Session: SYMP S-6: Reservoir Computing & Nonlinear Dynamics

Paper Number: 139435

139435 - Nonlinear Effect in Physical Reservoir Computing Using a Mechanical Oscillator 

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 shows potential for efficient on-board processing of sensory data. Despite the benefits of PRC, there remains an absence in designing mechanical systems that effectively embody reservoir computing for optimizing prediction performance. PRC leverages the nonlinear dynamics of a physical system as a computational resource to predict spatiotemporal input-output relationships. The nonlinearity in the reservoir transforms the input data into linearly separable information at the readout layer. This separated information then can be trained using a simple learning algorithm to produce a desired output relying only on the linear combination of the readout states. 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 collected the displacements of the masses in response to the input as the readouts for PRC analysis. We conducted a parametric study by tuning the nonlinear spring constant of the SMD system. Using a benchmark task of 2nd-order Nonlinear Autoregressive Moving Average (NARMA-2), we created 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 R-squared error between the target output and the estimated output. To visualize the information processing from a spectral perspective, we applied the Fast Fourier Transform (FFT) method to analyze the frequency contents of these signals throughout the system.

                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. Spectral analysis reveals that sufficient nonlinearity in the system gives rise to essential spectral components at the readouts which are necessary to recreate the specific frequency contents of the target output. In the other hand, linear systems lack in producing additional spectral information, while overly nonlinearity exhibits excessive information. 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 offers insights for designing optimal mechanical structures to function as effective physical embodiments of reservoir computing. 

Presenting Author: Shan He University of Florida

Presenting Author Biography: Shan is currently pursuing a PhD in Aerospace Engineering at the University of Florida. Her research focuses on applying a machine learning technique known as Physical Reservoir Computing (PRC) to mechanical systems.

Authors:

Shan He
Patrick Musgrave