Physics-Informed Neural Networks (PINNs) for Solving Maxwell's Equations in Heterogeneous Media with Absorbing Sources and Boundaries

This study validates physics-informed neural networks (PINNs) for complex electromagnetic simulation, solving Maxwell's equations in heterogeneous media with metric V/m accuracy. Eliminating numerical dispersion and overcoming the Courant stability limit, the proposed solver allows stable simulations with a CFL factor of 1.2 and offers a 10-fold reduction in computation time for high-complexity domains. Automatic differentiation ensures strict adherence to Gaussian law and energy conservation (0.4% deviation). In gradient-index media (variation from 1 to 12), the model faithfully captures phase compression and ohmic dissipation reaching 0.018 J. The framework minimizes Maxwell's equations in strong form, computing curls via the Jacobian matrix for mesh-independent accuracy. The Silver-Müller boundary condition ensures wave absorption with a residual reflection below -45 dB, while tangential continuity is imposed as a jump constraint. Combined Adam/L-BFGS optimization achieves convergence in 100 epochs. For a 0.12 S/m conductivity, the PINN predicts field attenuation conforming to Beer-Lambert's law. Unlike grid methods, it maintains a near-constant inference time (~10 s). Representing 65% of the learning weight, physics-based regularization delivers a completely mesh-free electromagnetic solver, eliminating long-distance phase errors and ensuring perfect correlation with exact solutions.