一种适用于大规模忆阻网络的忆阻器单元解析建模策略

An analytic modeling strategy for memristor cell applicable to large-scale memristive networks

忆阻网络是一种基于忆阻器单元的大规模非线性电路,在下一代人工智能、生物电子、高性能存储器等新兴研究领域发挥着重要作用.描述忆阻器单元物理和电学特性的模型对忆阻网络的性能仿真具有显著影响.然而,现有模型主要为非解析模型,应用于忆阻网络分析时可能存在收敛性问题.因此,提出了一种基于同伦分析法(homotopy analysis method,HAM)的忆阻器单元解析建模策略,该策略具有解析性和收敛性优化的特点,可提高忆阻器单元和相应忆阻网络的收敛性.此外,还提出了一种面向忆阻器单元模型的验证准则,以验证模型在大规模忆阻网络中的适用性.通过忆阻器单元和忆阻矩阵网络的长时演化实验以及与传统非解析(数值)方法的比较,验证了所提策略的解析性和收敛性优势;利用不同类型忆阻器单元和输入的实验,验证了该策略的扩展性.进一步地,基于上述实验,揭示了忆阻网络仿真出现收敛性问题的潜在原因.该策略可应用于基于忆阻网络的新兴研究.

Memristive networks are large-scale non-linear circuits based on memristor cells,playing a crucial role in developing the emerging researches such as next-generation artificial intelligence,bioelectronics,and high-performance memory.The performance of memristive networks is greatly affected by the memristor model describing physical and electrical characteristics of a memristor cell.However,existing models are mainly non-analytic and,accordingly,may have convergence issues in their applications in memristive networks’analyses.Therefore,aiming at improving convergence of memristive networks,we propose an analytic modeling strategy for memristor based on homotopy analysis method(HAM).In this strategy,the HAM is used to obtain an analytic memristor model through solving the state equations of memristors in original physical model.Specifically,the HAM is used to solve the analytic approximate solution of the core parameter of memristor—state variable,from the state equations,in the form of analytic homotopy series.Then the analytic approximate model of memristor is obtained by using the solved state variables.The characteristics of the proposed strategy are as follows.1)Its solution has a closed-form expression,i.e.an explicit function,2)its approximation error is optimized,thereby realizing the convergence optimization.Moreover,according to the characteristics of memristive networks,we introduce an analysis criterion for memristor model applicable to memristive networks.Through the long-time evolution experiments of a memristor cell and a benchmark memristive matrix network with different inputs,and the comparisons with the traditional non-analytic(numeric)method,we verify the analyticity and convergence superiority of the modeling strategy.Besides,based on this strategy and the comparison experiments,we reveal that one of the underlying reasons for non-convergence in the large-scale memristive network simulation possesses the non-analyticity of the used memristor model.The strategy can be further used for analyzing the performances of a memristor cell and memristive networks in long-time.It also has potential applications in emerging technologies.