×

zbMATH — the first resource for mathematics

Optimized sampling for multiscale dynamics. (English) Zbl 07033871
MSC:
65T99 Numerical methods in Fourier analysis
37M10 Time series analysis of dynamical systems
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
62K99 Design of statistical experiments
Software:
CoSaMP; CVX; SPGL1
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] T. Askham and J. N. Kutz, Variable projection methods for an optimized dynamic mode decomposition, SIAM J. Appl. Dyn. Systems, 17 (2018), pp. 380–416. · Zbl 1384.37122
[2] Z. Bai, S. L. Brunton, B. W. Brunton, J. N. Kutz, E. Kaiser, A. Spohn, and B. R. Noack, Data-driven methods in fluid dynamics: Sparse classification from experimental data, in Whither Turbulence and Big Data in the 21st Century, Springer, Cham, Switzerland, 2015, pp. 323–342.
[3] R. G. Baraniuk, Compressive sensing, IEEE Signal Process. Mag., 24 (2007), pp. 118–120.
[4] M. Barrault, Y. Maday, N. C. Nguyen, and A. T. Patera, An ‘empirical interpolation’ method: Application to efficient reduced-basis discretization of partial differential equations, C. R. Math., 339 (2004), pp. 667–672. · Zbl 1061.65118
[5] P. Benner, S. Gugercin, and K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems, SIAM Rev., 57 (2015), pp. 483–531. · Zbl 1339.37089
[6] D. A. Bistrian and I. M. Navon, Randomized dynamic mode decomposition for nonintrusive reduced order modelling, Internat. J. Numer. Methods Engrg., (2017).
[7] S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, Cambridge, 2004. · Zbl 1058.90049
[8] I. Bright, G. Lin, and J. N. Kutz, Compressive sensing and machine learning strategies for characterizing the flow around a cylinder with limited pressure measurements, Phys. Fluids, 25 (2013), 127102. · Zbl 1320.76003
[9] B. W. Brunton, L. A. Johnson, J. G. Ojemann, and J. N. Kutz, Extracting spatial–temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition, J. Neurosci. Methods, 258 (2016), pp. 1–15.
[10] S. L. Brunton, J. L. Proctor, J. H. Tu, and J. N. Kutz, Compressed sensing and dynamic mode decomposition, J. Comput. Dyn., 2 (2015), pp. 165–191. · Zbl 1347.94012
[11] S. L. Brunton, J. H. Tu, I. Bright, and J. N. Kutz, Compressive sensing and low-rank libraries for classification of bifurcation regimes in nonlinear dynamical systems, SIAM J. Appl. Dyn. Syst., 13 (2014), pp. 1716–1732. · Zbl 1354.37078
[12] M. Budišić, R. Mohr, and I. Mezić, Applied Koopmanism, Chaos, 22 (2012), 047510.
[13] P. Businger and G. H. Golub, Linear least squares solutions by Householder transformations, Numer. Math., 7 (1965), pp. 269–276. · Zbl 0142.11503
[14] E. J. Candès, J. Romberg, and T. Tao, Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information, IEEE Trans. Inform. Theory, 52 (2006), pp. 489–509. · Zbl 1231.94017
[15] S. Chaturantabut and D. C. Sorensen, Nonlinear model reduction via discrete empirical interpolation, SIAM J. Sci. Comput., 32 (2010), pp. 2737–2764. · Zbl 1217.65169
[16] I. Daubechies, Ten Lectures on Wavelets, CBMS-NSF Regional Conf. Ser. in Appl. Math. 61, SIAM, Philadelphia, 1992.
[17] S. T. Dawson, M. S. Hemati, M. O. Williams, and C. W. Rowley, Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition, Exp. Fluids, 57 (2016), 42.
[18] L. Debnath, Wavelet Transforms and their Applications, Birkhäuser, Boston, 2002. · Zbl 1019.94003
[19] D. L. Donoho, Compressed sensing, IEEE Trans. Inform. Theory, 52 (2006), pp. 1289–1306. · Zbl 1288.94016
[20] Z. Drmač and S. Gugercin, A new selection operator for the discrete empirical interpolation method—improved a priori error bound and extensions, SIAM J. Sci. Comput., 38 (2016), pp. A631–A648.
[21] N. B. Erichson, S. L. Brunton, and J. N. Kutz, Randomized Dynamic Mode Decomposition, preprint, (2017).
[22] R. Everson and L. Sirovich, Karhunen–Loève procedure for gappy data, J. Opt. Soc. Amer., 12 (1995), pp. 1657–1664.
[23] M. Grant, S. Boyd, and Y. Ye, CVX: MATLAB Software for Disciplined Convex Programming, (2008).
[24] J.-H. Han and I. Lee, Optimal placement of piezoelectric sensors and actuators for vibration control of a composite plate using genetic algorithms, Smart Mater. Struct., 8 (1999), pp. 257–268.
[25] M. S. Hemati, C. W. Rowley, E. A. Deem, and L. N. Cattafesta, De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets, Theoret. Comput. Fluid Dyn., 31 (2017), pp. 349–368.
[26] M. S. Hemati, M. O. Williams, and C. W. Rowley, Dynamic mode decomposition for large and streaming datasets, Phys. Fluids, 26 (2014), 111701.
[27] S. Joshi and S. Boyd, Sensor selection via convex optimization, IEEE Trans. Signal Process., 57 (2009), pp. 451–462. · Zbl 1391.90679
[28] M. R. Jovanović, P. J. Schmid, and J. W. Nichols, Sparsity-promoting dynamic mode decomposition, Phys. Fluids, 26 (2014), 024103.
[29] E. Kaiser, M. Morzyński, G. Daviller, J. N. Kutz, B. W. Brunton, and S. L. Brunton, Sparsity enabled cluster reduced-order models for control, J. Comput. Phys., 352 (2018), pp. 388–409. · Zbl 1375.76075
[30] B. Koopman and J. v. Neumann, Dynamical systems of continuous spectra, Proc. Natl. Acad. Sci. USA, 18 (1932), pp. 255–263. · Zbl 0006.22702
[31] B. O. Koopman, Hamiltonian systems and transformation in Hilbert space, Proc. Natl. Acad. Sci. USA, 17 (1931), pp. 315–318. · JFM 57.1010.02
[32] B. Kramer, P. Grover, P. Boufounos, S. Nabi, and M. Benosman, Sparse sensing and DMD-based identification of flow regimes and bifurcations in complex flows, SIAM J. Appl. Dyn. Syst., 16 (2017), pp. 1164–1196. · Zbl 1373.37185
[33] A. Krause, A. Singh, and C. Guestrin, Near-optimal sensor placements in Gaussian processes: Theory, efficient algorithms and empirical studies, J. Mach. Learn. Res., 9 (2008), pp. 235–284. · Zbl 1225.68192
[34] J. N. Kutz, Data-Driven Modeling & Scientific Computation: Methods for Complex Systems & Big Data, Oxford University Press, Oxford, 2013. · Zbl 1280.65002
[35] J. N. Kutz, S. L. Brunton, B. W. Brunton, and J. L. Proctor, Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems, SIAM, Philadelphia, 2016. · Zbl 1365.65009
[36] J. N. Kutz, X. Fu, and S. L. Brunton, Multiresolution dynamic mode decomposition, SIAM J. Appl. Dyn. Syst., 15 (2016), pp. 713–735. · Zbl 1338.37121
[37] J. N. Kutz, X. Fu, S. L. Brunton, and N. B. Erichson, Multi-resolution dynamic mode decomposition for foreground/background separation and object tracking, in 2015 IEEE International Conference on Computer Vision Workshop (ICCVW), IEEE Computer Society, Los Alamitos, CA, 2015, pp. 921–929.
[38] K. Manohar, B. W. Brunton, J. N. Kutz, and S. L. Brunton, Data-driven sparse sensor placement for reconstruction: Demonstrating the benefits of exploiting known patterns, IEEE Control Syst. Mag., 38 (2018), pp. 63–86.
[39] K. Manohar, S. L. Brunton, and J. N. Kutz, Environment identification in flight using sparse approximation of wing strain, J. Fluids Struct., 70 (2017), pp. 162–180.
[40] K. Manohar, E. Kaiser, S. L. Brunton, and J. N. Kutz, Code supplement to optimized sampling for multiscale dynamics’, (2019).
[41] A. G. Nair and K. Taira, Network-theoretic approach to sparsified discrete vortex dynamics, J. Fluid Mech., 768 (2015), pp. 549–571.
[42] D. Needell and J. A. Tropp, CoSaMP: Iterative signal recovery from incomplete and inaccurate samples, Commun. ACM, 53 (2010), pp. 93–100.
[43] S. D. Pendergrass, J. N. Kutz, and S. L. Brunton, Streaming GPU Singular Value and Dynamic Mode Decompositions, preprint, , 2016.
[44] J. L. Proctor, S. L. Brunton, and J. N. Kutz, Dynamic mode decomposition with control, SIAM J. Appl. Dyn. Syst., 15 (2016), pp. 142–161. · Zbl 1334.65199
[45] C. W. Rowley, I. Mezić, S. Bagheri, P. Schlatter, and D. Henningson, Spectral analysis of nonlinear flows, J. Fluid Mech., 645 (2009), pp. 115–127. · Zbl 1183.76833
[46] P. J. Schmid, Dynamic mode decomposition of numerical and experimental data, J. Fluid Mech., 656 (2010), pp. 5–28. · Zbl 1197.76091
[47] P. Seshadri, A. Narayan, and S. Mahadevan, Effectively subsampled quadratures for least squares polynomial approximations, SIAM/ASA J. Uncertain. Quantif., 5 (2017), pp. 1003–1023. · Zbl 1384.93159
[48] A. Sommariva and M. Vianello, Computing approximate Fekete points by QR factorizations of Vandermonde matrices, Comput. Math. Appl., 57 (2009), pp. 1324–1336. · Zbl 1186.65028
[49] J. A. Tropp and A. C. Gilbert, Signal recovery from random measurements via orthogonal matching pursuit, IEEE Trans. Inform. Theory, 53 (2007), pp. 4655–4666. · Zbl 1288.94022
[50] J. H. Tu, C. W. Rowley, J. N. Kutz, and J. K. Shang, Spectral analysis of fluid flows using sub-Nyquist-rate PIV data, Exp. Fluids, 55 (2014), pp. 1–13.
[51] J. H. Tu, C. W. Rowley, D. M. Luchtenburg, S. L. Brunton, and J. N. Kutz, On dynamic mode decomposition: Theory and applications, J. Comput. Dyn., 1 (2014), pp. 391–421. · Zbl 1346.37064
[52] E. van den Berg and M. P. Friedlander, SPGL1: A Solver for Large-Scale Sparse Reconstruction, (2007).
[53] E. van den Berg and M. P. Friedlander, Probing the Pareto frontier for basis pursuit solutions, SIAM J. Sci. Comput., 31 (2009), pp. 890–912. · Zbl 1193.49033
[54] K. Willcox, Unsteady flow sensing and estimation via the gappy proper orthogonal decomposition, Comput. Fluids, 35 (2006), pp. 208–226. · Zbl 1160.76394
[55] M. O. Williams, I. G. Kevrekidis, and C. W. Rowley, A data–driven approximation of the Koopman operator: Extending dynamic mode decomposition, J. Nonlinear Sci., 25 (2015), pp. 1307–1346. · Zbl 1329.65310
[56] M. O. Williams, C. W. Rowley, and I. G. Kevrekidis, A kernel-based method for data-driven Koopman spectral analysis, J. Comput. Dyn., 2 (2015), pp. 247–265. · Zbl 1366.37144
[57] J. Wright, A. Yang, A. Ganesh, S. Sastry, and Y. Ma, Robust face recognition via sparse representation, IEEE Trans. Pattern Anal. Mach. Intell., 31 (2009), pp. 210–227.
[58] B. Yildirim, C. Chryssostomidis, and G. E. Karniadakis, Efficient sensor placement for ocean measurements using low-dimensional concepts, Ocean Model., 27 (2009), pp. 160–173.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.