Embodying Computation into a 3D-printed ReLU Network via Physical Reservoir Computing

Physical Reservoir Computing (PRC) can harness the embodied computational capacity of a nonlinear vibratory structure; however, there is a gap in understanding how to design and realize mechanical PRCs. This study presents a 3D-printed mechanical PRC with physical nonlinearities based on the rectified linear unit (ReLU) activation function. The mechanical PRC is a two-dimensional spring-mass-damper network with a 5 x 5 network of masses, ReLU nonlinear stiffness elements connecting the masses, and material damping. Each physical ReLU element is an asymmetric beam with a bilinear stiffness profile that mimics the leaky ReLU activation function used in digital Neural Networks. The embodied computational capacity of the 3D printed ReLU network is experimentally demonstrated by computing different orders of the benchmark NARMA task (nonlinear autoregressive moving average) under a vibration input. The vibration input is delivered using a modal shaker, the readouts are the time-varying strains on the PRC structure captured with high-speed cameras and digital image correlation, and the NARMA tasks are computed by training the readouts via linear regression.The physical ReLU network successfully computes the NARMA2 and NARMA5 benchmark tasks with high accuracy (R2 error > 0.9) and can operate across a range of input frequencies and amplitudes.This physical ReLU network provides a promising nonlinear topology for embodying computation into a mechanical dynamic structure.