# A Compact Memristor Model Based on Physics-Informed Neural Networks

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## Abstract

**:**

## 1. Introduction

## 2. Physics Based Memristor Models

#### 2.1. Generalized Mean Metastable Switch (GMMS) Memristor Model

#### 2.2. Memristor Model of Messaris et al.

## 3. Physics-Informed Neural Network Model

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**PINN and Verilog-A implementation methodology. The hidden layer computation is performed via weight and bias for the input data V and t. The weight and bias obtained by PINN are implemented into a Verilog-A script.

**Figure 2.**Memristor state. (

**a**) Numerical solution data and (

**b**) PINN training data. The state changes according to the input data $V$= −0.2~0.2 and $t$ = 0~0.1. The state change is represented by a value between 0 and 1.

**Figure 3.**Error between numerical solution data and PINN training data. (

**a**) Three-dimensional plot and (

**b**) two-dimensional plot. The error is largest at the point where the time axis is zero, as well as at the inflection point of the state function.

**Figure 4.**History of PINN loss values. The learning rate and the number of iterations are fixed to 0.01 and to 1000, respectively. The loss function is computed up to 1000 epochs and converges at $6\times {10}^{-7}$.

**Figure 5.**The GMMS Model conductance. (

**a**) Input signal of a 10 Hz sin wave with an amplitude of 0.2 V. (

**b**) Input signal of a 100 Hz sin wave with an amplitude of 0.2 V. (

**c**) Input signal of a 1 kHz sin wave with an amplitude of 0.2 V.

**Figure 6.**Numerical solution data and PINN-predicted I–V characteristic curves from the GMMS model. (

**a**) Input frequency at 10 Hz sin wave with an amplitude of 0.2 V. (

**b**) Input frequency at 100 Hz sin wave with an amplitude of 0.2 V. (

**c**) Input frequency at 1 kHz sin wave with an amplitude of 0.2 V.

**Figure 7.**Resistive state of the positive region in the memristor model of Messaris et al. (

**a**) Numerical solution data and (

**b**) PINN training data. The state changes according to the input data $V$ = 0~1 and $t$ = 0~0.1. The state change is represented by a value between 0 and 1.

**Figure 8.**Error rate between numerical solution data and PINN training data in the positive region in the memristor model of Messaris et al. (

**a**) Three-dimensional plot and (

**b**) two-dimensional plot. The error is largest at the point where the time axis is zero, as well as at the inflection point of the state function.

**Figure 9.**Resistive state of the negative region in the memristor model of Messaris et al. (

**a**) Numerical solution data and (

**b**) PINN training data. The state changes according to the input data $V$ = −1~0 and $t$ = 0~0.1. The state change is represented by a value between 0 and 1.

**Figure 10.**Error rate between numerical solution data and PINN training data in the negative region in the memristor model of Messaris et al. (

**a**) Three-dimensional plot and (

**b**) two-dimensional plot. The error is largest at the point where the time axis is zero, as well as at the inflection point of the state function.

**Figure 11.**History of PINN loss function results: (

**a**) 1000 epochs in the positive region and (

**b**) 1000 epochs in the negative region.

**Figure 12.**The memristor model of Messaris et al. conductance. (

**a**) Input signal of a 10 Hz sin wave with an amplitude of 1 V. (

**b**) Input signal of a 100 Hz sin wave with an amplitude of 1 V. (

**c**) Input signal of a 1 kHz sin wave with an amplitude of 1 V.

**Figure 13.**I–V characteristic curves between numerical data and PINN data. (

**a**) Input signal of a 10 Hz sin wave with an amplitude of 1 V. (

**b**) Input signal of a 100 Hz sin wave with an amplitude of 1 V. (

**c**) Input signal of a 1 kHz sin wave with an amplitude of 1 V.

**Figure 14.**The memristor model of I–V characteristic curve. (

**a**) Input signal of a pulse wave with a frequency of 1 MHz in a GMMS model. (

**b**) Input signal of a pulse wave with a frequency of 1 MHz in the memristor model of Messaris et al.

$\mathit{V}$ | ${\mathit{R}}_{\mathit{O}\mathit{N}}\left(\mathsf{\Omega}\right)$ | ${\mathit{R}}_{\mathit{O}\mathit{F}\mathit{F}}\left(\mathsf{\Omega}\right)$ | ${\mathit{V}}_{\mathit{O}\mathit{N}}\left(\mathbf{V}\right)$ | ${\mathit{V}}_{\mathit{O}\mathit{F}\mathit{F}}\left(\mathbf{V}\right)$ | $\mathit{\tau}$ |
---|---|---|---|---|---|

$-0.2\le V<0.2$ | $5000$ | $\mathrm{100,000}$ | $0.2$ | $0.1$ | $0.0001$ |

$\mathit{V}$ | ${\mathit{a}}_{\mathit{p},\mathit{n}}$ | ${\mathit{t}}_{\mathit{p},\mathit{n}}$ | ${\mathit{r}}_{\mathit{p}0,\mathit{n}0}$ | ${\mathit{r}}_{\mathit{p}1,\mathit{n}1}$ | ${\mathit{R}}_{\mathit{m}\mathit{i}\mathit{n}}\left(\mathsf{\Omega}\right)$ | ${\mathit{R}}_{\mathit{m}\mathit{a}\mathit{x}}\left(\mathsf{\Omega}\right)$ |
---|---|---|---|---|---|---|

$V>0$ | $0.01$ | $2.45$ | $71.61$ | $4370$ | $4513$ | $7000$ |

$V\le 0$ | $-0.52$ | $2.72$ | $6006$ | $1279$ | $4513$ | $7000$ |

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**MDPI and ACS Style**

Lee, Y.; Kim, K.; Lee, J.
A Compact Memristor Model Based on Physics-Informed Neural Networks. *Micromachines* **2024**, *15*, 253.
https://doi.org/10.3390/mi15020253

**AMA Style**

Lee Y, Kim K, Lee J.
A Compact Memristor Model Based on Physics-Informed Neural Networks. *Micromachines*. 2024; 15(2):253.
https://doi.org/10.3390/mi15020253

**Chicago/Turabian Style**

Lee, Younghyun, Kyeongmin Kim, and Jonghwan Lee.
2024. "A Compact Memristor Model Based on Physics-Informed Neural Networks" *Micromachines* 15, no. 2: 253.
https://doi.org/10.3390/mi15020253