Smart, C. L. et al. Magnetically programmed diffractive robotics. Science 386, 1031 (2024).
Liu, Q. et al. Electronically configurable microscopic metasheet robots. Nat. Mater. 24, 109 (2025).
Coulais, C., Teomy, E., de Reus, K., Shokef, Y. & van Hecke, M. Combinatorial design of textured mechanical metamaterials. Nature 535, 529 (2016).
Overvelde, J. T. B., Weaver, J. C., Hoberman, C. & Bertoldi, K. Rational design of reconfigurable prismatic architected materials. Nature 541, 347 (2017).
Kim, Y., Yuk, H., Zhao, R., Chester, S. A. & Zhao, X. Printing ferromagnetic domains for untethered fast-transforming soft materials. Nature 558, 274 (2018).
Siéfert, E., Reyssat, E., Bico, J. & Roman, B. Bio-inspired pneumatic shape-morphing elastomers. Nat. Mater. 18, 24 (2019).
Choi, G. P. T., Dudte, L. H. & Mahadevan, L. Programming shape using kirigami tessellations. Nat. Mater. 18, 999 (2019).
Zareei, A., Deng, B. & Bertoldi, K. Harnessing transition waves to realize deployable structures. Proc. Natl Acad. Sci. USA 117, 4015 (2020).
Jin, L., Forte, A. E., Deng, B., Rafsanjani, A. & Bertoldi, K. Kirigami-inspired inflatables with programmable shapes. Adv. Mater. 32, 2001863 (2020).
Van Manen, T., Janbaz, S., Jansen, K. M. B. & Zadpoor, A. A. 4D printing of reconfigurable metamaterials and devices. Commun. Mater. 2, 56 (2021).
Hwang, D., Barron, E. J., Haque, A. B. M. T. & Bartlett, M. D. Shape morphing mechanical metamaterials through reversible plasticity. Sci. Robot. 7, eabg2171 (2022).
Gao, T., Bico, J. & Roman, B. Pneumatic cells toward absolute Gaussian morphing. Science 381, 862 (2023).
Meeussen, A. S. & Van Hecke, M. Multistable sheets with rewritable patterns for switchable shape-morphing. Nature 621, 516 (2023).
Melancon, D., Gorissen, B., García-Mora, C. J., Hoberman, C. & Bertoldi, K. Multistable inflatable origami structures at the metre scale. Nature 592, 545 (2021).
Stein-Montalvo, L., Ding, L., Hultmark, M., Adriaenssens, S. & Bou-Zeid, E. Kirigami-inspired wind steering for natural ventilation. J. Wind Eng. Ind. Aerodyn. 246, 105667 (2024).
Li, Y. et al. Adaptive hierarchical origami-based metastructures. Nat. Commun. 15, 6247 (2024).
Baines, R., Fish, F., Bongard, J. & Kramer-Bottiglio, R. Robots that evolve on demand. Nat. Rev. Mater. 9, 822 (2024).
Adrover, E. R. Deployable Structures (Hachette, 2015).
Bastien, R., Bohr, T., Moulia, B. & Douady, S. Unifying model of shoot gravitropism reveals proprioception as a central feature of posture control in plants. Proc. Natl Acad. Sci. USA 110, 755 (2013).
Talà, L., Fineberg, A., Kukura, P. & Persat, A. Pseudomonas aeruginosa orchestrates twitching motility by sequential control of type IV pili movements. Nat. Microbiol. 4, 774 (2019).
Noselli, G., Beran, A., Arroyo, M. & DeSimone, A. Swimming Euglena respond to confinement with a behavioural change enabling effective crawling. Nat. Phys. 15, 496 (2019).
Kramar, M. & Alim, K. Encoding memory in tube diameter hierarchy of living flow network. Proc. Natl Acad. Sci. USA 118, e2007815118 (2021).
Poole, W. et al. Chemical Boltzmann machines. In DNA Computing and Molecular Programming Vol. 10467 (eds Brijder, R. & Qian, L.) 210–231 (2017).
Stern, M., Arinze, C., Perez, L., Palmer, S. E. & Murugan, A. Supervised learning through physical changes in a mechanical system. Proc. Natl Acad. Sci. USA 117, 14843 (2020).
Stern, M., Hexner, D., Rocks, J. W. & Liu, A. J. Supervised learning in physical networks: from machine learning to learning machines. Phys. Rev. X 11, 021045 (2021).
Dillavou, S., Stern, M., Liu, A. J. & Durian, D. J. Demonstration of decentralized physics-driven learning. Phys. Rev. Appl. 18, 014040 (2022).
Stern, M. & Murugan, A. Learning without neurons in physical systems. Annu. Rev. Condens. Matter Phys. 14, 417 (2023).
Falk, M. J. et al. Learning to learn by using nonequilibrium training protocols for adaptable materials. Proc. Natl Acad. Sci. USA 120, e2219558120 (2023).
Patil, V. P., Ho, I. & Prakash, M. Self-learning mechanical circuits. Preprint at http://arxiv.org/abs/2304.08711 (2023).
Arinze, C., Stern, M., Nagel, S. R. & Murugan, A. Learning to self-fold at a bifurcation. Phys. Rev. E 107, 025001 (2023).
Altman, L. E., Stern, M., Liu, A. J. & Durian, D. J. Experimental demonstration of coupled learning in elastic networks. Phys. Rev. Appl. 22, 024053 (2024).
Dillavou, S. et al. Machine learning without a processor: emergent learning in a nonlinear analog network. Proc. Natl Acad. Sci. USA 121, e2319718121 (2024).
Mandal, R. et al. Learning dynamical behaviors in physical systems. Preprint at http://arxiv.org/abs/2406.07856 (2024).
Falk, M. J., Strupp, A. T., Scellier, B. & Murugan, A. Temporal contrastive learning through implicit non-equilibrium memory. Nat. Commun. 16, 2163 (2025).
Jani, J. M., Leary, M., Subic, A. & Gibson, M. A. A review of shape memory alloy research, applications and opportunities. Mater. Des. (1980–2015) 56, 1078 (2014).
Fruchart, M., Scheibner, C. & Vitelli, V. Odd viscosity and odd elasticity. Annu. Rev. Condens. Matter Phys. 14, 471 (2023).
Veenstra, J. et al. Non-reciprocal topological solitons in active metamaterials. Nature 627, 528 (2024).
Veenstra, J. et al. Adaptive locomotion of active solids. Nature 639, 935 (2025).
Movellan, J. R. Contrastive Hebbian learning in the continuous Hopfield model. In Connectionist Models (eds Touretzky, D. S. et al.) 10–17 (Morgan Kaufmann, 11991).
Scellier, B., Ernoult, M., Kendall, J. & Kumar, S. Energy-based learning algorithms for analog computing: a comparative study. In Proc. 37th International Conference on Neural Information Processing Systems 52705–52731 (2023).
Rocks, J. W., Ronellenfitsch, H., Liu, A. J., Nagel, S. R. & Katifori, E. Limits of multifunctionality in tunable networks. Proc. Natl Acad. Sci. USA 116, 2506 (2019).
Stern, M., Pinson, M. B. & Murugan, A. Continual learning of multiple memories in mechanical networks. Phys. Rev. X 10, 031044 (2020).
Semyon Aronovich, G. Über die Abgrenzung der Eigenwerte einer Matrix. Bull. Acad. Sci. USSR 6, 749–754 (1931).
Ijspeert, A. J., Crespi, A., Ryczko, D. & Cabelguen, J.-M. From swimming to walking with a salamander robot driven by a spinal cord model. Science 315, 1416 (2007).
Savoie, W. et al. A robot made of robots: emergent transport and control of a smarticle ensemble. Sci. Robot. 4, eaax4316 (2019).
Oliveri, G., van Laake, L. C., Carissimo, C., Miette, C. & Overvelde, J. T. B. Continuous learning of emergent behavior in robotic matter. Proc. Natl Acad. Sci. USA 118, e2017015118 (2021).
Li, S. et al. Robotic swimming in curved space via geometric phase. Proc. Natl Acad. Sci. USA 119, e2200924119 (2022).
Van Hecke, M. Profusion of transition pathways for interacting hysterons. Phys. Rev. E 104, 054608 (2021).
Purcell, E. M. Life at low Reynolds number. Am. J. Phys. 45, 3 (1977).
Lee, R. H., Mulder, E. A. B. & Hopkins, J. B. Mechanical neural networks: architected materials that learn behaviors. Sci. Robot. 7, eabq7278 (2022).
Bordiga, G. et al. Automated discovery of reprogrammable nonlinear dynamic metamaterials. Nat. Mater. 23, 1486 (2024).
Li, S. et al. Particle robotics based on statistical mechanics of loosely coupled components. Nature 567, 361 (2019).
Saintyves, B., Spenko, M. & Jaeger, H. M. A self-organizing robotic aggregate using solid and liquid-like collective states. Sci. Robot. 9, eadh4130 (2024).
Zou, S. et al. A retrofit sensing strategy for soft fluidic robots. Nat. Commun. 15, 539 (2024).
Dudek, K. K., Kadic, M., Coulais, C. & Bertoldi, K. Shape-morphing metamaterials. Nat. Rev. Mater. 10, 783 (2025).
Veenstra, J. et al. Wave coarsening drives time crystallization in active solids. Preprint at https://arxiv.org/abs/2508.20052 (2025).
Klos, C., Kalle Kossio, Y. F., Goedeke, S., Gilra, A. & Memmesheimer, R.-M. Dynamical learning of dynamics. Phys. Rev. Lett. 125, 088103 (2020).
Yao, D., van Mastrigt, R., Veenstra, J. & Coulais, C. Metamaterials that learn to change shape. Zenodo https://doi.org/10.5281/ZENODO.18544299 (2026).
Al-Izzi, S. C. et al. Nonreciprocal buckling makes active filaments polyfunctional. Proc. Natl Acad. Sci. USA 123, e2531723123 (2025).