Solving Multivariable Equations with Tandem Metamaterial Kernels

A fundamental building block in characterizing and tackling scientific and industrial questions boils down to the ability of quickly solving mathematical equations. However, with the ever-growing volume of information and unsustainable integration growth in electronic processors, a radically new modality for solving equations is highly imminent. Here, we introduce an electromagnetic counterpart to solve multivariable complex equations, where two metamaterialkernels are connected in series to form a closed-loop electromagnetic system. Complex-valued information is carried by electromagnetic fields, and the equation solution for arbitrary input signals can be recursively attained after a number of feedbacks. As an illustration, we present the capability of such system in solving eight complex equations, and inversely design two 4 × 4 metamaterialkernels by topology optimization, whose average element error is reduced to smaller than 10-4. Having accomplished all unknown coefficients with high fidelity, our work represents a conspicuous apparatus for a myriad of enticing applications in ultra-compact signal processing and neuromorphic computing.