Characterizing Memristive Nanowire Network Models via a Unified Computational Framework

TL;DR

MemNNetSim provides a standardized, Python-based framework to model static and dynamic random memristive NWNs, integrating graph representations, Modified Nodal Analysis, and a modular memristive-model interface. It includes three benchmark models (HP, Decay HP, SLT HP) and supports user-defined models with dimensionless state equations and window functions. Static analyses reproduce known Rs vs Rj and percolation scaling with a critical density $(n_w)_c \approx 0.115~\mu m^{-2}$ and exponents $\alpha \approx 1.11$–$1.27$, while dynamic simulations show $|\beta| \approx 1$ in power spectra for Decay HP and SLT HP. In reservoir computing experiments, Decay HP enables waveform transformations with RNMSE as low as $0.141$, illustrating the importance of short-term memory and harmonic content, whereas the HP model underperforms. These contributions, plus open-source availability, position MemNNetSim as a practical platform for exploring neuromorphic NWN hardware and informing design strategies.

Abstract

Randomly self-assembled nanowire networks (NWNs) are dynamical systems in which junctions between two nanowires can be modelled as memristive units viewed as adaptive resistors with memory. Various memristive models have been proposed to capture the complex mechanics of these junctions. Here, we showcase a novel computational framework named Memristive Nanowire Network Simulator (MemNNetSim) to simulate and analyze random memristive NWNs in a unified approach. Implemented using the Python programming language, MemNNetSim allows for the analysis of static and dynamic scenarios of NWNs under arbitrary memristive models. This provides a versatile foundation to build upon in further work, such as reservoir dynamics with NWNs, which has seen increased interest due to the interconnected architecture of NWNs. In this work, we introduce the package, demonstrate its utility in simulating NWNs, and then test advanced scenarios in which it can aid in the exploratory analysis of these systems, particularly in learning how to use NWNs as a physical reservoir in reservoir computing applications.

Figures (22)

• Figure 1: Workflow of MemNNetSim package detailing its main initialization procedures and simulation types: dynamical/time-dependent or static transport analysis in memristive random NWNs kasdorf_githubkasdorf_github_iokasdorf_pypi.
• Figure 2: Snapshot of the webpage hosting the complete MemNNetSim package in GitHub kasdorf_github_io. The package and documentation can also be accessed here kasdorf_githubkasdorf_pypi. These pages and the software are an ongoing work and will continue to be updated to different versions, extensions, and other model considerations.
• Figure 3: Voltage versus current (pinched) hysteresis loops for a random NWN with two wire density values and distinct memristive models. Results for a NWN of wire density 0.12 $\mu$m$^{-2}$ (sparser case) are depicted on the left panels, whereas for a NWN of wire density 0.20 $\mu$m$^{-2}$ (denser case) are depicted on the right panels. The hysteresis shown on the top (a,b) panels are for the HP model (simple linear drift), the mid panels (c,d) are for the Decay HP model, and the bottom (e,f) panels are for the SLT HP model. Three positive and negative voltage (half-cycles) sweeps within the $[-20,20]$ V voltage range are displayed, with the inner area of the hysteresis increasing with time evolution, evidencing that the baseline conductance of the NWN has improved upon repeated voltage cycling. All loops are counter-clockwise (CCW) in the positive voltage range and clockwise (CW) in the negative voltage range.
• Figure 4: (Main panel) Current evolution of a JDA NWN using the Decay HP model stressed with 20V DC for 100 seconds. The NWN dimensions are $56µ m \times 35µ m$, all nanowire lengths were set at 7µ m, and a nanowire density of 0.3µ m^-2 was maintained. A four-terminal electrode configuration was used, with two electrodes placed on the left side of the NWN and two others on its right side. The characteristic resistance of $R_\text{on} = 10Ω$ and resistance ratio of $R_\text{off}/R_\text{on} = 160$ were used in this result. (Inset) Log-Log plot of the absolute value of the Fourier transform of the main panel response. The dashed red line is the power law fitting of a function $y \propto f^{-\beta}$ conducted within the frequency ($f$) range delimited by the vertical dashed lines. The fitting gives an exponent of $\beta = 1.0077\pm0.0008$.
• Figure 5: Power law exponent $\beta$ fitted from the Fourier transformed current response in \ref{['fig:I-vs-t']} for a NWN modelled with the Decay HP model, partitioned into time windows of 5 seconds. The grey section indicates the region in which the fitted exponent had an uncertainty larger than 0.1, and therefore its values are not representative of a power law.