@inproceedings{fad231932203493baafc545ca74c897d,
title = "Low-Rank Dynamic Mode Decomposition using Riemannian Manifold Optimization",
abstract = "We present a method for non-intrusive data-driven reduced order modeling of high-dimensional dynamical systems using a new low-rank extension of Dynamic Mode Decomposition (DMD). A matrix optimization problem with a rank-constraint on the solution is formulated and results in a non-convex optimization problem. We propose two methods to solve the optimization problem. The first is an iterative subspace projection method that is computationally efficient but can only give the optimal solution under certain conditions. In the second method we perform Riemannian optimization on Grassmanian manifolds. Using a model equation for fluid flows, we evaluate the performance of the proposed methods on complex linearized Ginzburg-Landau equations in the supercritical globally unstable regime.",
author = "Palash Sashittal and Bodony, {Daniel J.}",
note = "This work was sponsored by the Office of Naval Research (ONR) as part of the Multidisciplinary University Research Initiatives (MURI) Program, under grant number N00014-16-1-2617. The views and conclusions contained herein are those of the authors only and should not be interpreted as representing those of ONR, the U.S. Navy or the U.S. Government.; 57th IEEE Conference on Decision and Control, CDC 2018 ; Conference date: 17-12-2018 Through 19-12-2018",
year = "2018",
month = jul,
day = "2",
doi = "10.1109/CDC.2018.8619400",
language = "English (US)",
series = "Proceedings of the IEEE Conference on Decision and Control",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "2265--2270",
booktitle = "2018 IEEE Conference on Decision and Control, CDC 2018",
address = "United States",
}