Data driven modelling of complex dynamical systems has recently become a popular approach with many scientific applications. One prominent algorithm for such modelling based on observations is the dynamical mode decomposition (DMD), which has a solid theoretical foundation based on the celebrated Koopman operator theory. Despite the large empirical evidence for the usefulness of DMD, it has two inherent shortcomings that significantly limit its applicability: (i) sensitivity to noise, and (ii) degraded performance when the number of observations is small.
In our work, we propose a method that attempts to alleviate these shortcomings. Our method is based on phase alignment that facilitates an appropriate data augmentation. In addition, our method consists of a new metric that approximates the augmentation error, which in turn is used for determining the most informative DMD components. We demonstrate the performance of the proposed method in applications to synthetic data and to real recordings from a Brain Computer Interface (BCI) task.
is supervised by Ronen Talmon Working in SIPL, Electrical Engineering faculty, Technion. His research focuses on the field of data driven modelling of complicated systems usingDynamical Mode Decomposition and Koopman theory. Aviad received BSc. in Electrical Engineering from the Technion, 2010. He did military service in the IDF, 2010-2017.
M.Sc. student under the supervision of Professor Ronen Talmon.
Online Zoom meeting link: https://technion.zoom.us/j/948