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

Paper Number: 140473

140473 - Multifractal Analysis of Physical Reservoir Computer Structures 

The ability to sense and quickly respond is paramount for numerous control systems. The physical reservoir computer looks to streamline this process by combining 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 of the system. 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 based structures in the physical reservoir computing framework. Fractal structures exhibit self-similarity at different length scales and can be characterized using a measure called the fractal dimension. The fractal dimension of a structure is defined as the ratio of change in geometry by the change in scale. The most commonly used method to calculate fractal dimension is called the box-counting method. Random fractal structures yield a range of fractal dimensions at different length scales. Mathematical deterministic fractals have one singular fractal dimension, while random fractals yield a range of fractal dimensions at different length scales. This variability in fractal dimension has led to these random fractal structures to be categorized as multifractals. Nature seems to prefer these multifractal structures and that could be due to this variability in dimension. It is hypothesized that the variability in fractal dimension for these natural structures may allow for some adaptability to different conditions and situations. Therefore, understanding the properties and behavior of multifractals can unlock new directions to advance smart materials and adaptive structures. The range of fractal dimensions that a random fractal exhibits can be quantified using the multifractal spectrum. The multifractal spectrum is based on a modified box-count dimension using Renyi entropy, which looks at the probability of the boxes in the overlaid grid containing the structure. The width of the multifractal spectrum describes the amount of variability in the fractal dimension, with a larger width indicating higher variability. This work aims to tune the fractal structures used in the physical reservoir computer using the multifractal spectrum to find the optimal range that maximizes the information processing potential of the system.

Presenting Author: Mario Carvajal FAMU/FSU College of Engineering

Presenting Author Biography: Doctoral Candidate pursuing a PhD in Mechanical Engineering at Florida AM University/Florida State University College of Engineering

Authors:

Mario Carvajal
Basanta Pahari
William Oates
Shan He
Patrick Musgrave