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.

翻译：近年来，在人工智能和科学计算等数据密集型应用的计算需求驱动下，模拟计算重新获得关注。鉴于计算任务的多样性以及模拟CMOS电路和电阻式存储器技术的最新进展，我们将这一不断演进的领域称为现代模拟计算。在此背景下，我们识别出三种核心计算原语：求解微分方程、求解矩阵方程和执行矩阵向量乘法，并探讨了它们之间的关联。我们还考察了这些模拟计算算子的多种硬件实现方案，包括基于分立元件、集成电路和电阻式存储器件构建的方案。其中，电阻式存储阵列因其实现效率而展现出尤为突出的潜力。本文随后综述了利用先进模拟CMOS电路和电阻式存储阵列通过现代模拟计算求解微分方程与矩阵方程的最新进展。最后，我们讨论了这些电路的应用场景、精度与可扩展性问题及其潜在解决方案、与存内计算的关系，以及模拟计算独特的计算复杂度。本文为模拟计算提供了统一视角，凸显其优势、当前进展与挑战，并将其定位为下一代计算前沿的关键推动力。