Conceptual diagram of our high-precision analog matrix inversion solver. Credit: Zhong Sun, Peking University.
Analog computers are systems that perform calculations by manipulating physical quantities such as electric current, which map mathematical variables, instead of representing information by abstraction with discrete binary values (i.e. 0 or 1), like digital computers.
Although analog computer systems can perform well in general tasks, they are known to be sensitive to noise (i.e., background or external interference) and less accurate than digital devices.
Researchers from Peking University and the Beijing Advanced Innovation Center for Integrated Circuits have developed a scalable analog computing device capable of solving matrix equations with remarkable precision. This new system, presented in an article published in Natural electronicswas built using tiny non-volatile memory devices called resistive random access memory (RRAM) chips.
“I have been working on analog computing since 2017,” Zhong Sun, an assistant professor at Peking University and lead author of the paper, told Tech Xplore.
“We call our approach modern analog computing, because it focuses on solving matrix equations – rather than differential equations as in traditional analog computing – using non-volatile resistive memory arrays instead of conventional CMOS circuits.”
Over the past decade, Sun and his colleagues have developed a wide range of analog computer systems. However, most of these systems have proven significantly less accurate than digital computers in performing desired operations, limiting their potential for real-world applications.
“Around 2022, we began to directly address this problem, aiming to achieve high-precision analog computing comparable to modern digital systems,” Sun said.
“In our recent paper, we demonstrate solving all-analog matrix equations with 24-bit fixed-point precision (comparable to FP32) by combining a low-precision matrix inversion circuit (first designed in 2019) with high-precision matrix-vector multiplication using bit-slicing across multiple resistive memory dies.”
The new analog matrix equation solver introduced by the team builds on a circuit developed by Sun and other researchers in 2019, while he was a postdoctoral researcher at Politecnico di Milano. Although this circuit can solve matrix equations having a specific form (Ax = b) in a single step, it has been found to be less accurate than digital systems.
“In our new study, we combined this low-precision solver with high-precision matrix-vector multiplication using a conventional bit-slicing technique, enabling iterative refinement of the solution,” Sun explained.
“In each iteration, the low-precision inversion circuit provides an approximate result, and the high-precision operation refines it by indicating the direction and magnitude of the correction. This hybrid approach converges quickly, much faster than conventional algorithms based on gradient descent.”
To demonstrate the scalability of their analog calculation method, the researchers fabricated a circuit based on an 8×8 matrix and tested its ability to solve various matrix equations. They found that the circuit could solve 16×16 matrix equations, and then progressively various other matrix equations (e.g. 32×32).
The matrix equation solver they developed could be further improved and could inspire the development of other precise analog computing systems. In the future, this could prove useful in advancing various technologies, ranging from wireless communications to artificial intelligence (AI).
“The most notable contribution is our demonstration that all-analog matrix computing can achieve high precision comparable to digital floating-point systems, while also ensuring scalability,” Sun added.
“Our next goal is to scale the system by building circuits based on larger arrays and integrating all components on one chip, integrating both matrix inversion and matrix-vector multiplication functionality into a single chip-level platform.”
Written for you by our author Ingrid Fadelli, edited by Sadie Harley, and fact-checked and revised by Robert Egan, this article is the result of painstaking human work. We rely on readers like you to keep independent science journalism alive. If this reporting interests you, consider making a donation (especially monthly). You will get a without advertising account as a thank you.
More information:
Pushen Zuo et al, Accurate and scalable resolution of analog matrix equations using resistive RAM chips, Natural electronics (2025). DOI: 10.1038/s41928-025-01477-0.
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