Mechanical neural networks: Architected materials that learn behaviors

Abstract

Aside from some living tissues, few materials can autonomously learn to exhibit desired behaviors as a consequence of prolonged exposure to unanticipated ambient loading scenarios. Still fewer materials can continue to exhibit previously learned behaviors in the midst of changing conditions (e.g., rising levels of internal damage, varying fixturing scenarios, and fluctuating external loads) while also acquiring new behaviors best suited for the situation at hand. Here, we describe a class of architected materials, called mechanical neural networks (MNNs), that achieve such learning capabilities by tuning the stiffness of their constituent beams similar to how artificial neural networks (ANNs) tune their weights. An example lattice was fabricated to demonstrate its ability to learn multiple mechanical behaviors simultaneously, and a study was conducted to determine the effect of lattice size, packing configuration, algorithm type, behavior number, and linear-versus-nonlinear stiffness tunability on MNN learning as proposed. Thus, this work lays the foundation for artificial-intelligent (AI) materials that can learn behaviors and properties.

Register and access this article for free

As a service to the community, this article is available for free.

Access the full article

View all access options to continue reading this article.

Supplementary Materials

This PDF file includes:

Materials and Methods

Figs. S1 to S13

Download
2.99 MB

Other Supplementary Material for this
manuscript includes the following:

Download
122.91 MB

REFERENCES AND NOTES

Y. LeCun, Y. Bengio, G. Hinton,Deep learning. Nature521,436–444 (2015).

A. N. Tait, T. F. de Lima, E. Zhou, A. X. Wu, M. A. Nahmias, B. J. Shastri, P. R. Prucnal,Neuromorphic photonic networks using silicon photonic weight banks. Sci. Rep.7,7430 (2017).

H. Gao, B. Cheng, J. Wang, K. Li, J. Zhao, D. Li,Object classification using CNN-based fusion of vision and LIDAR in autonomous vehicle environment. IEEE Trans. Industr. Inform.14,4224–4231 (2018).

W. S. McCulloch, W. Pitts,A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biol.5,115–133 (1943).

F. Rosenblatt,The perceptron: A probabilistic model for information storage and organization in the brain. Psychol. Rev.65,386–408 (1958).

O. I. Abiodun, A. Jantan, A. E. Omolara, K. V. Dada, A. M. Umar, O. U. Linus, H. Arshad, A. A. Kazaure, U. Gana, M. U. Kiru,Comprehensive review of artificial neural network applications to pattern recognition. IEEE Access7,158820–158846 (2019).

K. Hornik, M. Stinchcombe, H. White,Multilayer feedforward networks are universal approximators. Neural Netw.2,359–366 (1989).

M. Prezioso, F. Merrikh-Bayat, B. D. Hoskins, G. C. Adam, K. K. Likharev, D. B. Strukov,Training and operation of an integrated neuromorphic network based on metal-oxide memristors. Nature521,61–64 (2015).

H.-T. Zhang, T. J. Park, A. N. M. N. Islam, D. S. J. Tran, S. Manna, Q. Wang, S. Mondal, H. Yu, S. Banik, S. Cheng, H. Zhou, S. Gamage, S. Mahapatra, Y. Zhu, Y. Abate, N. Jiang, S. K. R. S. Sankaranarayanan, A. Sengupta, C. Teuscher, S. Ramanathan,Reconfigurable perovskite nickelate electronics for artificial intelligence. Science375,533–539 (2022).

S. Lee, H. Kim, S.-T. Lee, B.-G. Park, J.-H. Lee,SiO2 fin-based flash synaptic cells in AND array architecture for binary neural networks. IEEE Electron Device Lett.43,142–145 (2022).

R. Han, P. Huang, Y. Xiang, C. Liu, Z. Dong, Z. Su, Y. Liu, L. Liu, X. Liu, J. Kang,A novel convolution computing paradigm based on NOR flash array with high computing speed and energy efficiency. IEEE Trans. Circuits Syst. I: Reg. Papers.66,1692–1703 (2019).

S. Dillavou, M. Stern, A. J. Liu, D. J. Durian, Demonstration of decentralized, physics-driven learning. arXiv:2108.00275 [cond-mat.dis-nn] (2022).

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, M. Soljačić,Deep learning with coherent nanophotonic circuits. Nat. Photon.11,441–446 (2017).

H. Zhang, M. Gu, X. D. Jiang, J. Thompson, H. Cai, S. Paesani, R. Santagati, A. Laing, Y. Zhang, M. H. Yung, Y. Z. Shi, F. K. Muhammad, G. Q. Lo, X. S. Luo, B. Dong, D. L. Kwong, L. C. Kwek, A. Q. Liu,An optical neural chip for implementing complex-valued neural network. Nat. Commun.12,457 (2021).

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, A. Ozcan,All-optical machine learning using diffractive deep neural networks. Science361,1004–1008 (2018).

Z. Wu, M. Zhou, E. Khoram, B. Liu, Z. Yu,Neuromorphic metasurface. Photon. Res.8,46–50 (2020).

G. Furuhata, T. Niiyama, S. Sunada,Physical deep learning based on optimal control of dynamical systems. Phys. Rev. Appl.15,034092 (2021).

R. M. Füchslin, A. Dzyakanchuk, D. Flumini, H. Hauser, K. J. Hunt, R. H. Luchsinger, B. Reller, S. Scheidegger, R. Walker,Morphological computation and morphological control: Steps toward a formal theory and applications. Artif. Life19,9–34 (2013).

S. Boyd, L. Chua, Fading memory and the problem of approximating nonlinear operators with Volterra series. IEEE Transactions on Circuits and Systems 32, 1150–1161 (1985). 10.1109/TCS.1985.1085649.

W. Maass, T. Natschläger, H. Markram,Real-time computing without stable states: A new framework for neural computation based on perturbations. Neural Comput.14,2531–2560 (2002).

H. Hauser, A. J. Ijspeert, R. M. Füchslin, R. Pfeifer, W. Maass,Towards a theoretical foundation for morphological computation with compliant bodies. Biol. Cybern.105,355–370 (2011).

J. C. Coulombe, M. C. A. York, J. Sylvestre,Computing with networks of nonlinear mechanical oscillators. PLOS ONE12,e0178663 (2017).

K. K. Caluwaerts, M. D’Haene, D. Verstraeten, B. Schrauwen,Locomotion without a brain: Physical reservoir computing in tensegrity structures. Artif. Life19,35–66 (2013).

K. Caluwaerts, J. Despraz, A. Işçen, A. P. Sabelhaus, J. Bruce, B. Schrauwen, V. SunSpiral,Design and control of compliant tensegrity robots through simulation and hardware validation. J. R. Soc. Interface11,20140520 (2014).

H. Hauser, A. J. Ijspeert, R. M. Füchslin, R. Pfeifer, W. Maass,The role of feedback in morphological computation with compliant bodies. Biol. Cybern.106,595–613 (2012).

K. Nakajima, H. Hauser, T. Li, R. Pfeifer,Information processing via physical soft body. Sci. Rep.5,10487 (2015).

M. Hermans, M. Burm, T. V. Vaerenbergh, J. Dambre, P. Bienstman,Trainable hardware for dynamical computing using error backpropagation through physical media. Nat. Commun.6,6729 (2015).

L. G. Wright, T. Onodera, M. M. Stein, T. Wang, D. T. Schachter, Z. Hu, P. L. McMahon,Deep physical neural networks trained with backpropagation. Nature601,549–555 (2022).

T. A. Schaedler, W. B. Carter,Architected cellular materials. Annu. Rev. Mat. Res.46,187–210 (2016).

F. Zangeneh-Nejad, D. L. Sounas, A. Alù, R. Fleury,Analogue computing with metamaterials. Nat. Rev. Mater.6,207–225 (2021).

S. Zuo, Q. Wei, Y. Tian, Y. Cheng, X. Liu,Acoustic analog computing system based on labyrinthine metasurfaces. Sci. Rep.8,10103 (2018).

T. W. Hughes, I. A. D. Williamson, M. Minkov, S. Fan,Wave physics as an analog recurrent neural network. Sci. Adv.5,eaay6946 (2019).

M. Stern, D. Hexner, J. W. Rocks, A. J. Liu,Supervised learning in physical networks: From machine learning to learning machines. Phys. Rev. X.11,021045 (2021).

M. Stern, C. Arinze, L. Perez, S. E. Palmer, A. Murugan, Supervised learning through physical changes in a mechanical system. Proc. Natl. Acad. Sci. U.S.A 117, 14843–14850 (2020).

E. Brown, N. Rodenberg, J. Amend, A. Mozeika, E. Steltz, M. R. Zakin, H. Lipson, Universal robotic gripper based on the jamming of granular material. Proc. Natl. Acad. Sci. U.S.A 107, 18809–18814 (2010).

R. Poon, J. B. Hopkins, Phase-changing metamaterial capable of variable stiffness and shape morphing. Adv. Eng. Mater 21, 1900802 (2019).

P. R. Kuppens, M. A. Bessa, J. L. Herder, J. B. Hopkins, Monolithic binary stiffness building blocks for mechanical digital machines. Extreme Mech. Lett 42, 101120 (2021).

K. Wei, Q. Bai, G. Meng, L. Ye, Vibration characteristics of electrorheological elastomer sandwich beams. Smart Mater. Struct 20, 055012 (2011).

L. Blanc, A. Delchambre, P. Lambert, Flexible medical devices: Review of controllable stiffness solutions. Actuators 6, 23 (2017).

D. Whitley, An overview of evolutionary algorithms: Practical issues and common pitfalls. Inf. Softw. Technol 43, 817–831 (2001).

E. D. Dolan, R.M. Lewis, V. Torczon, On the local convergence of pattern search. SIAM J. O. 14, 567–583 (2003). 10.1137/S1052623400374495.