Dynamic Reservoir Computing with Physical Neuromorphic Networks

TL;DR

This work investigates dynamic reservoir computing using simulated physical neuromorphic nanowire networks with memristive edge dynamics. It presents a framework where reservoir states arise from coupled node-edge physics under Kirchhoff constraints, rather than fixed node activations. Using autonomous Lorenz63 prediction, it shows that intermediate network densities maximize dynamical richness, enabling both short-term forecasting and long-term attractor learning, while too sparse or too dense networks underperform. The results indicate design principles for hardware implementations of dynamic RC in neuromorphic nano-electronic systems.

Abstract

Reservoir Computing (RC) with physical systems requires an understanding of the underlying structure and internal dynamics of the specific physical reservoir. In this study, physical nano-electronic networks with neuromorphic dynamics are investigated for their use as physical reservoirs in an RC framework. These neuromorphic networks operate as dynamic reservoirs, with node activities in general coupled to the edge dynamics through nonlinear nano-electronic circuit elements, and the reservoir outputs influenced by the underlying network connectivity structure. This study finds that networks with varying degrees of sparsity generate more useful nonlinear temporal outputs for dynamic RC compared to dense networks. Dynamic RC is also tested on an autonomous multivariate chaotic time series prediction task with networks of varying densities, which revealed the importance of network sparsity in maintaining network activity and overall dynamics, that in turn enabled the learning of the chaotic Lorenz63 system's attractor behavior.

Figures (8)

• Figure 1: Schematic illustration of dynamic RC with a physical neuromorphic network. Input voltage signals $\mathbf{u}(t)$ weighted by $W_{\rm in}$ are delivered to a subset of nodes, while dynamical features $\mathbf{r_{\rm out}}(t)$ are read out from other nodes and used to train weights $W_{\rm out}$ in an output layer to generate $\mathbf{\hat{y}}(t)$ that best approximates the desired outputs $\mathbf{y}(t)$. The physical neuromorphic network is typically a nano-electronic circuit with coupled nonlinear neuro-synaptic dynamics on both the nodes and edges, so in general, the reservoir weights are conductance-based and evolve in time, in contrast to standard RC.
• Figure 2: Graph visualizations of a simulated $100$-node, $261$-edge neuromorphic network showing dynamic connectivity in response to a 0.5 V DC voltage pulse of 4 s duration. Snapshots are shown at times (a) $1$ s, (b) $2$ s, (c) $3.9$ s, (d) $5$ s, and (e) $9$ s, with the normalized conductance on edges indicated by the colorbar and the thickness of the respective edges. (f) Plots showing the input voltage pulse (blue) and the percentage of the network that is active (red) as a function of time.
• Figure 3: Graph representation of physical neuromorphic networks of varying densities: (a) a sparse, low density network with 100 nodes and 261 edges; (b) an intermediate density network with 100 nodes and 1517 edges; and (c) a fully--connected, high density network with 100 nodes and 4950 edges.
• Figure 4: Neuromorphic network input--output mapping. (a) Input signals (blue, 10 Fourier modes of a square wave); and readouts (red) for (b) sparse, (c) intermediate density and (d) fully--connected networks. All simulated networks have 100 nodes, with 261, 1517 and 4950 edges for the sparse, intermediate density and fully-connected networks, respectively, as depicted graphically in Fig. \ref{['fig:networks']}.
• Figure 5: (a) 24 input signals (blue) comprised of a random linear combination of the three chaotic Lorenz system signals. (b)--(d) Node readout signals (red), amplitude of the change of conductance $dG/dt$ averaged over all memristive edges (magenta), its standard deviation (light blue shaded region), and the resulting autonomously forecasted Lorenz attractor (orange) compared to the actual attractor (gray), which commences at the first time step after training; simulated networks are with 500-nodes of increasing density: 2119 edges, 9905 edges, and 123,671 edges, for (b)--(d) respectively. Time duration selected during the last stages of training.