Dynamic mode decomposition with optimal amplitude and time-delay embedding for reconstruction and prediction of local measurements

To enhance the applicability of dynamic mode decomposition with time-delay embedding (DMD-TD) and reduce its computational complexity and memory requirements, a new algorithm called dynamic mode decomposition with optimal amplitude and time-delay embedding (DMD-OA-TD) was introduced. This algorithm computes the mode amplitudes of DMD-TD by a least-squares optimization algorithm, which reduces the number of time-delay step, n, and improves the overall efficiency. The performance of DMD-TD and DMD-OA-TD is compared using fabricated pattern data with and without white Gaussian noise, as well as the local measurement data obtained from the cavity and the rearview mirror. The results show that DMD-OA-TD provided a shorter computation time and lower memory requirements than DMD-TD. For example, when RMS < 0.057 and the truncation number is 30, the computation time and n for DMD-TD are 3.8 times and 6.8 times greater than that of DMD-OA-TD, respectively.