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Title: On Computation of Koopman Operator from Sparse Data

Abstract

In this paper, we propose a novel approach to compute the Koopman operator from sparse time series data. In recent years there has a considerable interest in operator theoretic methods for data-driven analysis of dynamical systems and existing techniques for the approximation of the Koopman operator require rich enough data-sets. However, in many applications, the data set may not be rich enough to approximate the operators to acceptable limits. In this paper, using ideas from robust optimization, we propose an algorithm to compute the Koopman operator from sparse data. In particular, we enrich the sparse data set with artificial data points and use robust optimization techniques to obtain the transfer operator. We illustrate the efficiency of our proposed approach in three different dynamical systems, namely, a linear system, a nonlinear system and a dynamical system governed by a partial differential equation.

Authors:
 [1];  [2];  [3]
  1. BATTELLE (PACIFIC NW LAB)
  2. Iowa State University
  3. University of California, Santa Barbara
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1583163
Report Number(s):
PNNL-SA-138365
DOE Contract Number:  
AC05-76RL01830
Resource Type:
Conference
Resource Relation:
Conference: American Control Conference (ACC 2019), July 10-12, 2019, Philadephia, PA
Country of Publication:
United States
Language:
English

Citation Formats

Sinha, Subhrajit, Vaidya, Umesh, and Yeung, Enoch. On Computation of Koopman Operator from Sparse Data. United States: N. p., 2019. Web. doi:10.23919/ACC.2019.8814861.
Sinha, Subhrajit, Vaidya, Umesh, & Yeung, Enoch. On Computation of Koopman Operator from Sparse Data. United States. doi:10.23919/ACC.2019.8814861.
Sinha, Subhrajit, Vaidya, Umesh, and Yeung, Enoch. Wed . "On Computation of Koopman Operator from Sparse Data". United States. doi:10.23919/ACC.2019.8814861.
@article{osti_1583163,
title = {On Computation of Koopman Operator from Sparse Data},
author = {Sinha, Subhrajit and Vaidya, Umesh and Yeung, Enoch},
abstractNote = {In this paper, we propose a novel approach to compute the Koopman operator from sparse time series data. In recent years there has a considerable interest in operator theoretic methods for data-driven analysis of dynamical systems and existing techniques for the approximation of the Koopman operator require rich enough data-sets. However, in many applications, the data set may not be rich enough to approximate the operators to acceptable limits. In this paper, using ideas from robust optimization, we propose an algorithm to compute the Koopman operator from sparse data. In particular, we enrich the sparse data set with artificial data points and use robust optimization techniques to obtain the transfer operator. We illustrate the efficiency of our proposed approach in three different dynamical systems, namely, a linear system, a nonlinear system and a dynamical system governed by a partial differential equation.},
doi = {10.23919/ACC.2019.8814861},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2019},
month = {7}
}

Conference:
Other availability
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