Optimizing FDTD EM Boundary Conditions

Boundary conditions are critical in electromagnetic (EM) wave propagation simulations, ensuring that finite computational domains accurately replicate unbounded or infinite environments. This paper presents an automatic differentiation (AD) approach to optimize sponge boundary conditions for finitedifference time-domain (FDTD) methods. By formulating the damping profile as learnable parameters and integrating the forward modeling within a computational graph, our method directly minimizes the mismatch between a reference extendeddomain simulation and a smaller computational domain with absorbing boundaries. Numerical experiments demonstrate that the proposed approach achieves significantly better suppression of boundary reflections compared to standard absorbing boundary conditions (ABCs), performing on par with or exceeding Perfectly Matched Layer (PML) implementations yet offering a straightforward and automated route to parameter tuning. Evaluation on complex layered media further underscores the capability of this novel sponge boundary condition to deliver high-fidelity wavefield simulations in realistic, heterogeneous models.