Spectral Analysis of Mechanical Reservoir Computing With ReLU Spring Networks

Abstract Nonlinear dynamics are a pervasive phenomenon in natural and synthetic mechanical systems, which can be leveraged for novel control of vibrations and elastic wave propagation. A mechanical system with high dimensionality and nonlinear dynamics can perform information processing on the physical stimuli that act upon the system. This information processing (known as physical reservoir computing) results from the dimensional expansion that occurs in the dynamic system’s state as it reacts to the input. The enriched signal contains both nonlinear transformations as well as memory of the original input, which can be leveraged for machine learning and control applications. In this study, a two-dimensional network of nonlinear springs is studied for its capabilities as a mechanical reservoir computer. The reservoir is acted upon by a driving input force, resulting in a nonlinear, high dimensional response from the network of rectified linear unit (ReLU) springs. These ReLU springs possess bilinear force-displacement curves that resemble the leaky ReLU activation function used in neural networks. A spectral analysis is applied to understand both the dynamics and the computational capabilities of the spring reservoirs with different nonlinearities. Specifically, the frequency content of each reservoir was compared against that of the input signal and the output target. Reservoir computing performance of fitting the target output function improved when the spectral content of the system dynamics aligned with the spectral content of the target. We further analyzed the relationship between noise and number of readouts to investigate potential trade-offs in the selection and quantity of readouts.