论文标题
使用可重构的MetadeVices求解数学操作和方程式
Mathematical Operations and Equation Solving with Reconfigurable Metadevices
论文作者
论文摘要
使用元结构进行模拟计算是一种基于新兴波浪的范式,用于解决数学问题。对于此类设备,一个主要的挑战是它们的可重构性,尤其是不需要先验数学计算或计算强度的优化。它们的方程解决功能仅适用于具有特殊光谱(特征值)分布的矩阵。在这里,我们使用能够以完全可可的方式求解积分/微分方程的可调元素来报告基于波浪的元结构的理论和设计。我们考虑了两个架构:需要单数值分解的米勒体系结构,以及此处介绍的替代直觉直接复合 - 复合 - 摩托克(DCM)体系结构,不需要先验的数学分解。作为示例,我们使用系统级仿真工具,积分和微分方程的解决方案证明。然后,我们扩展了两种体系结构的矩阵反相功能,以评估广义的摩尔 - 柔性矩阵反转。因此,我们提供的证据表明,MetadeVices可以实施广义矩阵倒置,并充当解决各种问题的梯度下降方法的基础。最后,溶液收敛时间的一般上限揭示了这种MetadeVices可以为固定迭代方案提供的丰富潜力。
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.