# Modern analog computing for solving differential and matrix equations

arXiv: https://arxiv.org/abs/2606.13179 · HTML: https://mlsanity.com/paper/2606.13179/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 121 references that are in the map.
- First posted on arXiv 11 Jun 2026.

## Builds on (most cited first, 9 of 9)

- [Carbon Emissions and Large Neural Network Training](https://mlsanity.com/paper/2104.10350/) (2021)
- [One-step regression and classification with crosspoint resistive memory arrays](https://mlsanity.com/paper/2005.01988/) (2020)
- [Thermodynamic Natural Gradient Descent](https://mlsanity.com/paper/2405.13817/) (2024)
- [Analog Computation and Representation](https://mlsanity.com/paper/2012.05965/) (2020)
- [Thermodynamic Algorithms for Quadratic Programming](https://mlsanity.com/paper/2411.14224/) (2024)
- [RePAST: A ReRAM-based PIM Accelerator for Second-order Training of DNN](https://mlsanity.com/paper/2210.15255/) (2022)
- [Extremely-Fast, Energy-Efficient Massive MIMO Precoding with Analog RRAM Matrix Computing](https://mlsanity.com/paper/2211.03624/) (2022)
- [Realizing In-Memory Baseband Processing for Ultra-Fast and Energy-Efficient 6G](https://mlsanity.com/paper/2308.10009/) (2023)
- [BlockAMC: Scalable In-Memory Analog Matrix Computing for Solving Linear Systems](https://mlsanity.com/paper/2401.10042/) (2024)

## Abstract (arXiv)

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.