Fetching the paper…
Reading the bibliography…
Time-delay embeddings and dimensionality reduction are powerful techniques for discovering effective coordinate systems to represent the dynamics of physical systems.
B. O. Koopman, “Hamiltonian systems and transformation in Hilbert space,”
1931
Earlier work this paper cites.
M. Abramowitz and I. A. Stegun,
1948
Earlier work this paper cites.
E. N. Lorenz, “Deterministic nonperiodic flow,”
1963
Earlier work this paper cites.
M. D. Spivak,
1970
Earlier work this paper cites.
G. H. Golub and C. Reinsch, “Singular value decomposition and least squares solutions,” in
1971
Earlier work this paper cites.
W. P. London and J. A. Yorke, “Recurrent outbreaks of measles, chickenpox and mumps: I. seasonal variation in contact rates,”
1973
Earlier work this paper cites.
M. Pilté, S. Bonnabel, and F. Barbaresco, “Tracking the Frenet-Serret frame associated to a highly maneuvering target in 3D,” in
1974
Earlier work this paper cites.
O. E. Rössler, “An equation for continuous chaos,”
1976
Earlier work this paper cites.
——, “An equation for hyperchaos,”
1979
Earlier work this paper cites.
F. Takens, “Detecting strange attractors in turbulence,” in
1981
Earlier work this paper cites.
J.-N. Juang and R. S. Pappa, “An eigensystem realization algorithm for modal parameter identification and model reduction,”
1985
Earlier work this paper cites.
W. M. Schaffer and M. Kot, “Do strange attractors govern ecological systems?”
1985
Earlier work this paper cites.
C. Weiss and J. Brock, “Evidence for Lorenz-type chaos in a laser,”
1986
Earlier work this paper cites.
J. R. Partington, J. R. Partington
1988
Earlier work this paper cites.
D. S. Broomhead and R. Jones, “Time-series analysis,”
1989
Earlier work this paper cites.
A. Waibel, T. Hanazawa, G. Hinton, K. Shikano, and K. J. Lang, “Phoneme recognition using time-delay neural networks,”
1989
Earlier work this paper cites.
G. Sugihara and R. M. May, “Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series,”
1990
Earlier work this paper cites.
I. Joliffe and B. Morgan, “Principal component analysis and exploratory factor analysis,”
1992
Earlier work this paper cites.
J. F. Gibson, J. D. Farmer, M. Casdagli, and S. Eubank, “An analytic approach to practical state space reconstruction,”
1992
Earlier work this paper cites.
T. Shinbrot, C. Grebogi, J. Wisdom, and J. A. Yorke, “Chaos in a double pendulum,”
1992
Earlier work this paper cites.
B. R. Iyer and C. Vishveshwara, “Frenet-Serret description of gyroscopic precession,”
1993
Earlier work this paper cites.
D. Poland, “Cooperative catalysis and chemical chaos: a chemical model for the Lorenz equations,”
1993
Earlier work this paper cites.
N. Hemati, “Strange attractors in brushless DC motors,”
1994
Earlier work this paper cites.
E. T. Whittaker and G. N. Watson,
1996
Earlier work this paper cites.
D. Bini, F. de Felice, and R. T. Jantzen, “Absolute and relative Frenet-Serret frames and Fermi-Walker transport,”
1999
Earlier work this paper cites.
O. Alter, P. O. Brown, and D. Botstein, “Singular value decomposition for genome-wide expression data processing and modeling,”
2000
Earlier work this paper cites.
O. Santolík, M. Parrot, and F. Lefeuvre, “Singular value decomposition methods for wave propagation analysis,”
2003
Earlier work this paper cites.
I. Mezić and A. Banaszuk, “Comparison of systems with complex behavior,”
2004
Cited alongside, same era.
N. Muller, L. Magaia, and B. M. Herbst, “Singular value decomposition, eigenfaces, and 3d reconstructions,”
2004
Cited alongside, same era.
I. Mezić, “Spectral properties of dynamical systems, model reduction and decompositions,”
2005
Cited alongside, same era.
R. Ravani and A. Meghdari, “Velocity distribution profile for robot arm motion using rational Frenet–Serret curves,”
2006
Cited alongside, same era.
R. R. Coifman and S. Lafon, “Diffusion maps,”
2006
Cited alongside, same era.
J. Bongard and H. Lipson, “Automated reverse engineering of nonlinear dynamical systems,”
2007
Cited alongside, same era.
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,”
2016
Later among the works it cites.
M. P. Do Carmo,
2016
Later among the works it cites.
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,”
2016
Later among the works it cites.
S. L. Brunton, B. W. Brunton, J. L. Proctor, and J. N. Kutz, “Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control,”
2016
Later among the works it cites.
S. L. Brunton, B. W. Brunton, J. L. Proctor, E. Kaiser, and J. N. Kutz, “Chaos as an intermittently forced linear system,”
2017
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
P. Schmid and J. Sesterhenn, “Dynamic mode decomposition of numerical and experimental data,”
2008
Cited alongside, same era.
M. Schmidt and H. Lipson, “Distilling free-form natural laws from experimental data,”
2009
Cited alongside, same era.
C. W. Rowley, I. Mezić, S. Bagheri, P. Schlatter, D. Henningson
2009
Cited alongside, same era.
M. P. Knapp, “Sines and cosines of angles in arithmetic progression,”
2009
Cited alongside, same era.
P. J. Schmid, “Dynamic mode decomposition of numerical and experimental data,”
2010
Cited alongside, same era.
E. Bozzo, R. Carniel, and D. Fasino, “Relationship between singular spectrum analysis and Fourier analysis: Theory and application to the monitoring of volcanic activity,”
2010
Cited alongside, same era.
H. Arbabi and I. Mezic, “Ergodic theory, dynamic mode decomposition, and computation of spectral properties of the Koopman operator,”
2017
Later among the works it cites.
N. Dhir, A. R. Kosiorek, and I. Posner, “Bayesian delay embeddings for dynamical systems,” in
2017
Later among the works it cites.
M. S. Hemati, C. W. Rowley, E. A. Deem, and L. N. Cattafesta, “De-biasing the dynamic mode decomposition for applied Koopman spectral analysis,”
2017
Later among the works it cites.
B. Lusch, J. N. Kutz, and S. L. Brunton, “Deep learning for universal linear embeddings of nonlinear dynamics,”
2018
Later among the works it cites.
2018
Later among the works it cites.
T. Askham and J. N. Kutz, “Variable projection methods for an optimized dynamic mode decomposition,”
2018
Later among the works it cites.
S. L. Brunton and J. N. Kutz,
2019
Later among the works it cites.
K. Champion, B. Lusch, J. N. Kutz, and S. L. Brunton, “Data-driven discovery of coordinates and governing equations,”
2019
Later among the works it cites.
K. P. Champion, S. L. Brunton, and J. N. Kutz, “Discovery of nonlinear multiscale systems: Sampling strategies and embeddings,”
2019
Later among the works it cites.
S. Das and D. Giannakis, “Delay-coordinate maps and the spectra of Koopman operators,”
2019
Later among the works it cites.
J. Álvarez-Vizoso, R. Arn, M. Kirby, C. Peterson, and B. Draper, “Geometry of curves in
2019
Later among the works it cites.
N. B. Erichson, S. L. Brunton, and J. N. Kutz, “Compressed dynamic mode decomposition for background modeling,”
2019
Later among the works it cites.
B. Beckermann and A. Townsend, “Bounds on the singular values of matrices with displacement structure,”
2019
Later among the works it cites.
2019
Later among the works it cites.
K. Kaheman, E. Kaiser, B. Strom, J. N. Kutz, and S. L. Brunton, “Learning discrepancy models from experimental data,” in
2019
Later among the works it cites.
D. Giannakis, “Delay-coordinate maps, coherence, and approximate spectra of evolution operators,”
2020
Later among the works it cites.
W. Gilpin, “Deep learning of dynamical attractors from time series measurements,”
2020
Later among the works it cites.
S. Pan and K. Duraisamy, “On the structure of time-delay embedding in linear models of non-linear dynamical systems,”
2020
Later among the works it cites.
A. A. Kaptanoglu, K. D. Morgan, C. J. Hansen, and S. L. Brunton, “Characterizing magnetized plasmas with dynamic mode decomposition,”
2020
Later among the works it cites.
2020
Later among the works it cites.
2020
Later among the works it cites.
F. Van Van Breugel, J. N. Kutz, and B. W. Brunton, “Numerical differentiation of noisy data: A unifying multi-objective optimization framework,”
2020
Later among the works it cites.