- Perspective
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Perspective on physical systems with a purpose: Using tunable degrees of freedom to enable function
Phys. Rev. E 114, 041004 – Published 8 October, 2026
DOI: https://doi.org/10.1103/z1fd-78ty
Abstract
This perspective highlights an emerging framework for understanding evolved biological and designed physical systems as tunable materials. In analogy to supervised learning in artificial neural networks—where weights between nodes are adjusted to optimize a cost function during the training phase—recent work postulates that biological systems may be using similar tuning rules on their adjustable degrees of freedom to learn or perform tasks. Researchers are also using these algorithms to design synthetic physical systems that exhibit exotic mechanical responses or perform tasks like classification and regression. Here, we briefly review the algorithms that enable such behavior and highlight examples in both physical and biological systems, emphasizing major open questions in this nascent field. Our goal is to provide SPLASHY researchers with a jumping-off point for considering whether their own systems of interest might be a platform for tunable matter, and spur future work to address open questions.
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The SPLASHY+F road ahead: new dashes in soft matter physics
Dive into the future of soft matter physics through Perspectives at the SPLASHY+F frontier, where the field flows in new directions.
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References (58)
- M. Stern and A. Murugan, Learning without neurons in physical systems, Annu. Rev. Condens. Matter Phys. 14, 417 (2023).
- A. Momeni, B. Rahmani, B. Scellier, L. G. Wright, P. L. McMahon, C. C. Wanjura, Y. Li, A. Skalli, N. G. Berloff, T. Onodera, I. Oguz, F. Morichetti, P. del Hougne, M. Le Gallo, A. Sebastian, A. Mirhoseini, C. Zhang, D. Marković, D. Brunner, C. Moser, et al., Training of physical neural networks, Nature (London) 645, 53 (2025).
- S. Dillavou, M. Stern, A. J. Liu, and D. J. Durian, Demonstration of decentralized physics-driven learning, Phys. Rev. Appl. 18, 014040 (2022).
- H. Ronellenfitsch and E. Katifori, Phenotypes of vascular flow networks, Phys. Rev. Lett. 123, 248101 (2019).
- J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proc. Natl. Acad. Sci. USA 79, 2554 (1982).
- J. R. Movellan, Contrastive Hebbian learning in the continuous Hopfield model, in Connectionist Models (Morgan, Kaufmann, 1991), pp. 10–17..
- G. E. Hinton, Training products of experts by minimizing contrastive divergence, Neural Comput. 14, 1771 (2002).
- X. Xie and H. S. Seung, Equivalence of backpropagation and contrastive Hebbian learning in a layered network, Neural Comput. 15, 441 (2003).
- B. Scellier and Y. Bengio, Equilibrium propagation: Bridging the gap between energy-based models and backpropagation, Front. Comput. Neurosci. 11, 24 (2017).
- M. Stern, D. Hexner, J. W. Rocks, and A. J. Liu, Supervised learning in physical networks: From machine learning to learning machines, Phys. Rev. X 11, 021045 (2021).
- V. R. Anisetti, B. Scellier, and J. M. Schwarz, Learning by non-interfering feedback chemical signaling in physical networks, Phys. Rev. Res. 5, 023024 (2023).
- M. J. Falk, A. T. Strupp, B. Scellier, and A. Murugan, Temporal Contrastive Learning through implicit non-equilibrium memory, Nat. Commun. 16, 2163 (2025).
- R. Mandal, R. Huang, M. Fruchart, P. G. Moerman, S. Vaikuntanathan, A. Murugan, and V. Vitelli, Learning dynamical behaviors in physical systems, arXiv:2406.07856.
- M. Stern, A. G. Frim, R. Candás, A. J. Liu, and V. Balasubramanian, Contrastive learning in tunable dynamical systems, arXiv:2603.26969.
- R. Pool, Frontiers of Materials that Learn: Proceedings of a Workshop (National Academies Press, Washington, DC, 2026).
- L. G. Wright, T. Onodera, M. M. Stein, T. Wang, D. T. Schachter, Z. Hu, and P. L. McMahon, Deep physical neural networks trained with backpropagation, Nature (London) 601, 549 (2022).
- A. A. Evans, J. L. Silverberg, and C. D. Santangelo, Lattice mechanics of origami tessellations, Phys. Rev. E 92, 013205 (2015).
- V. F. Hagh, S. R. Nagel, A. J. Liu, M. L. Manning, and E. I. Corwin, Transient learning degrees of freedom for introducing function in materials, Proc. Natl. Acad. Sci. USA 119, e2117622119 (2022).
- L. Berthier and M. D. Ediger, Facets of glass physics, Phys. Today 69(1), 40 (2016).
- L. E. Altman, M. Stern, A. J. Liu, and D. J. Durian, Experimental demonstration of coupled learning in elastic networks, Phys. Rev. Appl. 22, 024053 (2024).
- N. Pashine, D. Hexner, A. J. Liu, and S. R. Nagel, Directed aging, memory, and nature's greed, Sci. Adv. 5, eaax4215 (2019).
- M. Stern, C. Arinze, L. Perez, S. E. Palmer, and A. Murugan, Supervised learning through physical changes in a mechanical system, Proc. Natl. Acad. Sci. USA 117, 14843 (2020).
- S. Dillavou, B. D. Beyer, M. Stern, A. J. Liu, M. Z. Miskin, and D. J. Durian, Machine learning without a processor: Emergent learning in a nonlinear analog network, Proc. Natl. Acad. Sci. USA 121, e2319718121 (2024).
- M. Aifer, Z. Belateche, S. Bramhavar, K. Y. Camsari, P. J. Coles, G. Crooks, D. J. Durian, A. J. Liu, A. Marchenkova, A. J. Martinez, et al., Solving the compute crisis with physics-based ASICs, arXiv:2507.10463.
- D. Kudithipudi, C. Schuman, C. M. Vineyard, T. Pandit, C. Merkel, R. Kubendran, J. B. Aimone, G. Orchard, C. Mayr, R. Benosman, J. Hays, C. Young, C. Bartolozzi, A. Majumdar, S. G. Cardwell, M. Payvand, S. Buckley, S. Kulkarni, H. A. Gonzalez, G. Cauwenberghs, et al., Neuromorphic computing at scale, Nature (London) 637, 801 (2025).
- B. J. Shastri, A. N. Tait, T. Ferreira de Lima, W. H. Pernice, H. Bhaskaran, C. D. Wright, and P. R. Prucnal, Photonics for artificial intelligence and neuromorphic computing, Nat. Photon. 15, 102 (2021).
- N. Stroev and N. G. Berloff, Analog photonics computing for information processing, inference, and optimization, Adv. Quantum Technol. 6, 2300055 (2023).
- J. J. Hopfield, Brain, neural networks, and computation, Rev. Mod. Phys. 71, S431 (1999).
- A. I. Weber and A. L. Fairhall, The role of adaptation in neural coding, Curr. Opin. Neurobiol. 58, 135 (2019).
- A. K. Chakraborty, A. Jayaraman, and D. P. Newton, How the immune system learns, PRX Life 4, 021001 (2026).
- T. Mora and A. M. Walczak, Towards a quantitative theory of tolerance, Trends Immunol. 44, 512 (2023).
- J. G. Cyster and P. C. Wilson, Antibody modulation of B cell responses—incorporating positive and negative feedback, Immunity 57, 1466 (2024).
- F. Camaglia, A. Ryvkin, E. Greenstein, S. Reich-Zeliger, B. Chain, T. Mora, A. M. Walczak, and N. Friedman, Quantifying changes in the T cell receptor repertoire during thymic development, eLife 12, e81622 (2023).
- H. S. Wong, K. Park, A. Gola, A. P. Baptista, C. H. Miller, D. Deep, M. Lou, L. F. Boyd, A. Y. Rudensky, P. A. Savage, G. Altan-Bonnet, J. S. Tsang, and R. N. Germain, A local regulatory T cell feedback circuit maintains immune homeostasis by pruning self-activated T cells, Cell 184, 3981 (2021).
- D. H. Rajan, A. Albright, H. Kim, U. Diaz, Y. Hudnall, N. Steube, G. Dey, T. Liu, and W. F. Marshall, Molecular pathways for learning in the single-cell Stentor coeruleus, Curr. Biol. 36, 2367 (2026).
- K. Trifonova, M. J. Falk, M. Rouches, S. Vaikuntanathan, M. Elowitz, and A. Murugan, Trainable computation in molecular networks, bioRxiv (2025), doi: 10.64898/2025.12.28.696421.
- D. S. Banerjee, M. J. Falk, M. L. Gardel, A. M. Walczak, T. Mora, and S. Vaikuntanathan, Learning via mechanosensitivity and activity in cytoskeletal networks, PRX Life 4, 013001 (2026).
- H. Wang, M. A. G. Cunha, J. C. Crocker, and A. J. Liu, Mechanosensitive remodeling sustains rigidity homeostasis in actin cortex models, bioRxiv (2025), doi: 10.1101/2025.10.05.680567.
- A. T. Grigas, R. S. Negi, E. Maniou, G. L. Galea, A. Michaut, A. Mongera, and M. L. Manning, Sparse mesenchymal cell networks as a fluid under tension, bioRxiv (2025), doi: 10.64898/2025.12.07.692626.
- S. Arzash, A. J. Liu, and M. L. Manning, Epithelial convergent extension as a tuning process, Proc. Natl. Acad. Sci. USA 123, e2532099123 (2026).
- S. Ameen, T. Zhang, and J. Schwarz, Training cell stress patterns in 3D cellular packings, arXiv:2604.25439.
- L. E. Altman, N. Aguilar, D. J. Durian, M. Ruiz-Garcia, and E. Katifori, Collective behavior and memory states in flow networks with tunable bistability, Nat. Commun. 17, 4782 (2026).
- K. Alim, G. Amselem, F. Peaudecerf, M. P. Brenner, and A. Pringle, Random network peristalsis in Physarum polycephalum organizes fluid flows across an individual, Proc. Natl. Acad. Sci. USA 110, 13306 (2013).
- J. W. Rocks and P. Mehta, Bias-variance decomposition of overparameterized regression with random linear features, Phys. Rev. E 106, 025304 (2022).
- R. Schaeffer, M. Khona, Z. Robertson, A. Boopathy, K. Pistunova, J. W. Rocks, I. R. Fiete, and O. Koyejo, Double descent demystified: Identifying, interpreting & ablating the sources of a deep learning puzzle, arXiv:2303.14151.
- S. Dillavou, J. W. Rocks, J. F. Wycoff, A. J. Liu, and D. J. Durian, Double descent without digital computation, Proc. Natl. Acad. Sci. USA 123, e2604421123 (2026).
- C. G. Evans, J. O'Brien, E. Winfree, and A. Murugan, Pattern recognition in the nucleation kinetics of non-equilibrium self-assembly, Nature (London) 625, 500 (2024).
- M. Z. Miskin, A. J. Cortese, K. Dorsey, E. P. Esposito, M. F. Reynolds, Q. Liu, M. Cao, D. A. Muller, P. L. McEuen, and I. Cohen, Electronically integrated, mass-manufactured, microscopic robots, Nature (London) 584, 557 (2020).
- Q. Liu, W. Wang, H. Sinhmar, I. Griniasty, J. Z. Kim, J. T. Pelster, P. Chaudhari, M. F. Reynolds, M. C. Cao, D. A. Muller, A. B. Apsel, N. L. Abbott, H. Kress-Gazit, P. L. McEuen, and I. Cohen, Electronically configurable microscopic metasheet robots, Nat. Mater. 24, 109 (2025).
- C. Li, N. Schramma, Z. Wang, N. F. Qari, M. Jalaal, M. I. Latz, and S. Cai, Ultrasensitive and robust mechanoluminescent living composites, Sci. Adv. 9, eadi8643 (2023).
- M. J. Webber and M. W. Tibbitt, Dynamic and reconfigurable materials from reversible network interactions, Nat. Rev. Mater. 7, 541 (2022).
- Y. Meroz, Plant tropisms as a window on plant computational processes, New Phytol. 229, 1911 (2021).
- M. S. Engel and T. Jackson, Insect Architecture: How Insects Build, Engineer, and Shape their World (Princeton University Press, Princeton, 2025).
- G. Gharooni-Fard, M. Byers, V. Deshmukh, E. Bradley, C. Mayo, C. M. Topaz, and O. Peleg, A computational topology-based spatiotemporal analysis technique for honeybee aggregation, npj Complex. 1, 3 (2024).
- A. Slezak and V. F. Hagh, Systematic design of local rules for directing emergent structure in bottom-up systems, arXiv:2604.12057.
- M. Sáez, J. Briscoe, and D. A. Rand, Dynamical landscapes of cell fate decisions, Interface Focus. 12, 20220002 (2022).
- W. Cui, R. Marsland III, and P. Mehta, Les Houches lectures on community ecology: From niche theory to statistical mechanics, arXiv:2403.05497.
- E. D. Sontag, Some new directions in control theory inspired by systems biology, IEE Proc. Syst. Bio. 1, 9 (2004).