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

TL;DR

The paper addresses inverse modeling of dielectric response (DR) in the time domain to estimate parameters of a parallel RC equivalent circuit from current measurements. It uses physics-informed neural networks (PINNs) that embed ECM dynamics into the learning process, with a temperature-subnetwork to capture Arrhenius-type resistance changes; training enforces both data fidelity and governing equations. On synthetic data with Gaussian noise, PINNs accurately recover up to five RC parameters and, in a temperature-enabled case, recover embedded nonlinear resistances across multiple temperatures. The approach is computationally efficient, scalable to simple architectures, and offers a path toward applying DR analysis to experimental data and to more complex ECM representations or frequency-domain problems.

Abstract

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.

Figures (5)

• Figure 1: A schematic representation of inverse modeling of DR in time domain using PINNs.
• Figure 2: PINN-predicted dielectric response for an ECM comprising one steady-state branch and two RC branches, trained on synthetic data with added Gaussian noise $\mathcal{N}(0,0.2^2)$.
• Figure 3: Convergence of estimated circuit parameters during training for five-parameter ECM with added Gaussian noise $\mathcal{N}(0,0.2^2)$.
• Figure 4: PINN-predicted DR across varying temperatures (294–324 K) for an ECM with one steady-state and one polarization branch. Results shown correspond to synthetic data with added Gaussian noise $\mathcal{N}(0,(0.4/I)^2)$.
• Figure 5: Learned functional approximations for $\hat{R}_0(T)$ and scaled $\hat{R}_1(T)$ with added Gaussian noise $\mathcal{N}(0,(0.4/I)^2).$