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arxiv: 2512.23624 · v2 · submitted 2025-12-29 · 💻 cs.AI · physics.app-ph

Physics-Informed Neural Networks for Device and Circuit Modeling: A Case Study of NeuroSPICE

Chien-Ting Tung , Chenming Hu This is my paper

Pith reviewed 2026-05-16 19:20 UTC · model grok-4.3

classification 💻 cs.AI physics.app-ph
keywords physics-informed neural networkscircuit simulationSPICEdevice modelingferroelectric memoriesdifferential-algebraic equationssurrogate modelswaveform modeling
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The pith

NeuroSPICE trains neural networks to solve circuit differential-algebraic equations by minimizing their residuals through backpropagation.

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

The paper introduces NeuroSPICE, a physics-informed neural network framework for simulating electronic devices and circuits. It replaces conventional time-discretized numerical solvers with a training process that enforces the governing equations directly. This produces analytical time-domain models of waveforms that carry exact temporal derivatives. The approach targets flexibility for emerging nonlinear systems such as ferroelectric memories. It also supplies surrogate models suited to design optimization and inverse problems, even though training does not claim speed or accuracy gains over standard SPICE.

Core claim

NeuroSPICE leverages PINNs to solve circuit differential-algebraic equations by minimizing the residual of the equations through backpropagation. It models device and circuit waveforms using analytical equations in time domain with exact temporal derivatives. While PINNs do not outperform SPICE in speed or accuracy during training, they offer unique advantages such as surrogate models for design optimization and inverse problems. NeuroSPICE's flexibility enables the simulation of emerging devices, including highly nonlinear systems such as ferroelectric memories.

What carries the argument

Physics-informed neural network trained to minimize residuals of circuit differential-algebraic equations, producing analytical time-domain waveform models with exact derivatives.

If this is right

  • Surrogate models become available for circuit design optimization tasks.
  • Inverse problems such as parameter extraction from observed behavior can be addressed directly.
  • Simulation of highly nonlinear emerging devices is supported without time discretization.
  • Exact temporal derivatives are obtained analytically rather than approximated numerically.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The trained network could serve as a differentiable component inside larger machine-learning pipelines for automated circuit tuning.
  • Integration with real measurement data might enable online model calibration without separate fitting steps.
  • The residual-minimization approach could extend to stochastic device variations for probabilistic design studies.

Load-bearing premise

Minimizing equation residuals during training produces accurate and stable solutions for highly nonlinear circuit systems without added constraints.

What would settle it

A ferroelectric memory circuit where the trained NeuroSPICE model produces waveforms that deviate substantially from measured data or from SPICE reference solutions.

Figures

Figures reproduced from arXiv: 2512.23624 by Chenming Hu, Chien-Ting Tung.

Figure 3
Figure 3. Figure 3: Unlike typical SPICE device models (for [PITH_FULL_IMAGE:figures/full_fig_p001_3.png] view at source ↗
Figure 1
Figure 1. Figure 1: The schematic diagram of NeuroSPICE. The loss function is the DAE of the circuit and the initial condition. The neural network will update its parameters to minimize loss. I.C. is the initial condition [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
read the original abstract

We present NeuroSPICE, a physics-informed neural network (PINN) framework for device and circuit simulation. Unlike conventional SPICE, which relies on time-discretized numerical solvers, NeuroSPICE leverages PINNs to solve circuit differential-algebraic equations (DAEs) by minimizing the residual of the equations through backpropagation. It models device and circuit waveforms using analytical equations in time domain with exact temporal derivatives. While PINNs do not outperform SPICE in speed or accuracy during training, they offer unique advantages such as surrogate models for design optimization and inverse problems. NeuroSPICE's flexibility enables the simulation of emerging devices, including highly nonlinear systems such as ferroelectric memories.

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 / 1 minor

Summary. The manuscript introduces NeuroSPICE, a physics-informed neural network (PINN) framework for device and circuit simulation. It solves circuit differential-algebraic equations (DAEs) by training neural networks to minimize equation residuals via backpropagation, employing analytical time-domain waveform expressions with exact auto-differentiated temporal derivatives. The approach is presented as complementary to conventional SPICE solvers, with claimed advantages for surrogate modeling in design optimization and inverse problems, particularly for highly nonlinear emerging devices such as ferroelectric memories, although the abstract notes that PINNs do not outperform SPICE in speed or accuracy.

Significance. If the residual-minimization approach can be shown to produce accurate and stable solutions for stiff nonlinear DAEs, NeuroSPICE could enable flexible surrogate models useful for optimization and inverse problems in circuit design. The framework's use of exact derivatives and analytical expressions is a methodological strength that could support reproducibility. However, the absence of any numerical results, residual norms, waveform error metrics, or direct comparisons to SPICE in the manuscript substantially weakens the assessed significance at present.

major comments (3)
  1. [Abstract] Abstract: the central claim that NeuroSPICE enables simulation of highly nonlinear systems such as ferroelectric memories rests on residual minimization alone, yet the text supplies no quantitative residual norms, waveform error metrics, or validation against a reference solver on the same device model; this leaves the mapping from low residual to physically consistent behavior unproven for stiff regimes.
  2. [Abstract] Abstract: the statement that PINNs 'do not outperform SPICE in speed or accuracy during training' is presented without supporting data or experimental setup details, making it impossible to evaluate the claimed unique advantages for surrogate models and inverse problems.
  3. [Method description] The method description: minimizing DAE residuals via backpropagation on analytical expressions is sound in principle, but for hysteretic nonlinear devices the manuscript does not address whether additional techniques (hard constraints on algebraic variables or post-training checks on held-out time intervals) are required to avoid local minima that only approximately satisfy the equations.
minor comments (1)
  1. [Abstract] The abstract would benefit from a brief statement of the specific circuit equations or device models used in the ferroelectric memory case study to ground the claims.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. The comments highlight important aspects of validation and methodological clarity that we will address in the revision. We provide point-by-point responses below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that NeuroSPICE enables simulation of highly nonlinear systems such as ferroelectric memories rests on residual minimization alone, yet the text supplies no quantitative residual norms, waveform error metrics, or validation against a reference solver on the same device model; this leaves the mapping from low residual to physically consistent behavior unproven for stiff regimes.

    Authors: We agree that quantitative evidence is necessary to substantiate the claims for stiff nonlinear regimes. In the revised manuscript, we will include residual norms, waveform error metrics, and direct comparisons against a reference SPICE solver for the ferroelectric memory example. These additions will explicitly map low residuals to physically consistent behavior. revision: yes

  2. Referee: [Abstract] Abstract: the statement that PINNs 'do not outperform SPICE in speed or accuracy during training' is presented without supporting data or experimental setup details, making it impossible to evaluate the claimed unique advantages for surrogate models and inverse problems.

    Authors: The statement reflects general observations from our development process, but we acknowledge the absence of detailed experimental data and setup in the current version. We will revise the abstract to qualify or remove the direct comparison and instead highlight the surrogate modeling and inverse problem advantages with supporting examples and metrics in the main text. revision: partial

  3. Referee: [Method description] The method description: minimizing DAE residuals via backpropagation on analytical expressions is sound in principle, but for hysteretic nonlinear devices the manuscript does not address whether additional techniques (hard constraints on algebraic variables or post-training checks on held-out time intervals) are required to avoid local minima that only approximately satisfy the equations.

    Authors: We appreciate the concern regarding local minima for hysteretic devices. The analytical expressions combined with exact derivatives and multi-start training help mitigate this, but we will add a dedicated discussion in the methods section explaining the approach for hysteretic nonlinearity. We will also include post-training checks on held-out time intervals to verify equation satisfaction beyond the training domain. revision: yes

Circularity Check

0 steps flagged

No circularity in NeuroSPICE PINN residual minimization

full rationale

The paper applies the standard PINN methodology: a neural network is trained to minimize the residual of circuit DAEs via backpropagation, with exact temporal derivatives obtained through automatic differentiation on analytical time-domain expressions. This is not self-definitional (the residual is an independent enforcement of the governing equations, not a redefinition of fitted outputs), nor a fitted-input-called-prediction. No load-bearing self-citations, uniqueness theorems, or ansatzes from prior author work are used to justify the core claim. The paper explicitly states that PINNs do not outperform SPICE in accuracy or speed and positions the method as a surrogate for optimization/inverse problems. The derivation chain is self-contained against external numerical solvers and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, invented entities, or detailed axioms beyond the standard PINN assumption that neural networks can represent solutions to differential equations.

axioms (1)
  • domain assumption Neural networks can approximate solutions to differential-algebraic equations when trained to minimize residuals
    Core premise of physics-informed neural networks invoked in the abstract description of the method.

pith-pipeline@v0.9.0 · 5409 in / 1096 out tokens · 105115 ms · 2026-05-16T19:20:11.223149+00:00 · methodology

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Reference graph

Works this paper leans on

15 extracted references · 15 canonical work pages

  1. [1]

    SPICE (Simulation Program with Integrated Circuit Emphasis),

    L. W. Nagel and D. O. Pederson, “SPICE (Simulation Program with Integrated Circuit Emphasis),” UCB/ERL M382, 1973

    work page 1973

  2. [2]

    ModSpec: An open, flexible specification framework for multi -domain device modelling,

    D. Amsallem and J. Roychowdhury, “ ModSpec: An open, flexible specification framework for multi -domain device modelling,” presented at the 2011 IEEE/ACM International Conference on Computer -Aided Design (ICCAD), Nov. 2011, pp. 367–374. doi: 10.1109/ICCAD.2011.6105356

    work page doi:10.1109/iccad.2011.6105356 2011

  3. [3]

    A Unified Memristor Compact Model for RRAM, FERAM/FTJ, and MRAM,

    C. -T. Tung, “A Unified Memristor Compact Model for RRAM, FERAM/FTJ, and MRAM,” IEEE Trans. Electron Devices , pp. 1–8, 2025, doi: 10.1109/TED.2025.3633652

    work page doi:10.1109/ted.2025.3633652 2025

  4. [4]

    Rapid Simulation of Photonic Integrated Circuits Using Verilog -A Compact Models,

    M. J. Shawon and V. Saxena, “ Rapid Simulation of Photonic Integrated Circuits Using Verilog -A Compact Models,” IEEE Trans. Circuits Syst. Regul. Pap. , vol. 67, no. 10, pp. 3331 – 3341, Oct. 2020, doi: 10.1109/TCSI.2020.2983303

    work page doi:10.1109/tcsi.2020.2983303 2020

  5. [5]

    Analytical Modeling of Tunnel-Junction Transistor Lasers,

    C. -T. Tung, H. -Y. Lin, S. -W. Chang, and C. -H. Wu, “Analytical Modeling of Tunnel-Junction Transistor Lasers,” IEEE J. Sel. Top. Quantum Electron. , vol. 28, no. 1: Semiconductor Lasers, pp. 1–8, Feb. 2022, doi: 10.1109/JSTQE.2021.3090527

    work page doi:10.1109/jstqe.2021.3090527 2022

  6. [6]

    Primer: Fast private transformer inference on encrypted data

    Z. Liu et al., “DeepOHeat: Operator Learning -based Ultra- fast Thermal Simulation in 3D -IC Design,” in 2023 60th ACM/IEEE Design Automation Conference (DAC) , July 2023, pp. 1 –6. doi: 10.1109/DAC56929.2023.10247998

    work page doi:10.1109/dac56929.2023.10247998 2023

  7. [7]

    Raissi, P

    M. Raissi, P. Perdikaris, and G. E. Karniadakis, “Physics - informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,” J. Comput. Phys. , vol. 378, pp. 686 –707, Feb. 2019, doi: https://doi.org/10.1016/j.jcp.2018.10.045

    work page doi:10.1016/j.jcp.2018.10.045 2019

  8. [8]

    PINNSim: A simulator for power system dynamics based on Physics -Informed Neural Networks,

    J. Stiasny, B. Zhang, and S. Chatzivasileiadis, “PINNSim: A simulator for power system dynamics based on Physics -Informed Neural Networks,” Electr. Power Syst. Res., vol. 235, p. 110796, Oct. 2024, doi: https://doi.org/10.1016/j.epsr.2024.110796

    work page doi:10.1016/j.epsr.2024.110796 2024

  9. [9]

    DAE -PINN: a physics -informed neural network model for simulating differential algebraic equations with application to power networks,

    C. Moya and G. Lin, “DAE -PINN: a physics -informed neural network model for simulating differential algebraic equations with application to power networks,” Neural Comput. Appl. , vol. 35, no. 5, pp. 3789–3804, Feb. 2023, doi: 10.1007/s00521-022-07886-y

    work page doi:10.1007/s00521-022-07886-y 2023

  10. [10]

    A Novel Neural -Network Device Modeling Based on Physics -Informed Machine Learning,

    B. Kim and M. Shin, “A Novel Neural -Network Device Modeling Based on Physics -Informed Machine Learning,” IEEE Trans. Electron Devices , vol. 70, no. 11, pp. 6021 –6025, 2023, doi: 10.1109/TED.2023.3316635

    work page doi:10.1109/ted.2023.3316635 2023

  11. [11]

    BSIM-CMG: Standard FinFET compact model for advanced circuit design,

    J. P. Duarte et al., “BSIM-CMG: Standard FinFET compact model for advanced circuit design,” presented at the ESSCIRC Conference 2015 - 41st European Solid -State Circuits Conference (ESSCIRC), Sept. 2015, pp. 196 –201. doi: 10.1109/ESSCIRC.2015.7313862

    work page doi:10.1109/esscirc.2015.7313862 2015

  12. [12]

    Compact Modeling of Emerging IC Devices for Technology -Design Co -development,

    G. Pahwa et al. , “Compact Modeling of Emerging IC Devices for Technology -Design Co -development,” presented at the 2022 International Electron Devices Meeting (IEDM), Dec. 2022, p. 8.1.1-8.1.4. doi: 10.1109/IEDM45625.2022.10019433

    work page doi:10.1109/iedm45625.2022.10019433 2022

  13. [13]

    Automatic differentiation in pytorch,

    A. Paszke et al. , “Automatic differentiation in pytorch,” 2017

    work page 2017

  14. [14]

    Self-adaptive loss balanced Physics -informed neural networks,

    Z. Xiang, W. Peng, X. Liu, and W. Yao, “Self-adaptive loss balanced Physics -informed neural networks,” Neurocomputing, vol. 496, pp. 11 –34, July 2022, doi: 4 https://doi.org/10.1016/j.neucom.2022.05.015

    work page doi:10.1016/j.neucom.2022.05.015 2022

  15. [15]

    On the anomalous absorption of sound near a second order phase transition point,

    L. D. Landau and I. M. Khalatnikov, “On the anomalous absorption of sound near a second order phase transition point,” Dokl Akad Nauk., vol. 96, pp. 469–472, May 1954

    work page 1954