Mathematical operations and equation solving with reconfigurable metadevices

Dimitrios C. Tzarouchis; Mario Junior Mencagli; Brian Edwards; Nader Engheta

doi:10.1038/s41377-022-00950-1

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Mathematical operations and equation solving with reconfigurable metadevices

Original Articles

- Mathematical operations and equation solving with reconfigurable metadevices
- Mathematical operations and equation solving with reconfigurable metadevices
- LSA 2022年11卷第10期页码：2365-2377
- Affiliations：
  
  1.University of Pennsylvania, Department of Electrical and Systems Engineering, Philadelphia, PA, 19104, USA
  2.University of North Carolina at Charlotte, Department of Electrical and Computer Engineering, Charlotte, NC, 28223, USA
- Author bio：
  
  Nader Engheta (engheta@ee.upenn.edu)
- Funds：
- DOI：10.1038/s41377-022-00950-1
  中图分类号：
- 纸质出版日期：2022-10-31，
  
  网络出版日期：2022-09-07，
  
  收稿日期：2021-11-19，
  
  修回日期：2022-07-15，
  
  录用日期：2022-08-02
- Accepted：
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Mathematical operations and equation solving with reconfigurable metadevices[J]. LSA, 2022,11(10):2365-2377.

Tzarouchis, D. C. et al. Mathematical operations and equation solving with reconfigurable metadevices. Light: Science & Applications, 11, 2365-2377 (2022).
Mathematical operations and equation solving with reconfigurable metadevices[J]. LSA, 2022,11(10):2365-2377. DOI： 10.1038/s41377-022-00950-1.

Tzarouchis, D. C. et al. Mathematical operations and equation solving with reconfigurable metadevices. Light: Science & Applications, 11, 2365-2377 (2022). DOI： 10.1038/s41377-022-00950-1.

摘要

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.

关键词

Keywords

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