Learning Chaotic Dynamics with Neuromorphic Network Dynamics

TL;DR

The paper investigates learning chaotic dynamics with memristive neuromorphic networks acting as physical reservoirs for reservoir computing. It demonstrates autonomous Lorenz63 forecasting using large-scale memristive networks and analyzes how external input parameters shape internal memristor-edge dynamics to optimize nonlinear processing. Key findings show that driving memristive edges through their full conductance range at moderate input amplitudes maximizes learning and that network coverage of input readouts suppresses less useful nonlinearities, while still enabling robust long-term dynamics. The work highlights the potential for scalable, energy-efficient physical RC in neuromorphic systems and outlines directions for optimizing network structure and computation beyond traditional RC frameworks.

Abstract

This study investigates how dynamical systems may be learned and modelled with a neuromorphic network which is itself a dynamical system. The neuromorphic network used in this study is based on a complex electrical circuit comprised of memristive elements that produce neuro-synaptic nonlinear responses to input electrical signals. To determine how computation may be performed using the physics of the underlying system, the neuromorphic network was simulated and evaluated on autonomous prediction of a multivariate chaotic time series, implemented with a reservoir computing framework. Through manipulating only input electrodes and voltages, optimal nonlinear dynamical responses were found when input voltages maximise the number of memristive components whose internal dynamics explore the entire dynamical range of the memristor model. Increasing the network coverage with the input electrodes was found to suppress other nonlinear responses that are less conducive to learning. These results provide valuable insights into how a physical neuromorphic network device can be feasibly optimised for learning complex dynamical systems using only external control parameters.

Figures (24)

• Figure 1: Schematic of the dynamic neuromorphic reservoir computer. A signal vector $\mathbf{u}(t)$, weighted by a fixed random $W_{\rm in}$ and scaled by a constant voltage $\alpha$, is input into the neuromorphic reservoir $\cal{N}$ via selected input nodes. Voltage signals $\mathbf{r}_{\rm in}(t)$ (which also include random bias values $\mathbf{b}_{\rm in}$) are mapped into a higher-dimensional dynamical feature space which is sampled from other nodes $\mathbf{r}_{\rm out}(t)$. Only the output weight matrix $W_{\rm out}$ is trained to learn estimates $\mathbf{\hat{y}(t)}$.
• Figure 2: Graph representations of simulated neuromorphic networks used in this study: (a) network with $2,000$ nodes and $47,946$ edges; (b) network with $500$ nodes and $9,905$ edges. The corresponding degree distributions are shown in Appendix Fig. \ref{['fig:degree_dist']}.
• Figure 3: Memristive edge normalised conductance ($g(x)/\max_x[g(x)]$) as a function of the internal state parameter $x$, for both the tunnelling memristor model (black) and the binary model (dotted red). The low, medium and high conductance states are indicated.
• Figure 4: Graph visualisations of a simulated $200$-node, $1,213$-edge neuromorphic network showing dynamic connectivity in response to a constant DC voltage bias of $2\, {\rm V}$. Snapshots are shown at times (a) $0.2$ s, (b) $0.5$ s and (c) $1.0$ s, with the normalised conductance on edges, $g(x)/\max_x[g(x)]$, indicated by the right colourbar and the thickness of the respective edges, the node voltages $\mathbf{r}_{\rm{out}}$ indicated by the colourbar on the left; (d) corresponding percentage of the network that is active with edge voltage $v_{ij}\geq V_{\rm set}$.
• Figure 5: Input--output mapping of a neuromorphic network with $2,000$ nodes and $47,946$ edges. (a) Input signals $\mathbf{r}_{\rm in}(t)$ (blue) constructed from a linear combination of the Lorenz system (cf. Eq. \ref{['eq:rin']}) and delivered to $80$ randomly selected nodes; (b) readout signals $\mathbf{r}_{\rm out}(t)$ (red) from $1,919$ randomly selected nodes (distinct from the input nodes). Time duration is the last 10 Lyapunov times of training.