Optimal information injection and transfer mechanisms for active matter reservoir computing

TL;DR

Overall, it is found that active matter agents forming liquid droplets are particularly well suited for RC, and consistently convex shape of the predictive performance landscapes, together with the observed phenomenological richness, conveys robustness and adaptivity.

Abstract

Reservoir computing (RC) is a state-of-the-art machine learning method that makes use of the power of dynamical systems (the reservoir) for real-time inference. When using biological complex systems as reservoir substrates, it serves as a testbed for basic questions about bio-inspired computation -- of how self-organization generates proper spatiotemporal patterning. Here, we use a simulation of an active matter system, driven by a chaotically moving input signal, as a reservoir. So far, it has been unclear whether such complex systems possess the capacity to process information efficiently and independently of the method by which it was introduced. We find that when switching from a repulsive to an attractive driving force, the system completely changes the way it computes, while the predictive performance landscapes remain nearly identical. The nonlinearity of the driver's injection force improves computation by decoupling the single-agent dynamics from that of the driver. Triggered are the (re-)growth, deformation, and active motion of smooth structural boundaries (interfaces), and the emergence of coherent gradients in speed -- features found in many soft materials and biological systems. The nonlinear driving force activates emergent regulatory mechanisms, which manifest enhanced morphological and dynamic diversity -- arguably improving fading memory, nonlinearity, expressivity, and thus, performance. We further perform RC in a broad variety of non-equilibrium active matter phases that arise when tuning internal (repulsive) forces for information transfer. Overall, we find that active matter agents forming liquid droplets are particularly well suited for RC. The consistently convex shape of the predictive performance landscapes, together with the observed phenomenological richness, conveys robustness and adaptivity.

Figures (51)

• Figure 1: Concept of reservoir computing with a driven, non-equilibrium active matter simulation. The reservoir consists of a collection of self-propelled particles (green dots). External information in the form of an external time series enters the reservoir through a special particle (driver, black spiked ball). All agents are subject to several forces specified in Sect. \ref{['sec:mm-interactions']} and \ref{['sec:new_forces']}. In this paper, we focus on the agent-agent repulsion force $\mathbf{F}_{r}$(for information propagation) and the driver-agent interaction $\mathbf{F}_{d}$(for information injection), which may be repulsive or attractive (see gray box). Other interactions include an attraction to the center of the simulation box $\mathbf{F}_{h}$, a speed-regulating force $\mathbf{F}_{sc}$ (not shown here), and a force clamp (not shown here). The response of the agents to the external driving signal is measured in a coarse-grained fashion through Gaussian observation kernels placed on the simulation canvas (symbolized through the turquoise, dotted circle) (see Sect. \ref{['sec:rc_setup']}). Observations are local densities of agent count and velocity. Swarm patterns generated by certain input time series patterns can then be mapped to future states of the input time series via a linear readout layer, which is trained using Ridge regression.
• Figure 2: Replacing the global attraction to the center of the simulation box and the local driver repulsion force with two different driver attraction forces. (a,b) Predictive performance for a speed-controller parameter scan with (a) an inversely driver attraction force $\sim 1/r_{i,d}$ (where $r_{i,d}$ is the distance between the driver $d$ and an agent $i$, see Eq. \ref{['eq:driver_attraction_inverse']}) and (b) a linearly attractive driver ($\sim r_{i,d}$), both with $K_d = 100.0$ (Eq. \ref{['eq:driver_attraction_linear']}). (b) Predictive performance for a speed-controller parameter scan with a driver homing force $\sim r_{i,d}$ with $K_d = 100.0$. (c) Snapshots of the driven swarm for different parameter combinations (symbols) in the parameter scans for each driver attraction force. Refer to Tab. \ref{['tab:supplementary_videos_driver_attraction_inverse']} and Tab. \ref{['tab:supplementary_videos_driver_attraction_linear']} for corresponding videos. Parameter values $(K_{sc}, s)$ for symbols: cross: (0.00005, 18.32981); diamond: (0.00379, 0.26367); square: (0.00886, 0.11288); pyramid: (0.02069, 0.04833); circle: (0.04833, 0.02069); nabla: (0.26367, 0.00379).
• Figure 3: Characterizing effects of different information injection mechanisms: inverse attraction ($\sim 1/r_{i,d}$; orange dashed line), linear attraction ($\sim r_{i,d}$; blue dotted line), and inverse repulsion plus linear homing ($\sim 1/r_{i,d} + \sim r_{i,h}$; green dash-dotted line) in the near-critically damped regime (pyramid symbol in Fig. \ref{['fig:driver_attraction_speed_controller']} and Fig. \ref{['fig:comparison_attractive_to_repulsive_driver']}). (a,b) Mean and standard deviations of agent trajectories for (a) position x coordinate and (b) speed. The driver time series is plotted as a solid, black line. (c,d) Mean and standard deviations of cross-correlations between agent and driver time series. (d) Radial distribution function of agents with respect to the driver position. (e) Agent speed in dependence on agents' distance from the driver. All plots were generated using 1,000 time steps after 1,000 burn-in steps that were not recorded; the bin size for sub-figures (d) and (e) is $\Delta r = 0.5$. The repulsion reference corresponds to the simulations performed in Ref. Gaimann2025.
• Figure 4: Agent-agent correlations for driven swarms with two different driver attraction interactions, for different speed-controller settings. (a,b) Absolute agent-averaged velocity auto-correlations for (a) inversely and (b) linearly attractive drivers. Error bands indicate the standard error of the mean over all evaluated time windows (see Sect. \ref{['sec:mm-simulation-details']} for details). Symbols correspond to parameter combinations changing speed-controller settings $(K_{sc}, s)$ (and resulting damping dynamics) as shown in Fig. \ref{['fig:driver_attraction_speed_controller']}. (c,d) Connected velocity correlations for (c) inversely and (d) linearly attractive drivers. (e) Visualizations of agent velocity fluctuations (agent velocities reduced by the center of mass velocity of the swarm). All plots were generated using 1,000 time steps after 1,000 burn-in steps that were not recorded. Refer to Tab. \ref{['tab:supplementary_videos_driver_attraction_inverse_fluctuations']} and Tab. \ref{['tab:supplementary_videos_driver_attraction_linear_flucts']} for corresponding videos of the velocity fluctuations. The Lyapunov timescale of the Lorenz-63 driver is $t^{\text{L63}}_{\text{lyap}} \approx 1.1$Viswanath1998.
• Figure 5: Varying the parameters governing the inverse driver attraction interaction. (a) Predictive performances for varying force strength $K_d$ and interaction radius $r_d$. (b) Snapshots of the active matter system corresponding to symbols in the heatmap in sub-figure (a). Refer to Tab. \ref{['tab:supplementary_videos_driver_attraction_nearcritdamped']} for corresponding videos.