Memristive devices have been extensively studied for data-intensive tasks such as artificial neural networks. These types of computing tasks are considered to be ‘soft’ as they can tolerate low computing precision without suffering from performance degradation. However, ‘hard’ computing tasks, which require high precision and accurate solutions, dominate many applications and are difficult to implement with memristors because the devices normally offer low native precision and suffer from high device variability. Here we report a complete memristor-based hardware and software system that can perform high-precision computing tasks, making memristor-based in-memory computing approaches attractive for general high-performance computing environments. We experimentally implement a numerical partial differential equation solver using a tantalum oxide memristor crossbar system, which we use to solve static and time-evolving problems. We also illustrate the practical capabilities of our memristive hardware by using it to simulate an argon plasma reactor.

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We acknowledge inspiring discussions with Z. Zhang, J. Moon and T. Chen. This work was support by the Defense Advanced Research Projects Agency (DARPA) through award HR0011-17-2-0018 and by the National Science Foundation (NSF) through grant CCF-1617315.

Author information

Author notes

    • Bing Chen

    Present address: College of Electronic Engineering and Information Science, Zhejiang University, Hangzhou, China

  1. These authors contributed equally to this work: Mohammed A. Zidan, YeonJoo Jeong.


  1. Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, Michigan, USA

    • Mohammed A. Zidan
    • , YeonJoo Jeong
    • , Jihang Lee
    • , Bing Chen
    • , Shuo Huang
    • , Mark J. Kushner
    •  & Wei D. Lu


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M.A.Z. and W.D.L. conceived the project and constructed the research frame. M.A.Z., Y.J., J.L. and B.C. prepared the memristor arrays and built the hardware and software package. M.A.Z. and Y.J. performed the hardware measurements. M.A.Z, Y.J., S.H., M.J.K. and W.D.L. analysed the experimental data and simulation results. W.D.L. directed the project. All authors discussed the results and implications and commented on the manuscript at all stages.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Wei D. Lu.

Supplementary information

  1. Supplementary Information

    Supplementary Figures 1–12 and Supplementary Notes 1–2

  2. Supplementary Video 1

    Solution obtained from the memristor hardware system showing the wave propagation in a shallow water system at different times.

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