A Data-Driven Implementation of Field Constitutive Relations for the FDTD Simulation of Dispersive Media

This paper introduces a novel data-driven framework for modeling dispersive media with the Finite-Difference Time-Domain (FDTD) method. Instead of employing the standard Auxiliary Differential Equation or Recursive Convolution methods to model dispersive material properties, we propose a pre-trained regression model that is scalable with respect to the type and order of the dispersion. By directly learning the mapping between the electric/magnetic flux density vectors and the electric/magnetic field vectors, this approach eliminates the need for multiple auxiliary variables or for recursive convolutions. Importantly, training is completed with 1-D cavity simulations, hence it is computationally efficient. Since the model learns temporal dispersion relations, it can be used in 2/3-D simulations once it is trained. We demonstrate this idea by coupling the regression model with FDTD for the modeling of wave propagation in a six-pole Debye medium.