Mathematical Operations and Equation Solving with Reconfigurable Metadevices
Abstract
Performing analog computations with metastructures is an emerging wave-based paradigm for solving mathematical problems. For such devices, one major challenge is their reconfigurability, especially without the need for a priori mathematical computations or computationally-intensive optimization. Their equation-solving capabilities are applied only to matrices with special spectral (eigenvalue) distribution. Here we report the theory and design of wave-based metastructures using tunable elements capable of solving integral/differential equations in a fully-reconfigurable fashion. We consider two architectures: the Miller architecture, which requires the singular-value decomposition, and an alternative intuitive direct-complex-matrix (DCM) architecture introduced here, which does not require a priori mathematical decomposition. As examples, we demonstrate, using system-level simulation tools, the solutions of integral and differential equations. We then expand the matrix inverting capabilities of both architectures toward evaluating the generalized Moore-Penrose matrix inversion. Therefore, we provide evidence that metadevices can implement generalized matrix inversions and act as the basis for the gradient descent method for solutions to a wide variety of problems. Finally, a general upper bound of the solution convergence time reveals the rich potential that such metadevices can offer for stationary iterative schemes.
Cite
@article{arxiv.2206.02549,
title = {Mathematical Operations and Equation Solving with Reconfigurable Metadevices},
author = {Dimitrios Tzarouchis and Mario Junior Mencagli and Brian Edwards and Nader Engheta},
journal= {arXiv preprint arXiv:2206.02549},
year = {2022}
}