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

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.

@article{esenov2025_2505.02258,
  title={ Inverse Modeling of Dielectric Response in Time Domain using Physics-Informed Neural Networks },
  author={ Emir Esenov and Olof Hjortstam and Yuriy Serdyuk and Thomas Hammarström and Christian Häger },
  journal={arXiv preprint arXiv:2505.02258},
  year={ 2025 }
}