Calculus equations serve as fundamental frameworks in mathematics, enabling describing an extensive range of natural phenomena and scientific principles, such as thermodynamics and electromagnetics. Analog computing with electromagnetic waves presents an intriguing opportunity to solve calculus equations with unparalleled speed, while facing an inevitable tradeoff in computing density and equation reconfigurability. Here, we propose a reconfigurable metamaterial processing unit (MPU) that solves arbitrary linear calculus equations at a very fast speed. Subwavelength kernels based on inverse-designed pixel metamaterials are used to perform calculus operations on time-domain signals. In addition, feedback mechanisms and reconfigurable components are used to formulate and solve calculus equations with different orders and coefficients. A prototype of this MPU with a compact planar size of 0.93λ₀×0.93λ₀ (λ₀ is the free-space wavelength) is constructed and evaluated in microwave frequencies. Experimental results demonstrate the MPU’s ability to successfully solve arbitrary linear calculus equations. With the merits of compactness, easy integration, reconfigurability, and reusability, the proposed MPU provides a potential route for integrated analog computing with high speed of signal processing.

微积分方程作为数学的基本框架，能够描述广泛的自然现象和科学原理，例如热力学和电磁学。电磁波模拟计算提供了一个以无与伦比的速度求解微积分方程的有趣机会，同时面临着计算密度和方程可重构性之间不可避免的权衡。在这里，我们提出了一种可重构的超材料处理单元（MPU），它能够以非常快的速度求解任意线性微积分方程。基于逆向设计的像素超材料的亚波长内核用于对时域信号执行微积分运算。此外，反馈机制和可重构组件用于制定和求解具有不同阶次和系数的微积分方程。构建并评估了该 MPU 原型，其平面尺寸为 0.93λ ₀ ×0.93λ ₀ （λ ₀ 为自由空间波长）在微波频率。实验结果证明了 MPU 能够成功求解任意线性微积分方程。所提出的MPU具有结构紧凑、易于集成、可重构和可重用等优点，为高速信号处理的集成模拟计算提供了潜在的途径。