Electrolyte Transistor-Based Reservoir Computing System for High-Efficiency Differential Equation Solving

DU Mingyang; HAN Mengtao; XING Qianye; CUI Hangyuan; WAN Changjin

doi:10.12263/DZXB.20260257

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Electrolyte Transistor-Based Reservoir Computing System for High-Efficiency Differential Equation Solving

Innovative Architectures and Electronic Systems for Efficient Artificial Intelligence | 更新时间：2026-10-16

- Electrolyte Transistor-Based Reservoir Computing System for High-Efficiency Differential Equation Solving
- ACTA ELECTRONICA SINICA Vol. 54, Issue 6, Pages: 2415-2425(2026)
- 作者机构：
  
  南京大学电子科学与工程学院，江苏南京 210023
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China(92364106;U25A20500);Postgraduate Research & Practice Innovation Program of Jiangsu Province (No.KYCX25_0278, No.KYCX25_0284)
- DOI：10.12263/DZXB.20260257
  CLC： TN386;TP183
- Received：22 February 2026，
  
  Accepted：19 April 2026，
  
  Published：25 June 2026
- 稿件说明：
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杜明阳, 韩孟涛, 邢千叶, 等. 面向高效微分求解电解质晶体管基储备池计算系统[J]. 电子学报, 2026, 54(06): 2415-2425.

DU Mingyang, HAN Mengtao, XING Qianye, et al. Electrolyte Transistor-Based Reservoir Computing System for High-Efficiency Differential Equation Solving[J]. Acta Electronica Sinica, 2026, 54(06): 2415-2425.
杜明阳, 韩孟涛, 邢千叶, 等. 面向高效微分求解电解质晶体管基储备池计算系统[J]. 电子学报, 2026, 54(06): 2415-2425. DOI：10.12263/DZXB.20260257

DU Mingyang, HAN Mengtao, XING Qianye, et al. Electrolyte Transistor-Based Reservoir Computing System for High-Efficiency Differential Equation Solving[J]. Acta Electronica Sinica, 2026, 54(06): 2415-2425. DOI：10.12263/DZXB.20260257

摘要

物理储备池计算（Physical Reservoir Computing，PRC）凭借其低训练成本与高并行效率，已成为时序信号处理与复杂动力学系统建模的新兴范式。该方法主要依赖于器件物理特性中的非线性与短时记忆动力学特性，实现对时序信号的高维映射，获得丰富的储备池状态，从而实现对复杂状态方程较为精确的求解及预测。PRC仅需求解输出层权重、推理功耗低、少样本数据驱动等优势，为在端侧硬件上实现混沌微分方程与偏微分方程的实时求解提供了全新路径。然而，如何将高阶复杂时序任务的处理算法与物理器件的本征调控机制有效适配，仍是制约其实际部署的关键瓶颈。本文提出了一种基于铟镓锌氧化物（Indium Gallium Zinc Oxide，IGZO）电解质晶体管的高效物理储备池计算系统，成功实现了混沌含时微分方程序列的求解预测，并提出了基于物理计算系统的偏微分方程求解。借助IGZO器件的低功耗特性、连续非线性映射能力，设计了轻量化的储备池训练推理与方程求解协同算法，对IGZO晶体管的电学响应与离子迁移动力学行为进行了精确建模表征，并在现场可编程门阵列（Field Programmable Gate Array，FPGA）平台上完成了系统级仿真验证。资源评估表明，相较于传统四阶Runge-Kutta算法实现，本方案在保持同等精度的前提下，数字信号处理单元（Digital Signal Processor，DSP）与触发器（Flip-Flop，FF）资源占用分别降低约64%与50%，整体逻辑开销显著优化。求解性能方面，实验选取Mackey-Glass、Lorenz这两类混沌微分方程及一维热扩散方程为基准，与主流数值方法（Runge-Kutta）及现有物理计算平台进行对比。结果表明，该系统在混沌微分方程求解中展现出约11 μs的延迟，相比Runge-Kutta方法功耗降低15%，归一化均方根误差（Normalized Root Mean Square Error，NRMSE≈0.04）与现有大多数高效物理计算系统相当；针对一维热扩散偏微分方程，计算时间较二阶Runge-Kutta缩短至1/400，且精度方面NRMSE≈0.008也与之相当。本研究不仅验证了IGZO基PRC系统在通用微分方程求解中的高效性与准确性，更为下一代轻量化、低功耗的端侧科学计算与神经形态硬件平台提供了可拓展的架构基础与工程实践参考。

Abstract

Physical reservoir computing (PRC)

characterized by its low training cost and high parallel efficiency

has emerged as a promising paradigm for temporal signal processing and complex dynamical system modeling. By leveraging the intrinsic nonlinearity and short-term memory dynamics of physical devices

PRC maps temporal inputs into a high-dimensional state space

generating rich reservoir states that enable accurate solving and prediction of complex state equations. With advantages such as readout-layer-only training

low inference power consumption

and few-shot data driven

PRC offers a novel pathway for real-time solving of chaotic differential and partial differential equations on edge hardware. However

effectively co-designing high-order temporal processing algorithms with the intrinsic modulation mechanisms of physical devices remains a key bottleneck hindering practical deployment. Here

we report a highly efficient PRC system based on indium gallium zinc oxide (IGZO) electrolyte transistors

achieving the solving and prediction of time-dependent chaotic differential equations and partial differential equations. Leveraging the low-power characteristics and continuous nonlinear mapping capability of IGZO devices

we designed a lightweight algorithm co-optimizing reservoir training

inference

and equation solving. The electrical response and ion migration dynamics of the IGZO transistors were accurately modeled and characterized

followed by system-level validation on the field programmable gate array (FPGA). Resource evaluation demonstrates that

compared to a conventional fourth-order Runge-Kutta (RK4) implementation

our approach reduces digital signal processor (DSP) and flip-flop utilization by approximately 64% and 50%

respectively

while maintaining equivalent accuracy. In performance benchmarks using the Mackey-Glass equation

Lorenz chaotic sequence

and one-dimensional heat diffusion equation

our system achieves an inference latency of 11 μs and reduces power consumption by 15%

with a normalized root mean square error (NRMSE≈0.04) comparable to the Runge-Kutta method. For the partial differential equation (PDE) task

computation time is reduced to 1/400 of that required by the second-order Runge-Kutta (RK2) method

while maintaining a comparable NRMSE≈0.008. This work not only validates the efficiency and accuracy of IGZO-based PRC in solving general differential equations

but also provides a scalable architectural foundation and practical engineering reference for next-generation lightweight

low-power edge scientific computing and neuromorphic hardware platforms.

关键词

Keywords

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