Leveraging Interactions for Efficient Swarm-Based Brownian Computing

TL;DR

This work tackles energy-efficient optimization in complex landscapes by introducing a swarm of Brownian quasiparticles that interact via short-range attraction and move in a spatial temperature field. A coarse-grained lattice model translates the continuous Langevin dynamics into a Markovian framework simulated with the Gillespie algorithm, enabling scalable analysis of swarm behavior. The study finds an intermediate regime of interaction strength and swarm size where the collective behaves cooperatively to reliably identify the global minimum and adapt rapidly to time-varying landscapes, outperforming non-interacting searchers. The results point to a physical platform for unconventional computing that leverages intrinsic material-level scalability and robust dynamic adaptation across various potential realizations.

Abstract

Drawing inspiration from swarm intelligence, we show that short-range attractive interactions between thermally driven Brownian quasiparticles enable energy-efficient optimization. As quasiparticles can be generated directly within a material, the swarm size can be adjusted with minimal energy overhead. Using an optimization task defined by a spatially varying temperature landscape, we quantitatively show that interacting swarms reliably identify global optima and significantly outperform non-interacting searchers within a well-defined regime of interaction strength and swarm size. This improvement arises from emergent cooperative behavior, where local interactions guide the swarm toward high-quality solutions without central coordination. To link our physical model to experimental realizations, we coarse-grain the quasiparticle dynamics onto a sensor lattice and generate trajectories emulating particle-tracking measurements. We further show that the interacting swarm adapts robustly to landscapes that evolve over time. These findings establish interacting Brownian quasiparticles as a physical platform for scalable and energy-efficient unconventional computing.

Figures (3)

• Figure 1: Schematic representation of swarm-based Brownian computing. a) Snapshot of interacting Brownian quasiparticles diffusing toward the global optimum $s_0$, indicated by the green square, within the temperature landscape shown in color. b) Discrete, coarse-grained representation of the system configuration ${\boldsymbol{\rho}}$ at a fixed time. c) Single-particle probability distribution $\hat{{\boldsymbol{p}}}$, obtained from the time-averaged occupation vector ${\boldsymbol{\rho}}(t)$. The yellow star indicates the position $s_*$ of the statistical mode of the probability distribution. The system is confined to a square domain of size $L\times L$, and discretized into $M=\ell^2$ sensors.
• Figure 2: Computational performance of swarm-based Brownian computing as a function of the dimensionless interaction strength $\epsilon/k_B T_0$ and filling fraction $\nu = N/M$. a) Ensemble-averaged success ratio $\mathcal{R}$. Colored squares mark the parameter combinations illustrated in detail in panels the other panels. (b)--(c) Manhattan distance of the mode position and the position of the global temperature minimum as a function of the time-averaging length characterized by $K$. Dots show the average, and the shaded background color indicates one standard deviation. (d)--(i) Representative steady-state probability distributions $\hat{{\boldsymbol{p}}}$ for $K=25.000$ and selected parameters $\epsilon/k_B T_0$ and $\nu$ indicated in (a). As in Fig. \ref{['fig:1']}, the green box indicates the global temperature minimum and the yellow star the position $s_*$ of the statistical mode of the probability distribution.
• Figure 3: Dynamic computational performance of swarm-based Brownian computing as a function of the dimensionless interaction strength $\epsilon/k_B T_0$ and filling fraction $\nu = N/M$. (a, c) Temperature landscapes before and after the instantaneous switch of the global minimum from site $s_0$ to $s_1$ at time $J_{\text{sw}}\Delta t$. Panels (d) and (f) show representative steady-state probability distributions $\hat{{\boldsymbol{p}}}$ for $\epsilon/k_B T_0=-2$ and $\nu=0.06$, before and after the switch. (b, e) Time evolution of the ensemble-averaged Manhattan distance $\langle d(s_\star,s_1;J)\rangle$ between the distribution mode $s_\star$ and the target minimum $s_1$ for different values of $\nu$ and $\epsilon/k_B T_0$ corresponding to the color-coded squares in panels (g) and (h). Shaded regions indicate error bars with one standard deviation. Solid lines represent the logistic fit, see Eq. \ref{['eq:fit']}. (g) Adaptation accuracy $\mathcal{A}$, defined in Eq. \ref{['eq:accuracy']}, quantifying the success of the transition from the initial to the final global minimum. For the adaptation timescale $J_r$ we only show results for $\mathcal{A}>0.85$ in panel h).