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.
This is a preview of subscription content, access via your institution
Open Access articles citing this article.
npj Microgravity Open Access 24 November 2022
Nature Communications Open Access 10 August 2022
Communications Physics Open Access 21 June 2022
Subscribe to Nature+
Get immediate online access to Nature and 55 other Nature journal
Subscribe to Journal
Get full journal access for 1 year
only $8.25 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
Mehta, P. et al. A high-bias, low-variance introduction to machine learning for physicists. Phys. Rep. 810, 1–124 (2019).
Das Sarma, S., Deng, D. L. & Duan, L. M. Machine learning meets quantum physics. Phys. Today 72, 48–54 (2019).
Waller, L. & Tian, L. Machine learning for 3D microscopy. Nature 523, 416–417 (2015).
Barbastathis, G., Ozcan, A. & Situ, G. On the use of deep learning for computational imaging. Optica 6, 921–943 (2019).
Brunton, S. L., Noack, B. R. & Koumoutsakos, P. Machine learning for fluid mechanics. Annu. Rev. Fluid Mech. 52, 477–508 (2020).
Webb, S. Deep learning for biology. Nature 554, 555–557 (2018).
Bechinger, C. et al. Active particles in complex and crowded environments. Rev. Mod. Phys. 88, 045006 (2016).
Ruelle, D. Chance and Chaos (Princeton Univ. Press, 1991).
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).
Sengupta, A., Carrara, F. & Stocker, R. Phytoplankton can actively diversify their migration strategy in response to turbulent cues. Nature 543, 555–558 (2017).
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).
Durham, W. M. et al. Turbulence drives microscale patches of motile phytoplankton. Nat. Commun. 4, 2148 (2013).
Yeomans, J. M. Nature’s engines: active matter. Europhys. News 48, 21–25 (2017).
Urzay, J., Doostmohammadi, A. & Yeomans, J. M. Multi-scale statistics of turbulence motorized by active matter. J. Fluid Mech. 822, 762–773 (2017).
Doostmohammadi, A., Ignés-Mullol, J., Yeomans, J. M. & Sagués, F. Active nematics. Nat. Commun. 9, 3246 (2018).
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).
Buttinoni, I. et al. Dynamical clustering and phase separation in suspensions of self-propelled colloidal particles. Phys. Rev. Lett. 110, 238301 (2013).
Charlesworth, H. J. & Turner, M. S. Intrinsically motivated collective motion. Proc. Natl Acad. Sci. USA 116, 15362–15367 (2019).
Strandburg-Peshkin, A. et al. Visual sensory networks and effective information transfer in animal groups. Curr. Biol. 23, R709–R711 (2013).
Attanasi, A. et al. Information transfer and behavioural inertia in starling flocks. Nat. Phys. 10, 691–696 (2014).
Trianni, V. Evolutionary Swarm Robotics (Springer, 2008).
Doncieux, S., Bredeche, N., Mouret, J.-B. & Eiben, A. E. G. Evolutionary robotics: what, why, and where to. Front. Robot. AI https://doi.org/10.3389/frobt.2015.00004 (2015).
Bayındır, L. A review of swarm robotics tasks. Neurocomputing 172, 292–321 (2016).
Khadka, U., Holubec, V., Yang, H. & Cichos, F. Active particles bound by information flows. Nat. Commun. 9, 3864 (2018).
Marchetti, M. C. et al. Hydrodynamics of soft active matter. Rev. Mod. Phys. 85, 1143–1189 (2013).
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).
Frenkel, D. & Smit, B. Understanding Molecular Simulation: From Algorithms to Applications (Elsevier, 2001).
Rosenbluth, M. N. Genesis of the Monte Carlo algorithm for statistical mechanics. AIP Conf. Proc. 690, 22–30 (2003).
Wolfram, S. Cellular automata as models of complexity. Nature 311, 419–424 (1984).
Lauga, E. & Powers, T. R. The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72, 096601 (2009).
Floreano, D. & Mattiussi, C. Bio-inspired Artificial Intelligence: Theories, Methods, and Technologies (MIT Press, 2008).
LeCun, Y., Bengio, Y. & Hinton, G. Deep learning. Nature 521, 436–444 (2015).
Rabault, J., Kolaas, J. & Jensen, A. Performing particle image velocimetry using artificial neural networks: a proof-of-concept. Meas. Sci. Tech. 28, 125301 (2017).
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).
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).
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).
Helgadottir, S., Argun, A. & Volpe, G. Digital video microscopy enhanced by deep learning. Optica 6, 506–513 (2019).
Mehlig, B. Artificial neural networks. Preprint at https://arxiv.org/abs/1901.05639 (2019).
Rivenson, Y. et al. Deep learning microscopy. Optica 4, 1437–1443 (2017).
Wu, Y. et al. Extended depth-of-field in holographic imaging using deep-learning-based autofocusing and phase recovery. Optica 5, 704–710 (2018).
Pinkard, H., Phillips, Z., Babakhani, A., Fletcher, D. A. & Waller, L. Deep learning for single-shot autofocus microscopy. Optica 6, 794–797 (2019).
Ling, H. et al. Behavioural plasticity and the transition to order in jackdaw flocks. Nat. Commun. 10, 5174 (2019).
Ouellette, N. T. Flowing crowds. Science 363, 27–28 (2019).
Jeckel, H. et al. Learning the space-time phase diagram of bacterial swarm expansion. Proc. Natl Acad. Sci. USA 116, 1489–1494 (2019).
Regev, A. et al. The human cell atlas. eLife 6, e27041 (2017).
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).
Bo, S., Schmidt, F., Eichhorn, R. & Volpe, G. Measurement of anomalous diffusion using recurrent neural networks. Phys. Rev. E 100, 010102(R) (2019).
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).
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).
Borgnino, M. et al. Alignment of nonspherical active particles in chaotic flows. Phys. Rev. Lett. 123, 138003 (2019).
Schmidt, M. & Lipson, H. Distilling free-form natural laws from experimental data. Science 324, 81–85 (2009).
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).
Rudy, S. H., Brunton, S. L., Proctor, J. L. & Kutz, J. N. Data-driven discovery of partial differential equations. Sci. Adv. 3, e1602614 (2017).
Cvitanović, P. Recurrent flows: the clockwork behind turbulence. J. Fluid Mech. 726, 1–4 (2013).
Fonda, E., Pandey, A., Schumacher, J. & Sreenivasan, K. R. Deep learning in turbulent convection networks. Proc. Natl Acad. Sci. USA 116, 8667–8672 (2019).
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).
Pearce, P. et al. Learning dynamical information from static protein and sequencing data. Nat. Commun. 10, 5368 (2019).
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).
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).
Muiños-Landin, S., Ghazi-Zahedi, K. & Cichos, F. Reinforcement learning of artificial microswimmers. Preprint at https://arxiv.org/abs/1803.06425 (2018).
Kiørboe, T. A Mechanistic Approach to Plankton Ecology (Princeton Univ. Press, 2008).
Colabrese, S., Gustavsson, K., Celani, A. & Biferale, L. Flow navigation by smart microswimmers via reinforcement learning. Phys. Rev. Lett. 118, 158004 (2017).
Yoo, B. & Kim, J. Path optimization for marine vehicles in ocean currents using reinforcement learning. J. Mar. Sci. Tech. 21, 334–343 (2015).
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).
Schneider, E. & Stark, H. Optimal steering of a smart active particle. Europhys. Lett. 127, 34003 (2019).
Reddy, G., Celani, A., Sejnowski, T. J. & Vergassola, M. Learning to soar in turbulent environments. Proc. Natl Acad. Sci. USA 113, E4877–E4884 (2016).
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).
Vicsek, T. & Zafeiris, A. Collective motion. Phys. Rep. 517, 71–140 (2012).
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).
Mijalkov, M., McDaniel, A., Wehr, J. & Volpe, G. Engineering sensorial delay to control phototaxis and emergent collective behaviors. Phys. Rev. X 6, 011008 (2016).
Leyman, M., Ogemark, F., Wehr, J. & Volpe, G. Tuning phototactic robots with sensorial delays. Phys. Rev. E 98, 052606 (2018).
Volpe, G. & Wehr, J. Effective drifts in dynamical systems with multiplicative noise: a review of recent progress. Rep. Prog. Phys. 79, 053901 (2016).
Palmer, G. & Yaida, S. Optimizing collective fieldtaxis of swarming agents through reinforcement learning. Preprint at https://arxiv.org/abs/1709.02379 (2017).
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).
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).
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).
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).
Hüttenrauch, M., Šošić, A. & Neumann, G. Deep reinforcement learning for swarm systems. J. Mach. Learn. Res. 20, 1–31 (2019).
Jones, S., Winfield, A. F., Hauert, S. & Studley, M. Onboard evolution of understandable swarm behaviors. Adv. Intell. Sys. 1, 1900031 (2019).
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).
Halloy, J. et al. Social integration of robots into groups of cockroaches to control self-organized choices. Science 318, 1155–1158 (2007).
Rubenstein, M., Cornejo, A. & Nagpal, R. Programmable self-assembly in a thousand-robot swarm. Science 345, 795–799 (2014).
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).
R., S. & J. R., S. Ecology and physics of bacterial chemotaxis in the ocean. Microbiol. Mol. Biol. Rev. 76, 792–812 (2012).
Zahedi, K. & Ay, N. Quantifying morphological computation. Entropy 15, 1887–1915 (2013).
Bray, D. Protein molecules as computational elements in living cells. Nature 376, 307–312 (1995).
Qian, L., Winfree, E. & Bruck, J. Neural network computation with dna strand displacement cascades. Nature 475, 368–372 (2011).
Kirkpatrick, J. et al. Overcoming catastrophic forgetting in neural networks. Proc. Natl Acad. Sci. USA 114, 3521–3526 (2017).
Abbe, E. & Sandon, C. Provable limitations of deep learning. Preprint at https://arxiv.org/abs/1812.06369 (2019).
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).
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).
Jakobi, N., Husbands, P. & Harvey, I. In Advances in Artificial Life (eds Morán, F. et al.) 704–720 (Springer, 1995).
Birattari, M. et al. Automatic off-line design of robot swarms: a manifesto. Front. Robot. AI https://doi.org/10.3389/frobt.2019.00059 (2019).
Domingos, P. A few useful things to know about machine learning. Commun. ACM 55, 78 (2012).
Chicco, D. Ten quick tips for machine learning in computational biology. BioData Min. 10, 35 (2017).
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).
Hand, D. J. Classifier technology and the illusion of progress. Stat. Sci. 21, 1–14 (2006).
Smith, G. The AI Delusion (Oxford Univ. Press, 2018).
Goodfellow, I., Bengio, Y. & Courville, A. Deep Learning (MIT Press, 2016).
Rumelhart, D. E., Hinton, G. E. & Williams, R. J. Learning internal representations by error propagation. Nature 323, 533–536 (1986).
Lipton, Z. C., Berkowitz, J. & Elkan, C. A critical review of recurrent neural networks for sequence learning. Preprint at https://arxiv.org/abs/1506.00019 (2015).
Ho, T. K. Random decision forests. In Proc. 3rd Int. Conf. Document Analysis Recognition Vol. 1, 278–282 (IEEE, 1995).
Oja, E. A simplified neuron model as a principal component analyzer. J. Math. Biol. 15, 267–273 (1982).
Kohonen, T. Self-organized formation of topologically correct feature maps. Biol. Cybernetics 43, 59–69 (1982).
Bengio, Y., Courville, A. & Pascal, V. Representation learning: a review and new perspectives. IEEE Trans. Pattern Anal. Mach. Intell. 35, 1798–1828 (2013).
Jain, A. K. Data clustering: 50 years beyond K-means. Pattern Recognit. Lett. 31, 651–666 (2010).
Xu, D. & Tian, Y. A comprehensive survey of clustering algorithms. Ann. Data Sci. 2, 165–193 (2015).
Sutton, R. S. & Barto, A. G. Reinforcement Learning: An Introduction (MIT Press, 2018).
Neftci, E. O. & Averbeck, B. B. Reinforcement learning in artificial and biological systems. Nat. Mach. Intell. 1, 133–143 (2002).
Mnih, V. et al. Human-level control through deep reinforcement learning. Nature 518, 529–533 (2015).
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).
Davis, L. Handbook of Genetic Algorithms (Van Nostrand Reinhold, 1991).
Goodfellow, I. et al. Generative adversarial nets. In Proc. 27th Int. Conf. Neural Information Processing Systems 2672–2680 (NIPS, 2014).
The authors declare no competing interests.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Cichos, F., Gustavsson, K., Mehlig, B. et al. Machine learning for active matter. Nat Mach Intell 2, 94–103 (2020). https://doi.org/10.1038/s42256-020-0146-9
This article is cited by
Communications Physics (2022)
Autonomous environment-adaptive microrobot swarm navigation enabled by deep learning-based real-time distribution planning
Nature Machine Intelligence (2022)
Nature Climate Change (2022)
Automated machine learning for differentiation of hepatocellular carcinoma from intrahepatic cholangiocarcinoma on multiphasic MRI
Scientific Reports (2022)
npj Microgravity (2022)