Reservoir Computing with a Single Oscillating Gas Bubble: Emphasizing the Chaotic Regime

TL;DR

This work introduces a physics-inspired reservoir computing system based on a single gas bubble trapped in liquid, leveraging the bubble’s nonlinear dynamics to process information with high energy efficiency. By encoding inputs as acoustic pressure driving and sampling the bubble’s radiated response, the authors create a reservoir with “virtual” nodes that enables effective time-series prediction and pattern classification using a simple linear readout. They show that operating the bubble in a chaotic regime near the edge of chaos yields superior performance, achieving low NMSE on the Hénon map with a minimal number of virtual neurons and demonstrating robust short-term forecasting in free-running mode, as well as high-accuracy binary classification. The results highlight the potential of ultra-small, energy-efficient physical reservoirs for onboard neuromorphic computing and open avenues for exploring bubble-size variation and multi-reservoir configurations for enhanced performance.

Abstract

The rising computational and energy demands of artificial intelligence systems urge the exploration of alternative software and hardware solutions that exploit physical effects for computation. According to machine learning theory, a neural network-based computational system must exhibit nonlinearity to effectively model complex patterns and relationships. This requirement has driven extensive research into various nonlinear physical systems to enhance the performance of neural networks. In this paper, we propose and theoretically validate a reservoir computing system based on a single bubble trapped within a bulk of liquid. By applying an external acoustic pressure wave to both encode input information and excite the complex nonlinear dynamics, we showcase the ability of this single-bubble reservoir computing system to forecast complex benchmarking time series and undertake classification tasks with high accuracy. Specifically, we demonstrate that a chaotic physical regime of bubble oscillation proves to be the most effective for this kind of computations.

Figures (6)

• Figure 1: (a) Schematic illustration of a traditional RC system. The reservoir consists of a network of interconnected artificial neurons that generate a vector of neural activations $\mathbf{x}_n$ from a dataset of input values $\mathbf{u}_n$. Only the linear readout is trained to produce the output $\mathbf{y}_n$. (b) Bubble-based RC system. The input data are encoded in the peak amplitude of the acoustic pressure waves. Neural activations are extracted by sampling the acoustic response of the oscillating bubble, as detailed in the main text and summarized in the inset table. The training and exploitation procedures for the physical RC system mirror those of the traditional algorithmic RC system.
• Figure 2: (a) Theoretical bifurcation curve of a single bubble functioning as an RC system and excited with a sinusoidal acoustic wave with the peak pressure $P_a$. (b) Spectral representation of the nonlinear dynamical regimes of oscillation.
• Figure 3: Predictive mode output of the bubble-based RC systems operating in the chaotic regime. (a) The $x$-components of the Hénon map. The data points to the left and right of the vertical dashed line represent the performance of the RC system in the training and exploitation regimes, respectively. (b) Two-dimensional representation of the predicted Hénon map, with the ground truth data points shown as black dots and predicted points marked in magenta.
• Figure 4: Predictive mode NMSE plotted as a function of the reservoir size, defined as the total number of virtual nodes $k \times N$, for both periodic and chaotic physical regimes of bubble oscillation.
• Figure 5: Free-running mode output of the bubble-based RC systems operating the chaotic regime. (a) A one-dimensional plot of the $x$-components of the Hénon map. The RC system is trained on the training portion of the time series (up to the vertical dashed line) and an iterative windowing approach is used to generate predictions. (b) Two-dimensional phase space representation of Hénon map, where the data points are shown as black dots and the generated points from the RC system are marked with magenta dots.