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

Paper Number: 141014

141014 - Spectral Analysis of Mechanical Reservoir Computing With Relu Spring Networks 

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. Different spring geometries can be used to tune the strength of the nonlinearity in the force-displacement curve. The spring geometries specifically consisted of stiff, center plungers connected by compliant arcs that control the soft tension mode of the spring.  The effective stiffness of the arc was readily tunable through control of the thickness, arc radius and location of the arc center. 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 characterized and binned according to its proximity to the input signal, the output target, and the overall distribution in the mechanical spring reservoir. Reservoir computing performance of fitting the target output function improved when the spectral content of the system dynamics synergized with the spectral content of the target.  Mechanical reservoirs with linear springs did a better job of retaining the input signal frequency content, which resulted in excellent output function fitting for memory-oriented task, such a sine delay function.  In contrast, the ReLU spring system performed better on nonlinear functions of the input, such as the ReLU of the input signal, as the spectral content of the reservoir and the output function were a better match. Additionally, the ReLU spring systems were more robust against readout noise in the system, as the spectral content related to noise disrupted the linear system’s ability to fine-tune the fit of the output function. We further analyzed the relationship between noise and number of readouts to investigate potential trade-offs in the selection and quantity of readouts.

Presenting Author: Philip Buskohl AFRL

Presenting Author Biography: Philip R. Buskohl is a Research Engineer in the Functional Materials Division at the U.S. Air Force Research Laboratory. The Division delivers materials and processing solutions to revolutionize AF capabilities in Survivability, Directed Energy, Reconnaissance, Integrated Energy and Human Performance. Phil has authored over 55 peer-reviewed papers ranging from the chemical-mechanical feedback of self-oscillating gels, design of reconfigurable origami structures and mechanical computing concepts. His research interests include nonlinear elasticity, topology optimization for material design, and mechanically adaptive materials.

Authors:

Daniel Nelson
Steven Kiyabu
Timothy Vincent
Andrew Gillman
Amanda Criner
Philip R. Buskohl