On-the-Fly Dynamic Mode Decomposition for Rapid Time-Extrapolation and Analysis of Cavity Resonances

The application of time-domain solvers for characterizing high-quality (
$Q$
) factor electromagnetic (EM) cavities enables the acquisition of broadband data from a single run, and thus, provides effective discovery of multiple frequency resonances. However, the need for sharp frequency resolution requires a very large number of time steps, and hence, computation time. Time-extrapolation techniques based on reduced-order models (ROMs), such as dynamic mode decomposition (DMD) can be used not only to reduce the computation time but also to provide additional physical insights for diagnostic purposes. In this work, we present a data-driven ROM based on Hankel-DMD for rapid analysis and extrapolation of time-domain EM responses in resonant cavities. High-fidelity training data are obtained from the partial (short-time) finite-difference time-domain (FDTD) simulations. We apply the Hankel-DMD algorithm on the FDTD data to extract the underlying key spatial (DMD modes) and temporal (DMD frequencies) features to build an accurate reduced-order predictive model. We then use the ROM to forecast the cavity electric field at any time instant with a very small computation cost. Since FDTD data are used for DMD training, we also devise an on-the-fly sliding-window DMD method to optimize data acquisition and automate the handoff from the FDTD simulation to the DMD algorithm.