A Physics-Informed Neural Network Approach to Modeling Dielectric Response Data

Journal article, 2026

This paper presents a physics-informed neural network (PINN) framework for parameter extraction and modeling of dielectric response (DR) data in the frequency domain. The method embeds the governing equations of the polarization relaxation model along with initial conditions directly into the training loss of a neural network, enabling joint estimation of permittivity, DC conductivity and relaxation times. The PINN accurately recovers all parameters from supplied synthetic data, including cases with multiple polarization processes and DC conductivity under significant Gaussian noise, and remains robust due to the regularizing effect of the physics-based loss terms. The approach requires minimal hyperparameter tuning, small network architectures, and achieves rapid convergence on standard hardware. To extend the framework, we introduce dedicated subnetworks that capture functional dependencies of material parameters on external variables. Applied to experimental data from polypropylene–meso-erythritol compounds, the model learns smooth and physically consistent dependencies of the DR on filler concentration and is able to extrapolate beyond the measured frequency range by enforcing the governing physics at collocation points. While discrepancies emerge at higher additive concentrations, particularly overly sharp dissipation peaks, indicating the need of utilizing more flexible dielectric relaxation models for implementing physical constrains. Overall, the results demonstrate that PINNs provide a practical, interpretable, and flexible tool for DR analysis and materials characterization.