Low-Rank Dynamic Mode Decomposition using Riemannian Manifold Optimization

Palash Sashittal, Daniel J Bodony

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2265-2270
Number of pages6
ISBN (Electronic)9781538613955
DOIs
StatePublished - Jan 18 2019
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: Dec 17 2018Dec 19 2018

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2018-December
ISSN (Print)0743-1546

Conference

Conference57th IEEE Conference on Decision and Control, CDC 2018
CountryUnited States
CityMiami
Period12/17/1812/19/18

Fingerprint

Riemannian Manifold
Decomposition
Decompose
Optimization
Optimization Problem
Reduced-order Modeling
Subspace Methods
Complex Ginzburg-Landau Equation
Nonconvex Optimization
Nonconvex Problems
Projection Method
Data-driven
Fluid Flow
Flow of fluids
Dynamical systems
High-dimensional
Optimal Solution
Dynamical system
Unstable
Evaluate

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Sashittal, P., & Bodony, D. J. (2019). Low-Rank Dynamic Mode Decomposition using Riemannian Manifold Optimization. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 2265-2270). [8619400] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2018.8619400

Low-Rank Dynamic Mode Decomposition using Riemannian Manifold Optimization. / Sashittal, Palash; Bodony, Daniel J.

2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. p. 2265-2270 8619400 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Sashittal, P & Bodony, DJ 2019, Low-Rank Dynamic Mode Decomposition using Riemannian Manifold Optimization. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8619400, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers Inc., pp. 2265-2270, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 12/17/18. https://doi.org/10.1109/CDC.2018.8619400
Sashittal P, Bodony DJ. Low-Rank Dynamic Mode Decomposition using Riemannian Manifold Optimization. In 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc. 2019. p. 2265-2270. 8619400. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2018.8619400
Sashittal, Palash ; Bodony, Daniel J. / Low-Rank Dynamic Mode Decomposition using Riemannian Manifold Optimization. 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 2265-2270 (Proceedings of the IEEE Conference on Decision and Control).
@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}",
year = "2019",
month = "1",
day = "18",
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",

}

TY - GEN

T1 - Low-Rank Dynamic Mode Decomposition using Riemannian Manifold Optimization

AU - Sashittal, Palash

AU - Bodony, Daniel J

PY - 2019/1/18

Y1 - 2019/1/18

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85062189547&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85062189547&partnerID=8YFLogxK

U2 - 10.1109/CDC.2018.8619400

DO - 10.1109/CDC.2018.8619400

M3 - Conference contribution

AN - SCOPUS:85062189547

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 2265

EP - 2270

BT - 2018 IEEE Conference on Decision and Control, CDC 2018

PB - Institute of Electrical and Electronics Engineers Inc.

ER -