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 datadriven analysis of dynamical systems and existing techniques for the approximation of the Koopman operator require rich enough datasets. 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:

 BATTELLE (PACIFIC NW LAB)
 Iowa State University
 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):
 PNNLSA138365
 DOE Contract Number:
 AC0576RL01830
 Resource Type:
 Conference
 Resource Relation:
 Conference: American Control Conference (ACC 2019), July 1012, 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 datadriven analysis of dynamical systems and existing techniques for the approximation of the Koopman operator require rich enough datasets. 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}
}