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...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.展开更多
基金This work was supported in part by the US Air Force Office of Scientifc Research(AFOSR)Multidisciplinary University Research Initiative(MURI)grant number FA9550-17-1-0002The authors also thank Mark Saffan for the valuable discussions on the AWR■ Microwave Office simulations.
文摘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.
