Mechanical ReLU Spring Networks as a Physical Computing Resource

Nonlinear dynamics are a pervasive phenomena in natural and synthetic mechanical systems, which can be leveraged for novel control of vibrations and elastic wave propagation. The nonlinearity produces complex mappings between the input and output dynamics that have the potential to operate as a mechanical computing resource. To explore this concept, we numerically investigated the computing capacity of 2D nonlinear spring networks using a reservoir computing approach. Reservoir computing is a class of recurrent neural networks that trains only a readout layer of the network dynamics in contrast to tuning all the internal parameters of the network. We introduce a mechanical analog for the rectified linear unit (ReLU) activation function from the neural network community and benchmark the memory capacity, nonlinearity, and output tasks of mechanical ReLU networks sampled from a distribution of spring properties. Preliminary results indicate that the stiffness ratio of the ReLU spring (ie. ratio of the bilinear slopes) is a key driver of the nonlinearity score of the network, even more so than the incidence of activating the spring nonlinearity. In addition, spring networks with a mixture of linear and ReLU springs exhibit a marked loss in memory capacity even at low ReLU spring fractions. Collectively, the results highlight the potential to harness dynamics, and relatively simple mechanical nonlinearities, to perform physical computations to augment the computing capacity of mechanical systems.