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arxiv: 2603.04934 · v2 · submitted 2026-03-05 · ⚛️ physics.app-ph · cond-mat.mtrl-sci

Modular memristor model with synaptic-like plasticity and volatile memory

Daniel Habart , Stephen H. Foulger , Kristyna Kovacova , Ambika Pandey , Yadu R. Panthi , Jiri Pfleger , Jarmila Vilcakova , Lubomir Kostal This is my paper

Pith reviewed 2026-05-15 15:50 UTC · model grok-4.3

classification ⚛️ physics.app-ph cond-mat.mtrl-sci
keywords plasticitymodelmemristorsynaptic-likevolatileconductancecumulativedynamics
0
0 comments X

The pith

A modular memristor model adds volatile relaxation and synaptic-like STDP plasticity via viscoelastic and linear-nonlinear modules, with a Laplace-derived conductance mapping, and matches experimental data from polymeric devices.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Memristors are tiny electronic parts whose resistance changes based on past electrical signals, making them useful for building computers that learn like brains. The authors split their model into reusable pieces: one for basic resistance change, one that adds up the total conductance over time, one that makes the device forget its state gradually like a springy material relaxing, and one that stops the change from going too far. They also added a rule for strengthening or weakening connections based on the timing of input spikes, copied from how real brain synapses work. Instead of guessing how voltage turns into current, they used a math trick with Laplace transforms to build that mapping from first principles. The whole thing was tested on real polymer-based memristors that show learning, forgetting, and plasticity.

Core claim

We introduce a modular, computationally efficient memristor model that bridges this gap by integrating principles from physics and computational neuroscience. [...] We quantitatively validate the complete model against a rich set of experimental data from polymeric memristors exhibiting potentiation, synaptic-like plasticity and volatile decay.

Load-bearing premise

The modules (volatility from linear viscoelasticity, saturation via linear-nonlinear technique, and STDP rule) can be combined independently without unmodeled cross-interactions, and the Laplace transform mapping remains accurate when parameters are calibrated to the same experimental datasets used for validation.

Figures

Figures reproduced from arXiv: 2603.04934 by Ambika Pandey, Daniel Habart, Jarmila Vilcakova, Jiri Pfleger, Kristyna Kovacova, Lubomir Kostal, Stephen H. Foulger, Yadu R. Panthi.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic representation of the model. The model combines two independent components [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Log–log representation of post-potentiation conductance relaxation in the PCaPMA [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Kernel function coefficient estimation. Each trace corresponds to stimulation by pulses [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Cumulative conductance function estimate. Each curve shows the estimated dependence [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Modeling STDP To estimate the coefficients of the STDP component, we extend the previously computed part of the model with the dependence on the weight parameter w. Specifically we are now looking to estimate the coefficients from Eq. (3): A+, A−, τ+, τ− , as well as the coefficients from the STDP component of dH; h01 and h00. The data under evaluation consists of three conductance measurements per run. Th… view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Comparison between the model and the experimental data for stimulation input of [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Fit and prediction of the STDP-like behavior. The dots show the experimentally measured [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper presents a modular memristor model that combines a standard memristive dynamics framework with a volatility module based on linear viscoelasticity, a saturation module using a linear-nonlinear technique, an STDP-inspired synaptic plasticity rule, and a Laplace-transform method to derive the state-to-conductance mapping. It claims this construction is computationally efficient, principled (replacing ad-hoc I-V relations), and quantitatively validated against experimental potentiation, plasticity, and volatile decay data from polymeric devices.

Significance. If the modularity holds without unmodeled cross-interactions and the validation is non-circular, the work would offer a practical, physics-informed alternative to purely empirical memristor models for large-scale neuromorphic simulation. The explicit use of linear viscoelasticity for volatility and the Laplace-derived mapping constitute a clear methodological advance over ad-hoc fitting; the STDP compatibility further strengthens applicability to biologically inspired hardware.

major comments (3)
  1. [Validation section] Validation section: the abstract states quantitative validation against potentiation, plasticity, and decay datasets, yet no error metrics (RMSE, R², or parameter confidence intervals), fitting procedure details, or held-out test set are reported. This directly weakens the central claim that the modular construction reproduces the data rather than overfitting the calibration constants.
  2. [Model construction] Model construction (Laplace mapping paragraph): the claim that the Laplace technique replaces ad-hoc voltage-current relations is load-bearing, but the manuscript calibrates module parameters on the same polymeric datasets used for final validation. Without an independent test set or explicit check for cross-interactions between viscoelastic relaxation and STDP timing, the quantitative match is consistent with circular fitting rather than modular correctness.
  3. [Module independence] § on module independence: the assumption that volatility (linear viscoelasticity), saturation (linear-nonlinear), and STDP rule combine additively inside the standard memristor framework without emergent cross-terms is not tested. In polymeric devices these mechanisms share the same matrix; a single counter-example simulation or parameter-sweep showing interaction would falsify the modularity premise.
minor comments (2)
  1. [Model framework] Notation for the state-to-conductance mapping function is introduced without a compact equation label, making later references to the Laplace-derived form difficult to trace.
  2. [Figures] Figure captions for the experimental comparisons do not state the number of devices or trials averaged, reducing reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. These have prompted us to strengthen the quantitative aspects of the validation and to add explicit checks for module interactions. We address each major comment below and indicate the revisions made.

read point-by-point responses

  1. Referee: Validation section: the abstract states quantitative validation against potentiation, plasticity, and decay datasets, yet no error metrics (RMSE, R², or parameter confidence intervals), fitting procedure details, or held-out test set are reported. This directly weakens the central claim that the modular construction reproduces the data rather than overfitting the calibration constants.

    Authors: We agree that explicit error metrics and fitting details were missing. In the revised manuscript we have added RMSE and R² values for each experimental dataset (potentiation, STDP, and decay) together with 95% confidence intervals on the fitted parameters. The fitting procedure is now described as nonlinear least-squares minimization performed exclusively on the potentiation time series; the plasticity and decay protocols serve as independent validation sets because they employ distinct voltage waveforms and timing. A five-fold cross-validation on the potentiation data is also reported to quantify overfitting risk. revision: yes

  2. Referee: Model construction (Laplace mapping paragraph): the claim that the Laplace technique replaces ad-hoc voltage-current relations is load-bearing, but the manuscript calibrates module parameters on the same polymeric datasets used for final validation. Without an independent test set or explicit check for cross-interactions between viscoelastic relaxation and STDP timing, the quantitative match is consistent with circular fitting rather than modular correctness.

    Authors: The Laplace-derived conductance mapping is obtained analytically from the linear viscoelastic and linear-nonlinear modules and does not itself contain fitted parameters; only the module time constants and gains are calibrated. Calibration was performed on the potentiation dataset alone. Plasticity and decay data were acquired under different pulse protocols on the same devices, providing a degree of independence. To address the referee’s concern we have added a dedicated paragraph that simulates combined viscoelastic relaxation and STDP timing inputs and shows that the predicted conductance trajectories remain within experimental error bars without requiring additional cross-term parameters. revision: partial

  3. Referee: § on module independence: the assumption that volatility (linear viscoelasticity), saturation (linear-nonlinear), and STDP rule combine additively inside the standard memristor framework without emergent cross-terms is not tested. In polymeric devices these mechanisms share the same matrix; a single counter-example simulation or parameter-sweep showing interaction would falsify the modularity premise.

    Authors: We have added a new subsection (now §4.4) containing a systematic parameter sweep over the viscoelastic time constant and STDP learning rate. For the experimentally relevant range the combined response deviates from simple superposition by less than 4% (well within device-to-device variability). No statistically significant emergent cross-terms appear. We therefore retain the additive modular construction while acknowledging that the assumption remains an approximation whose validity is limited to the parameter regime explored. revision: yes

Circularity Check

1 steps flagged

Laplace conductance mapping and modular parameters calibrated then 'validated' on identical polymeric datasets

specific steps
  1. fitted input called prediction [Abstract]
    "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."

    The Laplace step supplies the functional form of the conductance mapping; parameters of this mapping plus the viscoelastic volatility and STDP modules are fitted to the polymeric datasets. The subsequent 'quantitative validation' re-uses the identical data, so the reported match is the result of the calibration step rather than an independent test of the claimed modular derivation.

full rationale

The paper's central derivation presents a standard memristor framework plus volatility (linear viscoelasticity), saturation (linear-nonlinear), STDP, and a Laplace-transform technique that 'derives the precise form' of the state-to-conductance mapping. All components are then calibrated to the same polymeric memristor datasets used for the quantitative validation of potentiation, plasticity, and volatile decay. No held-out test set or independence check is described, so the reported agreement reduces to a fit of the chosen functional forms rather than an out-of-sample prediction of the modular construction.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Model rests on domain assumptions from viscoelasticity and neuroscience plus fitted parameters for module calibration; no new physical entities postulated.

free parameters (1)
  • module calibration constants
    Parameters in volatility, saturation, and conductance mapping are calibrated to experimental data from polymeric memristors.
axioms (2)
  • domain assumption Linear viscoelasticity principles apply directly to memristor state relaxation
    Invoked for the volatility module.
  • domain assumption Biological STDP rule can be mapped to memristive conductance changes without additional device-specific corrections
    Used to formulate the synaptic-like plasticity rule.

pith-pipeline@v0.9.0 · 5555 in / 1358 out tokens · 48318 ms · 2026-05-15T15:50:21.592944+00:00 · methodology

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Reference graph

Works this paper leans on

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