Abstract

Ordinary differential equations (ODEs) are widely used in science, engineering, and mathematics, but their numerical solution on traditional Von Neumann hardware is time- and energy-consuming, especially for high-order ODEs. Here, we present a high-concurrency memristor-based ODE solver supporting arbitrary order and three configurable modes: coarse, fine, and coarse-to-fine look-ahead, to meet diverse accuracy requirements. History-based memristor programming (HMP) accelerates device conductance programming by up to 3.29 × without compromising accuracy. The reconfigurable hardware implements coarse solver via analog compute-in-memory, fine solver via digital compute-in-memory, and coarse-to-fine solver using Parareal methods for high-concurrency numerical integration. We demonstrate its performance on exponential functions, Lorenz attractors, and three-body problems, achieving 601 × ~ 6.92 × 103 × speedup and 1.71 × 103 × ~ 3.93 × 103 × energy improvement over CPU/GPU, respectively, when solving the same ODE tasks. The memristor-based tri-mode solver pushes ODE solver hardware performance to a new paradigm with orders of magnitude concurrency improvements.

Data availability

The data generated in this study are provided in the Source Data file. The data used in this study are available in the Zenodo database46. Source data are provided in this paper.

Code availability

The code that needs to run on our memristor-based ODE solver hardware platform is available in the Zenodo database47.

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Acknowledgements

This work has been supported by the National Key R&D Program of China (2023YFB4502200; Y.Y.), Guangdong Provincial Key Laboratory of In-Memory Computing Chips (2024B1212020002; Y.Y.), Shenzhen Science and Technology Program (JCYJ20241202125907011; Y.Y.), Beijing Natural Science Foundation (L234026, L257010; Y.Y.), National Natural Science Foundation of China (92164302; Y.Y.), and Financial Support for Outstanding Scientific and Technological Innovation Talents Training Fund in Shenzhen (Y.Y.). This work has been supported by the New Cornerstone Science Foundation (Y.Y.).

Author information

Authors and Affiliations

New Cornerstone Science Laboratory, Beijing Advanced Innovation Center for Integrated Circuits, School of Integrated Circuits, Peking University, Beijing, China

Lianfeng Yu, Teng Zhang, Yang Han, Bowen Wang, Ziang Xie, Haochen Zhang, Jiaxin Liu, Longhao Yan, Pek Jun Tiw, Daijing Shi, Lei Cai, Yaoyu Tao & Yuchao Yang 1.

New Cornerstone Science Laboratory, Guangdong Provincial Key Laboratory of In-Memory Computing Chips, School of Electronic and Computer Engineering, Shenzhen Graduate School, Peking University, Shenzhen, China

Ziang Xie & Yuchao Yang 1.

Center for Artificial Intelligence Chips, Institute of Artificial Intelligence, Peking University, Beijing, China

Yaoyu Tao & Yuchao Yang 1.

PKU-Wuhan Institute for Artificial Intelligence, Peking University, Wuhan, China

Yaoyu Tao 1.

Center for Brain Inspired Intelligence, Chinese Institute for Brain Research (CIBR), Beijing, China

Yuchao Yang

Authors

1. Lianfeng Yu
2. Teng Zhang
3. Yang Han
4. Bowen Wang
5. Ziang Xie
6. Haochen Zhang
7. Jiaxin Liu
8. Longhao Yan
9. Pek Jun Tiw
10. Daijing Shi
11. Lei Cai
12. Yaoyu Tao
13. Yuchao Yang

Contributions

L.Y. and Y.T. designed the entire concept and experiment. L.Y., Y.T., and T.Z. were in charge of the hardware system integration, designed experimental methodologies for each part, and conducted related data analysis. L.Y., Y.T., T.Z., Y.H., B.W., Z.X., H.Z., J.L., L.Y., P.J.T., D.S., and L.C. contributed to memristor testing, chip design, chip fabrication, circuit design, PCB integration, hardware system verification and software simulations. L.Y., Y.T., Y.H., and Z.X. contributed to the interpretation of results. L.Y., Y.T., and Y.Y. wrote the paper with input from all authors. Y.T. and Y.Y. supervised the whole project.

Corresponding authors

Correspondence to Yaoyu Tao or Yuchao Yang.

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Nature Communications thanks Jianhua Yang, who co-reviewed with Wenhao Song, and the other anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

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Yu, L., Zhang, T., Han, Y. et al. High-concurrency tri-mode memristor-based ordinary differential equation solver. Nat Commun (2026). https://doi.org/10.1038/s41467-025-68122-4

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Received: 03 June 2025

Accepted: 18 December 2025

Published: 08 January 2026

DOI: https://doi.org/10.1038/s41467-025-68122-4