Nonlinear Effect in Physical Reservoir Computing Using a Mechanical Oscillator

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Abstract Physical reservoir computing (PRC) has emerged as a promising machine learning technique owing to its simplified training and minimal computational demands. When applied to mechanical systems, such as autonomous vehicles, PRC offers potential for efficient on-board processing of sensory data. Despite the benefits of PRC, there remains an absence in designing of mechanical systems that effectively embody reservoir computing for optimizing prediction performance. PRC leverages the nonlinear dynamics of a physical system to predict spatiotemporal input-output relationships, where the majority of the information is processed within the physical body of the system itself, thus achieving computational efficiency. This simple training process and low computational requirements enable real-time sensing and rapid decision-making in autonomous mechanical systems. To design optimal mechanical systems as physical implementation of reservoir computing, it is necessary to understand how the physical properties of these systems affect their ability to process information. In this study, we investigated the relationship between the nonlinearity and the information processing capability of a one-dimensional Spring-Mass-Damper (SMD) network as a physical implementation of reservoir computing. We established a numerical model of the SMD network as a test system and conducted a parametric study by tuning the nonlinear spring stiffness of the system. Using a benchmark task of 2nd-order Nonlinear Autoregressive Moving Average (NARMA-2), we generated a target output for performance evaluation. We trained the system using linear regression to determine a set of optimal weights which relate between the target output and the mass displacement readouts. We then estimated the output using a linear summation of the displacement readout signals with their corresponding trained weights. We computed the prediction accuracy using a performance metric of R2 error between the target output and the estimated output. Our result indicates that optimal level of nonlinearity in the springs of the SMD system significantly improves PRC prediction performance. However, both linear and overly nonlinear systems result in poor performance. These findings emphasize the importance of a balanced level of nonlinearity in the SMD system’s dynamics, as it significantly influences its ability to process information and the PRC prediction. This study deepens our understanding of how nonlinearity affects PRC performance, providing insights for the design of optimal mechanical structures to serve as effective physical reservoir computers.