Modern analog computing for solving differential and matrix equations

Analog computing is gaining renewed interest from artificial intelligence and scientific computing demands. We term the evolving landscape modern analog computing, identifying three core primitives—solving differential equations, solving matrix equations, and performing matrix-vector multiplications—and exploring their interconnections and hardware implementations, from discrete components to integrated circuits and resistive memory devices. We then survey recent progress in solving differential and matrix equations using CMOS analog circuits and resistive memory arrays. Finally, we discuss applications, precision and scalability challenges, in-memory computing relationships, and the computational complexity of analog computing, providing a unified perspective on this emerging field.