arXiv:2505.02258eess.SYcs.LG2025-05被引 2

用物理神经网络反推绝缘材料的介电响应参数,精度高且需求少。

Inverse Modeling of Dielectric Response in Time Domain using Physics-Informed Neural Networks

  • 用物理约束的神经网络反解时间域介电响应,基于并联RC电路模型
  • 可准确恢复最多5个未知电路参数,对噪声有强鲁棒性
  • 适合高压设备绝缘设计,也适用于温度依赖性建模

绝缘材料的介电响应是设计高压电气绝缘系统和确定安全运行条件的关键输入。由于不同极化与导电过程在不同时间尺度上发生,原始测量数据难以物理解读。通常采用等效电路模型(ECMs)简化系统复杂性,用若干电路元件表征主导响应。本文研究利用物理信息神经网络(PINNs)对时间域介电响应进行逆向建模,基于并联RC电路。为评估性能,我们在从对应ECM解析解生成的合成数据上测试,加入高斯噪声模拟测量误差。结果表明,PINNs在良好条件下的逆问题中表现优异,仅需少量网络规模、训练时长与超参数调优即可准确估计最多五个未知RC参数。此外,我们扩展了ECM以包含温度依赖性,证明PINNs能从多温点噪声数据中准确恢复嵌入的非线性温度函数。该研究为依赖等效电路模型的领域提供了基于机器学习的科学计算新方案。

原文摘要 · Abstract (English)

Dielectric response (DR) of insulating materials is key input information for designing electrical insulation systems and defining safe operating conditions of various HV devices. In dielectric materials, different polarization and conduction processes occur at different time scales, making it challenging to physically interpret raw measured data. To analyze DR measurement results, equivalent circuit models (ECMs) are commonly used, reducing the complexity of the physical system to a number of circuit elements that capture the dominant response. This paper examines the use of physics-informed neural networks (PINNs) for inverse modeling of DR in time domain using parallel RC circuits. To assess their performance, we test PINNs on synthetic data generated from analytical solutions of corresponding ECMs, incorporating Gaussian noise to simulate measurement errors. Our results show that PINNs are highly effective at solving well-conditioned inverse problems, accurately estimating up to five unknown RC parameters with minimal requirements on neural network size, training duration, and hyperparameter tuning. Furthermore, we extend the ECMs to incorporate temperature dependence and demonstrate that PINNs can accurately recover embedded, nonlinear temperature functions from noisy DR data sampled at different temperatures. This case study in modeling DR in time domain presents a solution with wide-ranging potential applications in disciplines relying on ECMs, utilizing the latest technology in machine learning for scientific computation.

介电响应神经网络物理模型逆问题

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