Modern analog computing for solving differential and matrix equations

2026-06-11

AI Summary

This work addresses the urgent need for efficient solutions to differential and matrix equations in artificial intelligence and scientific computing by transcending the energy-efficiency and speed limitations of conventional digital computation. It pioneers a unified framework that integrates both classes of equations within a modern analog computing paradigm. Leveraging hardware platforms such as analog CMOS circuits and memristor crossbar arrays, the study systematically constructs a computational primitive centered on matrix-vector multiplication, thereby uncovering intrinsic connections among differential equation solvers, matrix equation solvers, and in-memory computing. The research highlights the superior energy efficiency and parallelism offered by memristor arrays while rigorously examining critical challenges including numerical precision and scalability, ultimately establishing analog computing as a promising enabler for next-generation high-performance computing.

Abstract

In recent years, driven by the computational demands of data-intensive applications such as artificial intelligence and scientific computing, analog computing has gained renewed interest. Given the diversity of computational tasks and recent advancements in analog CMOS circuits and resistive memory technologies, we refer to the evolving landscape as modern analog computing. In this context, we identify three core computational primitives: solving differential equations, solving matrix equations, and performing matrix-vector multiplications, and we explore the connections among them. We also examine various hardware implementations of these analog computing operators, including those built with discrete components, integrated circuits, and resistive memory devices. Among these, resistive memory arrays emerge as particularly promising due to their implementation efficiency. The paper then surveys recent progress in leveraging modern analog computing to solve differential and matrix equations using both advanced analog CMOS circuits and resistive memory arrays. Finally, we discuss the applications of these circuits, the precision and scalability issues and their potential solutions, the relationship with in-memory computing, and the unique computational complexity of analog computing. This paper provides a unified perspective on analog computing, highlighting its strengths, current developments, and challenges, and positioning it as a pivotal enabler of next-generation computational frontiers.

Problem

• analog computing
• differential equations
• matrix equations
• resistive memory
• computational primitives

Innovation

• modern analog computing
• resistive memory arrays
• differential equations
• matrix equations
• in-memory computing