, A. Deep Learning (MIT Press, 2016).

  100. 100.

    Rumelhart, D. E., Hinton, G. E. & Williams, R. J. Learning internal representations by error propagation. Nature 323, 533–536 (1986).

    MATH  Google Scholar 

  101. 101.

    Lipton, Z. C., Berkowitz, J. & Elkan, C. A critical review of recurrent neural networks for sequence learning. Preprint at (2015).

  102. 102.

    Ho, T. K. Random decision forests. In Proc. 3rd Int. Conf. Document Analysis Recognition Vol. 1, 278–282 (IEEE, 1995).

  103. 103.

    Oja, E. A simplified neuron model as a principal component analyzer. J. Math. Biol. 15, 267–273 (1982).

    MathSciNet  MATH  Google Scholar 

  104. 104.

    Kohonen, T. Self-organized formation of topologically correct feature maps. Biol. Cybernetics 43, 59–69 (1982).

    MATH  Google Scholar 

  105. 105.

    Bengio, Y., Courville, A. & Pascal, V. Representation learning: a review and new perspectives. IEEE Trans. Pattern Anal. Mach. Intell. 35, 1798–1828 (2013).

    Google Scholar 

  106. 106.

    Jain, A. K. Data clustering: 50 years beyond K-means. Pattern Recognit. Lett. 31, 651–666 (2010).

    Google Scholar 

  107. 107.

    Xu, D. & Tian, Y. A comprehensive survey of clustering algorithms. Ann. Data Sci. 2, 165–193 (2015).

    Google Scholar 

  108. 108.

    Sutton, R. S. & Barto, A. G. Reinforcement Learning: An Introduction (MIT Press, 2018).

  109. 109.

    Neftci, E. O. & Averbeck, B. B. Reinforcement learning in artificial and biological systems. Nat. Mach. Intell. 1, 133–143 (2002).

    Google Scholar 

  110. 110.

    Mnih, V. et al. Human-level control through deep reinforcement learning. Nature 518, 529–533 (2015).

    Google Scholar 

  111. 111.

    Foerster, J. N., Assael, I. A., de Freitas, N. & Whiteson, S. Learning to communicate with deep multi-agent reinforcement learning. In Proc. 30th Int. Conf. Neural Information Processing Systems 2137–2145 (NIPS, 2016).

  112. 112.

    Davis, L. Handbook of Genetic Algorithms (Van Nostrand Reinhold, 1991).

  113. 113.

    Goodfellow, I. et al. Generative adversarial nets. In Proc. 27th Int. Conf. Neural Information Processing Systems 2672–2680 (NIPS, 2014).

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Correspondence to Frank Cichos or Kristian Gustavsson or Bernhard Mehlig or Giovanni Volpe.

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Cichos, F., Gustavsson, K., Mehlig, B. et al. Machine learning for active matter. Nat Mach Intell 2, 94–103 (2020).

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