Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

In materia reservoir computing with a fully memristive architecture based on self-organizing nanowire networks

Abstract

Neuromorphic computing aims at the realization of intelligent systems able to process information similarly to our brain. Brain-inspired computing paradigms have been implemented in crossbar arrays of memristive devices; however, this approach does not emulate the topology and the emergent behaviour of biological neuronal circuits, where the principle of self-organization regulates both structure and function. Here, we report on in materia reservoir computing in a fully memristive architecture based on self-organized nanowire networks. Thanks to the functional synaptic connectivity with nonlinear dynamics and fading memory properties, the designless nanowire complex network acts as a network-wide physical reservoir able to map spatio-temporal inputs into a feature space that can be analysed by a memristive resistive switching memory read-out layer. Computing capabilities, including recognition of spatio-temporal patterns and time-series prediction, show that the emergent memristive behaviour of nanowire networks allows in materia implementation of brain-inspired computing paradigms characterized by a reduced training cost.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Physical RC based on memristive NW networks.
Fig. 2: Nonlinear dynamics and fading memory properties of the memristive NW network reservoir.
Fig. 3: Fully memristive RC implementation and spatio-temporal evolution of the NW network reservoir state.
Fig. 4: Pattern classification with a fully memristive nanoarchitecture based on self-organized memristive NW networks.
Fig. 5: NW network reservoir as a generic scalable computational substrate for multiple tasks.

Similar content being viewed by others

Data availability

The data that support the findings of this study are available on Zenodo (https://doi.org/10.5281/zenodo.5153335). All other data are available from the authors.

Code availability

The codes used to generate datasets of simulations can be accessed on GitHub (https://github.com/MilanoGianluca/Nanowire_Network_Reservoir_Computing).

References

  1. Mead, C. Neuromorphic electronic systems. Proc. IEEE 78, 1629–1636 (1990).

    Article  Google Scholar 

  2. Wang, Z. et al. Resistive switching materials for information processing. Nat. Rev. Mater. 5, 173–195 (2020).

    Article  CAS  Google Scholar 

  3. Milano, G. et al. Self-limited single nanowire systems combining all-in-one memristive and neuromorphic functionalities. Nat. Commun. 9, 5151 (2018).

    Article  Google Scholar 

  4. Wang, Z. et al. Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing. Nat. Mater. 16, 101–108 (2017).

    Article  CAS  Google Scholar 

  5. Jo, S. H. et al. Nanoscale memristor device as synapse in neuromorphic systems. Nano Lett. 10, 1297–1301 (2010).

    Article  CAS  Google Scholar 

  6. Xia, Q. & Yang, J. J. Memristive crossbar arrays for brain-inspired computing. Nat. Mater. 18, 309–323 (2019).

    Article  CAS  Google Scholar 

  7. Lin, P. et al. Three-dimensional memristor circuits as complex neural networks. Nat. Electron. 3, 225–232 (2020).

    Article  Google Scholar 

  8. Kandel, E. R., Schwartz, J. H., Jessell, T. M., Siegelbaum, S. A. & Hudspeth, A. J. Principles of Neural Science 5th edn (McGraw-Hill Professional, 2013).

  9. Essen, V. & Tononi, G. in Fundamentals of Brain Network Analysis (eds Fornito, A. et al.) 1–35 (Elsevier, 2016); https://doi.org/10.1016/B978-0-12-407908-3.00001-7

  10. Suárez, L. E., Markello, R. D., Betzel, R. F. & Misic, B. Linking structure and function in macroscale brain networks. Trends Cogn. Sci. 24, 302–315 (2020).

    Article  Google Scholar 

  11. Stieg, A. Z. et al. Emergent criticality in complex Turing B-type atomic switch networks. Adv. Mater. 24, 286–293 (2012).

    Article  CAS  Google Scholar 

  12. Milano, G. et al. Brain-inspired structural plasticity through reweighting and rewiring in multi-terminal self-organizing memristive nanowire networks. Adv. Intell. Syst. https://doi.org/10.1002/aisy.202000096 (2020).

  13. Tanaka, H. et al. A molecular neuromorphic network device consisting of single-walled carbon nanotubes complexed with polyoxometalate. Nat. Commun. 9, 2693 (2018).

    Article  Google Scholar 

  14. Pike, M. D. et al. Atomic scale dynamics drive brain-like avalanches in percolating nanostructured networks. Nano Lett. 20, 3935–3942 (2020).

    Article  CAS  Google Scholar 

  15. Diaz-Alvarez, A. et al. Emergent dynamics of neuromorphic nanowire networks. Sci. Rep. 9, 14920 (2019).

    Article  Google Scholar 

  16. Sillin, H. O. et al. A theoretical and experimental study of neuromorphic atomic switch networks for reservoir computing. Nanotechnology 24, 384004 (2013).

    Article  Google Scholar 

  17. Fu, K. et al. in 2020 International Joint Conference on Neural Networks (IJCNN) 1–8 (IEEE, 2020); https://doi.org/10.1109/IJCNN48605.2020.9207727

  18. Milano, G., Porro, S., Valov, I. & Ricciardi, C. Recent developments and perspectives for memristive devices based on metal oxide nanowires. Adv. Electron. Mater. 5, 1800909 (2019).

    Article  Google Scholar 

  19. Bose, S. K. et al. Evolution of a designless nanoparticle network into reconfigurable Boolean logic. Nat. Nanotechnol. 10, 1048–1052 (2015).

    Article  CAS  Google Scholar 

  20. Demis, E. C. et al. Nanoarchitectonic atomic switch networks for unconventional computing. Jpn J. Appl. Phys. 55, 1102B2 (2016).

    Article  Google Scholar 

  21. Massey, M. K. et al. Evolution of electronic circuits using carbon nanotube composites. Sci. Rep. 6, 32197 (2016).

    Article  CAS  Google Scholar 

  22. Hochstetter, J. et al. Avalanches and edge-of-chaos learning in neuromorphic nanowire networks. Nat. Commun. 12, 4008 (2021).

    Article  CAS  Google Scholar 

  23. Zhu, R. et al. Information dynamics in neuromorphic nanowire networks. Sci. Rep. 11, 13047 (2021).

    Article  CAS  Google Scholar 

  24. Lilak, S. et al. Spoken digit classification by in-materio reservoir computing with neuromorphic atomic switch networks. Front. Nanotechnol. https://doi.org/10.3389/fnano.2021.675792 (2021).

  25. Jaeger, H. The ‘Echo State’ Approach to Analysing and Training Recurrent Neural Networks GMD Technical Report 148 (German National Research Center for Information Technology, 2001).

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

    Article  Google Scholar 

  27. Tanaka, G. et al. Recent advances in physical reservoir computing: a review. Neural Netw. 115, 100–123 (2019).

    Article  Google Scholar 

  28. Nakajima, K. Physical reservoir computing—an introductory perspective. Jpn J. Appl. Phys. 59, 060501 (2020).

    Article  CAS  Google Scholar 

  29. Torrejon, J. et al. Neuromorphic computing with nanoscale spintronic oscillators. Nature 547, 428–431 (2017).

    Article  CAS  Google Scholar 

  30. Prychynenko, D. et al. Magnetic skyrmion as a nonlinear resistive element: a potential building block for reservoir computing. Phys. Rev. Appl. 9, 014034 (2018).

    Article  CAS  Google Scholar 

  31. Vandoorne, K. et al. Experimental demonstration of reservoir computing on a silicon photonics chip. Nat. Commun. 5, 3541 (2014).

    Article  Google Scholar 

  32. Van der Sande, G., Brunner, D. & Soriano, M. C. Advances in photonic reservoir computing. Nanophotonics 6, 561–576 (2017).

    Article  Google Scholar 

  33. Du, C. et al. Reservoir computing using dynamic memristors for temporal information processing. Nat. Commun. 8, 2204 (2017).

    Article  Google Scholar 

  34. Moon, J. et al. Temporal data classification and forecasting using a memristor-based reservoir computing system. Nat. Electron. 2, 480–487 (2019).

    Article  Google Scholar 

  35. Zhu, X., Wang, Q. & Lu, W. D. Memristor networks for real-time neural activity analysis. Nat. Commun. 11, 2439 (2020).

    Article  CAS  Google Scholar 

  36. Midya, R. et al. Reservoir computing using diffusive memristors. Adv. Intell. Syst. 1, 1900084 (2019).

    Article  Google Scholar 

  37. Zhong, Y. et al. Dynamic memristor-based reservoir computing for high-efficiency temporal signal processing. Nat. Commun. 12, 408 (2021).

    Article  CAS  Google Scholar 

  38. Manning, H. G. et al. Emergence of winner-takes-all connectivity paths in random nanowire networks. Nat. Commun. 9, 3219 (2018).

    Article  Google Scholar 

  39. Li, Q. et al. Dynamic electrical pathway tuning in neuromorphic nanowire networks. Adv. Funct. Mater. 30, 2003679 (2020).

    Article  CAS  Google Scholar 

  40. Jackman, S. L. & Regehr, W. G. The mechanisms and functions of synaptic facilitation. Neuron 94, 447–464 (2017).

    Article  CAS  Google Scholar 

  41. Ielmini, D. & Wong, H.-S. P. In-memory computing with resistive switching devices. Nat. Electron. 1, 333–343 (2018).

    Article  Google Scholar 

  42. Mackey, M. & Glass, L. Oscillation and chaos in physiological control systems. Science 197, 287–289 (1977).

    Article  CAS  Google Scholar 

  43. Jaeger, H. Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication. Science 304, 78–80 (2004).

    Article  CAS  Google Scholar 

  44. Appeltant, L. et al. Information processing using a single dynamical node as complex system. Nat. Commun. 2, 468 (2011).

    Article  CAS  Google Scholar 

  45. Milano, G. et al. Mapping time-dependent conductivity of metallic nanowire networks by electrical resistance tomography toward transparent conductive materials. ACS Appl. Nano Mater. https://doi.org/10.1021/acsanm.0c02204 (2020).

  46. Burger, J. & Teuscher, C. in 2013 IEEE/ACM International Symposium on Nanoscale Architectures (NANOARCH) 1–6 (IEEE, 2013); https://doi.org/10.1109/NanoArch.2013.6623028

  47. Aimone, J. B. A roadmap for reaching the potential of brain-derived computing. Adv. Intell. Syst. https://doi.org/10.1002/aisy.202000191 (2020).

  48. Miranda, E., Milano, G. & Ricciardi, C. Modeling of short-term synaptic plasticity effects in ZnO nanowire-based memristors using a potentiation-depression rate balance equation. IEEE Trans. Nanotechnol. 19, 609–612 (2020).

    Article  CAS  Google Scholar 

  49. Kingma, D. P. & Ba, J. Adam: a method for stochastic optimization. 3rd International Conference for Learning Representations https://arxiv.org/abs/1412.6980 (2014).

  50. Ielmini, D. & Pedretti, G. Device and circuit architectures for in-memory computing. Adv. Intell. Syst. (2020).

Download references

Acknowledgements

We acknowledge support by M. Raimondo in helping with SEM measurements. Device fabrication was performed at Nanofacility Piemonte, a facility supported by the Compagnia di San Paolo foundation, and at PoliFAB, the micro- and nanofabrication facility of Politecnico di Milano. Part of this work was supported by the European project MEMQuD, code 20FUN06. This project (EMPIR 20FUN06 MEMQuD) has received funding from the European Metrology Programme for Innovation and Research (EMPIR) cofinanced by the participating states and from the European Union’s Horizon 2020 research and innovation programme. This article received funding from the European Union’s Horizon 2020 research and innovation program (grant agreement no. 824164).

Author information

Authors and Affiliations

Authors

Contributions

G.M., D.I. and C.R. generated the idea and designed the experiments. G.M. performed NW network fabrication and characterization. G.P. and G.M. performed multielectrode NW network characterization. S.R. and S.H. performed fabrication and characterization of the ReRAM read-out. G.M. and K.M. developed the NW network model and performed RC simulations. G.M., K.M. and G.P. analysed data. G.M. and C.R. prepared the manuscript. L.B., D.I. and C.R. supervised the research. All authors participated in the discussion of results and revision of the manuscript.

Corresponding authors

Correspondence to Gianluca Milano, Daniele Ielmini or Carlo Ricciardi.

Ethics declarations

Competing interests

The device configuration and implementation method of reservoir computing are currently under patent filing (Italian priority application number 102021000019277). Patent applicants: Politecnico di Torino, Politecnico di Milano, Istituto Nazionale di Ricerca Metrologica; Inventors: G.M., G.P., K.M., D.I. and C.R.

Additional information

Peer review information Nature Materials thanks John Boland and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–34, Tables 1 and 2, Notes 1–11 and references.

Supplementary Video 1

Animation of the spatio-temporal evolution of the conductive path formation and following dissolution in two-terminal configuration with a voltage pulse (2 V, 100 s). The animation with the grid-graph model refers to Fig. 2a. According to the grid-graph model discussed in Supplementary Note 3, short-term conductance dynamics of each edge are modelled through a potentiation–depression rate balance equation. Red intensity of edges is proportional to the edge conductance, blue intensity of each node is proportional to the node voltage, arrows indicate the current direction and black nodes represent input pads. During modelling, the left electrode was biased while the right one was kept as a ground.

Supplementary Video 2

Animation of the spatio-temporal evolution of the conductivity map under stimulation in a multi-terminal configuration, with a voltage pulse applied to pad 1 (5 V, 10 ms) while keeping other electrodes at ground. The animation with the grid-graph model refers to Supplementary Fig. 12. The output voltages were monitored by applying a small d.c. voltage bias (Vread = 100 mV) to pad 4, according to the schematization of the experimental set-up reported in Supplementary Fig. 12b. Red intensity of edges is proportional to the edge conductance, blue intensity of each node is proportional to the node voltage, arrows indicate the current direction and black nodes represent input pads. As can be observed, stimulation in the multi-terminal configuration results in the formation of conductive pathways resulting from the voltage distribution across the sample during stimulation.

Supplementary Video 3

Animation of the spatio-temporal evolution of the conductivity map under pattern stimulation. The animation with the grid-graph model refers to Fig. 3 (evolution of the conductivity map) and Supplementary Fig. 17 (evolution of output signal time traces). The output voltages were monitored by applying a small d.c. voltage bias (Vread = 100 mV) to pad 4, according to the schematization of the experimental set-up reported in Supplementary Fig. 12b. Red intensity of edges is proportional to the edge conductance, blue intensity of each node is proportional to the node voltage, arrows indicate the current direction and black nodes represent input pads. As can be observed, the peculiar evolution of the conductivity map depends on the spatial and temporal sequence of inputs.

Supplementary Video 4

Animation of in materia reservoir computing process where a digit pattern (from the MNIST handwritten dataset) is fed into the NW network physical reservoir as a spatio-temporal input, and the final reservoir output is then passed as input to a read-out one-layer fully connected neural network to perform classification. The animation shows the process of binarization and subsequent chopping and merging of the pattern to transform the digit into a spatio-temporal input with 196 pulse streams with four time frames applied to different pads of the sample. Then, the spatio-temporal evolution of the conductivity map and corresponding evolution of the reservoir output after stimulation with the digit ‘6’ according to the grid-graph model are shown. The output voltages were monitored by applying a small d.c. voltage bias (Vread = 100 mV) to the pad highlighted in Supplementary Fig. 24 of the manuscript, according to the schematization of the experimental set-up reported in the same figure. Red intensity of edges is proportional to the edge conductance, blue intensity of each node is proportional to the node voltage, arrows indicate the current direction and black nodes represent input pads. At the end of pattern stimulation, the final reservoir output voltages (at time frame t4) are then passed as input to the read-out one-layer neural network for classification.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Milano, G., Pedretti, G., Montano, K. et al. In materia reservoir computing with a fully memristive architecture based on self-organizing nanowire networks. Nat. Mater. 21, 195–202 (2022). https://doi.org/10.1038/s41563-021-01099-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41563-021-01099-9

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing