Reservoir Computing using Percolating Networks of Nanoparticles
J. B. Mallinson1, Z. E. Heywood2, R. K. Daniels1, M. D. Arnold3, P. J. Bones2, and S. A. Brown1
1

The MacDiarmid Institute for Advanced Materials and Nanotechnology, School of Physical and Chemical Sciences, University of Canterbury,Christchurch 8140, New Zealand.
2
Electrical and Computer Engineering, University of Canterbury, Christchurch 8140, New Zealand.
3
School of Mathematical and Physical Sciences, University of Technology Sydney, Sydney 2007, Australia.

Summary. Percolating networks of nanoparticles (PNNs) have been postulated as suitable systems
for physical reservoir computing due to their nonlinear memristive tunnel gaps and scale-freenetwork topology. We demonstrate the computational ability of PNNs as reservoirs, and investigate
the roles of their scale-free topology and heterogeneous tunnel gap sizes.

Reservoir computing (RC) has attracted significant interest as a framework for the implementation ofnovel neuromorphic computing systems. Originally framed as the echo state [1] (or liquid-state [2])approach to training recurrent neural networks, the RC scheme has traditionally been used with softwarebased reservoirs. Literature on echo-state networks (ESNs) has demonstrated that both the reservoir size
[3] and topology [4, 5] play a role in task performance. In particular, functional advantage has been
attributed to larger reservoirs with small-world and/or scale-free connectivity and edge-of-chaos and/or
critical dynamics.
It appears widely expected within neuromorphic literature that hardware-based reservoirs will also
benefit from these topological and dynamical properties [6]. However, in systems such as electronic
memristor networks, the mechanisms which couple with reservoir topology and thereby produce thereservoir dynamics are very different from those of ESNs. Thus, the effect of reservoir size and topology
on the computational performance of physical RC systems is yet to be fully elucidated [7].
Here we compare the performance of several memristive reservoir models in a range of RC tasks thatare chosen to highlight different system requirements. We consider regular and scale-free topologies in
networks of both uniform and heterogeneous memristive tunnel gaps (MTGs), as found experimentally inpercolating networks of nanoparticles (PNNs). PNNs are novel self-assembled nanoscale systems thatexhibit scale-free [8] and small-world [9] topologies and critical avalanche dynamics [10].
We find that the performance of regular arrays of uniform MTGs are limited by their symmetry andconsequent low output diversity. This symmetry can be broken either by a heterogeneous distribution ofmemristor properties or a scale-free topology, each leading to more diverse reservoir outputs and improved
computational performance. The best performance across all tasks is observed for a scale-free network ofuniform MTGs. We further consider task performance as a function of reservoir size and find that
performance improves with size but saturates for large systems.
These results provide insight into the roles of reservoir size, MTG heterogeneity and network topology
in neuromorphic reservoirs, as well as an overview of the computational performance of PNNs in a rangeof benchmark tasks.

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R. K. Daniels, M. D. Arnold, Z. E. Heywood, J. B. Mallinson, P. J. Bones, and S. A. Brown, “Brain-likenetworks of nanowires and nanoparticles : a change of perspective,” (Submitted), 2023.
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Fig. 1: (a) Schematic representation of a percolating network of nanoparticles (PNN) with multiple gold electrodes. (b)Schematic particle representation of a PNN with bias applied on the left side of the network and the right side held at
ground potential. (c) Vertex graph representation of the percolating network shown in (b). Nodes represent the geometriccentres of the individual groups while edges represent memristive tunnel gaps (MTGs) between group boundaries. (d)Similar graph representation of a 36x36 array network. (e) A schematic showing the growth and relaxation of a hillock
in a MTG. Left: MTG with no bias applied to the network. Middle: A hillock of height z forms in response to bias applied
to the left side of the network. 𝐹𝐸 represents the electric force driving hillock growth while 𝐹𝑅 represents the restorative
force induced by surface tension. Right: Under reduced bias the hillock relaxes to a smaller height 𝑧, and both 𝐹𝐸 and𝐹𝑅 decrease proportionately. (f) A schematic showing how a PNN (or array network) can be used as a physical reservoir
to perform the NARMA-10 task. Input voltages are applied to all left-hand edge groups, output signals are taken fromall right-hand edge groups.