Physics-Informed Neural Networks for Electrical Circuit Analysis: Applications in Dielectric Material Modeling

Abstract: Scientific machine learning (SciML) represents a significant advancement in integrating ML with scientific methodologies. At the forefront of this development are Physics-Informed Neural Networks (PINNs), which offer a promising approach by incorporating physical laws directly into the learning process, thereby reducing the need for extensive datasets. However, when data is limited or the system becomes more complex, PINNs can face challenges, such as instability and difficulty in accurately fitting the training data. In this article, we explore the capabilities and limitations of the DeepXDE framework, a tool specifically designed for implementing PINNs, in addressing both forward and inverse problems related to dielectric properties. Using RC circuit models to represent dielectric materials in HVDC systems, we demonstrate the effectiveness of PINNs in analyzing and improving system performance. Additionally, we show that applying a logarithmic transformation to the current (ln(I)) significantly enhances the stability and accuracy of PINN predictions, especially in challenging scenarios with sparse data or complex models. In inverse mode, however, we faced challenges in estimating key system parameters, such as resistance and capacitance, in more complex scenarios with longer time domains. This highlights the potential for future work in improving PINNs through transformations or other methods to enhance performance in inverse problems. This article provides pedagogical insights for those looking to use PINNs in both forward and inverse modes, particularly within the DeepXDE framework.