Modular memristor model with synaptic-like plasticity and volatile memory

TL;DR

This work presents a new paradigm for memristor modeling that is both practical for large-scale simulation and rich in explanatory power, providing a principled tool for the design of next-generation neuromorphic hardware.

Abstract

Compact models of memristors are essential for simulating large-scale neuromorphic systems, yet they often do not include description of complex dynamics like volatile relaxation and synaptic plasticity. We introduce a modular, computationally efficient memristor model that bridges this gap by integrating principles from physics and computational neuroscience. The model defines a framework consisting of a standard formulation of memristive device dynamics, a functional rule mapping state variables to cumulative conductance, a volatility module inspired by the theory of linear viscoelasticity and a saturation module implementing a linear-nonlinear technique. Additionally, we develop a formulation of synaptic-like plasticity inspired by a biological spike-timing-dependent plasticity (STDP) rule, which is compatible with the general framework for memristive devices. Finally, we propose a Laplace transform-based technique to derive the precise form of the mapping from state variables to cumulative conductance, replacing ad hoc voltage-current relationships with principled construction. We quantitatively validate the complete model against a rich set of experimental data from polymeric memristors exhibiting potentiation, synaptic-like plasticity and volatile decay. Our work presents a new paradigm for memristor modeling that is both practical for large-scale simulation and rich in explanatory power, providing a principled tool for the design of next-generation neuromorphic hardware.

Figures (7)

• Figure 1: Schematic representation of the model. The model integrates two independent components into the cumulative conductance function $H(s,w)$: voltage-controlled switching dynamics (state variable $s$) providing the memristive core, and STDP-like synaptic plasticity (state variable $w$) implementing learning rules through eligibility traces. The function then undergoes volatile decay through viscoelastic-inspired convolution with a decay kernel $\ker()$. The final conductance $G$ emerges after saturation nonlinearity, reproducing both volatile memory and synaptic plasticity observed in polymeric memristors. This modular approach enables near-independent optimization of each functional component.
• Figure 2: Log–log representation of post-potentiation conductance relaxation in the PCaPMA memristor. Each curve shows the decay of conductance after a train of trigger pulses with different total stimulation time $T_j$. When plotted in double-logarithmic coordinates, the initial segments of all traces are close to straight lines over more than two decades in time, indicating a power-law-like decay and ruling out a simple exponential relaxation.
• Figure 3: Kernel function coefficient estimation. Each trace corresponds to stimulation by pulses over the duration $T_j$. For each trace, a fit $g_j(t) = b_j \, (\frac{1}{(x+\varepsilon)^\alpha}- \frac{1}{(x+\varepsilon + T_j)^\alpha}) + c_j$ is performed using two trace-specific parameters $b_j$ and $c_j$ together with the global coefficient $\alpha$ to be estimated.
• Figure 4: Cumulative conductance function estimate. Each curve shows the estimated dependence of $\partial_s H(s)$ on the state variable $s$, reconstructed from relaxation traces with different stimulation durations $T$ using the procedure in \ref{['sub:ccform']}. The parameters $h_0$, $h_1$ are chosen so that the traces for all $T$ collapse onto a power-law-like curve with a common $a = -0.585$, well approximated by the parametric form $dH(s) = (h_1\,|s|^a + h_0)\,\dot s$. This justifies the simple functional form of $dH$ used in the main text.
• Figure 5: Comparison between the model and the experimental data for a relatively long stimulation input ($T=35$ s). The measured conductance decays after potentiation by a pulse train of total duration $T$ and the solid line shows the corresponding numerical simulation of the model.