Multifractal Analysis of Physical Reservoir Computer Structures

Abstract Physical reservoir computers combine sensing physical inputs and information processing in one single component to reduce the delay caused by data transmission. Physical reservoir computing uses the nonlinear dynamics of physical systems to process information and acts as a neural network for machine learning, allowing for prediction of target signals in real-time. This method significantly reduces the amount of computing and time required for the control system to respond to stimuli. The geometry and physical properties of the physical reservoir structure govern the overall performance. The structure must have enough complexity and nonlinearity when stimulated while not descending into unpredictable chaos to maximize its performance. This work investigates the utilization of fractal structures in the physical reservoir computing framework. Fractal structures exhibit self-similarity at different scales and can be characterized using a measure called the fractal dimension. Random fractal structures (multifractals) yield a range of fractal dimensions at different length scales. The multifractal spectrum is a measure used to quantify this variability in fractal dimension. This work aims to tune the physical reservoir computer using the multifractal spectrum to find the optimal range that maximizes the information processing potential of the system.