The sense-assess-respond feedback loop is a critical aspect of intelligence in both living and material systems. Physical reservoir computing is a strategy toward embodying intelligence into a system by leveraging nonlinear dynamics to perform nonlinear computations. While mechanical reservoirs typically produce nonlinear dynamics due to some material nonlinearity, geometric nonlinearity can also produce nonlinear dynamics due to the finite displacements and rotations in the network. This study examines the effect of both network node degree and geometry on the nonlinear computing performance of simulated mass-spring-damper systems comprised of linear springs. Smaller node degrees and sharper equilibrium angles in the network tended to produce greater nonlinear frequency content. However, the equilibrium geometry is not sufficient to characterize the reservoir performance as the dynamic variation in the spring angles also significantly correlates with nonlinear frequency content. This study highlights the significance of both network topology and dynamic geometry on the performance of mechanical reservoir computers.
AltmanLESternMLiuAJ, et al. (2024) Experimental demonstration of coupled learning in elastic networks. Physical Review Applied22(2): 024053.
3.
AlùAArrietaAFDottoreED, et al. (2025) Roadmap on embodying mechano-intelligence and computing in functional materials and structures. Smart Materials and Structures34(6): 063501.
4.
AtiyaAFParlosAG (2000) New results on recurrent network training: Unifying the algorithms and accelerating convergence. IEEE Transactions on Neural Networks11(3): 697–709.
5.
AubinCAGorissenBMilanaE, et al. (2022) Towards enduring autonomous robots via embodied energy. Nature602(7897): 393–402.
6.
AvenTJensenJHTufteG (2024) Lattice reservoirs: Symmetry breaking and information flow in physical reservoir computing. In: Artificial life conference proceedings, 2024, vol. 36, p. 49. Cambridge: MIT Press.
7.
BhovadPLiS (2021) Physical reservoir computing with origami and its application to robotic crawling. Scientific Reports11(1): 13002.
8.
CaluwaertsKD’HaeneMVerstraetenD, et al. (2013) Locomotion without a brain: Physical reservoir computing in tensegrity structures. Artificial Life19(1): 35–66.
9.
CarrollTL (2020) Path length statistics in reservoir computers. Chaos: An Interdisciplinary Journal of Nonlinear Science30(8): 083130.
10.
CarrollTLPecoraLM (2019) Network structure effects in reservoir computers. Chaos: An Interdisciplinary Journal of Nonlinear Science29(8): 083130.
11.
CoulaisCTeomyEde ReusK, et al. (2016) Combinatorial design of textured mechanical metamaterials. Nature535(7613): 529–532.
12.
DaleMO’KeefeSSebaldA, et al. (2021) Reservoir computing quality: Connectivity and topology. Natural Computing20(2): 205–216.
13.
DormandJRPrincePJ (1980) A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics6(1): 19–26.
14.
El HelouCGrossmannBTaborCE, et al. (2022) Mechanical integrated circuit materials. Nature608(7924): 699–703.
15.
El HelouCHyattLPBuskohlPR, et al. (2024) Intelligent electroactive material systems with self-adaptive mechanical memory and sequential logic. Proceedings of the National Academy of Sciences121(14): e2317340121.
16.
FaberJAUdaniJPRileyKS, et al. (2020) Dome-patterned metamaterial sheets. Advanced Science7(22): 2001955.
17.
FangYYashinVVLevitanSP, et al. (2016) Pattern recognition with “materials that compute”. Science Advances2(9): e1601114.
18.
FernandoCSojakkaS (2003) Pattern recognition in a bucket. In: European conference on artificial life, Dortmund, Germany, pp. 588–597. Springer.
19.
GallicchioC (2018) Chasing the echo state property. arXiv preprint. arXiv:1811.10892.
20.
GallicchioC (2020) Sparsity in reservoir computing neural networks. In: 2020 International conference on innovations in intelligent systems and applications (INISTA), Novi Sad, Serbia, pp. 1–7. IEEE.
21.
GallicchioCMicheliAPedrelliL (2017) Deep reservoir computing: A critical experimental analysis. Neurocomputing268: 87–99.
22.
GhoshalPGibertJMBajajAK (2025) Exploiting bistability and viscoelasticity in reservoir computing. Nonlinear Dynamics113(25): 34205–34222.
23.
GotoKNakajimaKNotsuH (2021) Twin vortex computer in fluid flow. New Journal of Physics23(6): 063051.
24.
HafizovicSHeerFUgniwenkoT, et al. (2007) A cmos-based microelectrode array for interaction with neuronal cultures. Journal of Neuroscience Methods164(1): 93–106.
25.
HauserHIjspeertAJFüchslinRM, et al. (2011) Towards a theoretical foundation for morphological computation with compliant bodies. Biological Cybernetics105: 355–370.
26.
HeilmannO (2023) Multifunctional echo state networks: Effects of topology and memory on the reconstruction of chaotic attractors. PhD Thesis, Ludwig-Maximilians-Universität.
27.
HeSMusgraveP (2025a) Physical reservoir computing on a soft bio-inspired swimmer. Neural Networks181: 106766.
28.
HeSMusgravePF (2025b) The role of nonlinearity, dimensionality, memory, and input on a mechanical oscillator reservoir computer. Neurocomputing652: 131158.
NakajimaK (2020) Physical reservoir computing—An introductory perspective. Japanese Journal of Applied Physics59: 060501.
36.
NakajimaKHauserHLiT, et al. (2015) Information processing via physical soft body. Scientific Reports5(1): 10487.
37.
NelsonDKiyabuSVincentT, et al. (2024) Spectral analysis of mechanical reservoir computing with ReLu spring networks. In: Smart materials, adaptive structures, and intelligent systems conference, Atlanta, GA. American Society of Mechanical Engineers.
38.
PaquotYDuportFSmerieriA, et al. (2012) Optoelectronic reservoir computing. Scientific Reports2(1): 287.
39.
PerkinsE (2025a) The mechanical duffing adaptive oscillator physical reservoir computer. Mechanical Systems and Signal Processing233: 112711.
40.
PerkinsE (2025b) Noise-enhanced learning in duffing adaptive oscillator. Proceedings of the Royal Society A481(2315): 20250002.
41.
SchrauwenBBuesingLLegensteinR (2008) On computational power and the order-chaos phase transition in reservoir computing. Advances in Neural Information Processing Systems21: 1–8.
42.
ShklyaevOEBalazsAC (2024) Interlinking spatial dimensions and kinetic processes in dissipative materials to create synthetic systems with lifelike functionality. Nature Nanotechnology19(2): 146–159.
43.
TaniguchiTTsunegiSMiwaS, et al. (2021) Reservoir computing based on spintronics technology. In: NakajimaKFischerI (eds) Reservoir Computing: Theory, Physical Implementations, and Applications. Springer, Singapore. pp. 331–360.
44.
Van der SandeGBrunnerDSorianoMC (2017) Advances in photonic reservoir computing. Nanophotonics6(3): 561–576.
45.
VerstraetenDDambreJDutoitX, et al. (2010) Memory versus non-linearity in reservoirs. In: 2010 international joint conference on neural networks (IJCNN), Barcelona, Spain, pp. 1–8. IEEE.
46.
VincentTGunasekaranSMonginM, et al. (2024) Development of an experimental testbed to study cavity flow as a processing element for flow disturbances. In: 2024 American Institute of Aeronautics and Astronautics Science and Technology Forum and Exposition (AIAA SciTech Forum), Orlando, FL. p. 1732.
47.
VincentTNelsonDGrossmannB, et al. (2023) Open-Cavity Fluid Flow as an Information Processing Medium. American Institute of Aeronautics and Astronautics. Available at: https://arc.aiaa.org/doi/abs/10.2514/6.2023-1393
48.
VirtanenPGommersROliphantTE, et al. (2020) SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods17(3): 261–272.
49.
WallisWD (2007) A Beginner’s Guide to Graph Theory. Springer.
50.
WangJQiaoZZhangW, et al. (2025) Proprioceptive and exteroceptive information perception in a fabric soft robotic arm via physical reservoir computing with minimal training data. Advanced Intelligent Systems7(4): 2400534.
51.
YasudaHBuskohlPRGillmanA, et al. (2021) Mechanical computing. Nature598(7879): 39–48.
52.
YewdallNAMasonAFvan HestJCM (2018) The hallmarks of living systems: Towards creating artificial cells. Interface Focus8(5): 20180023.
53.
Yılmaz BingölGGünayE (2025) Reservoir computing and multi-scroll attractors: How network topologies shape prediction performance. Chaos: An Interdisciplinary Journal of Nonlinear Science35(7): 073147.
54.
YuZSadatiSMHPereraS, et al. (2023) Tapered whisker reservoir computing for real-time terrain identification-based navigation. Scientific Reports13(1): 5213.
55.
ZhangYDeshmukhAWangKW (2023) Embodying multifunctional mechano-intelligence in and through phononic metastructures harnessing physical reservoir computing. Advanced Science10(34): 2305074.
56.
ZhangYWangK (2022a) Enabling mechano-intelligence in adaptive structures utilizing physical computing. Active and Passive Smart Structures and Integrated Systems XVI12043: 409–417.
57.
ZhangYWangKW (2022b) Harnessing physical reservoir computing in nonlinear mechanical metastructures. In: AIAA SCITECH 2022 forum. American Institute of Aeronautics and Astronautics.
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