Finding Koopman Invariant Subspaces via Personalized PageRank | Paper Citation Record

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Finding Koopman Invariant Subspaces via Personalized PageRank Unresolved cited work

Reference 1

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This paper cites Koopman and John von Neumann.

Finding Koopman Invariant Subspaces via Personalized PageRank Koopman and John von Neumann

Reference 2

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This paper cites Comparison of systems with complex behavior.Physica D: Nonlinear Phenomena, 197(1):101–133, 2004.

Finding Koopman Invariant Subspaces via Personalized PageRank Comparison of systems with complex behavior.Physica D: Nonlinear Phenomena, 197(1):101–133, 2004

Reference 3

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This paper cites Spectral properties of dynamical systems, model reduction and decompositions.Nonlinear Dynamics, 41(1):309–325, Aug 2005.

Finding Koopman Invariant Subspaces via Personalized PageRank Spectral properties of dynamical systems, model reduction and decompositions.Nonlinear Dynamics, 41(1):309–325, Aug 2005

Reference 4

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This paper cites Applied koopmanism.Chaos: An Interdisciplinary Journal of Nonlinear Science, 22(4):047510, 12 2012.

Finding Koopman Invariant Subspaces via Personalized PageRank Applied koopmanism.Chaos: An Interdisciplinary Journal of Nonlinear Science, 22(4):047510, 12 2012

Reference 5

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This paper cites Analysis of fluid flows via spectral properties of the Koopman operator.Annual Review of Fluid Mechanics, 45(V olume 45, 2013):357–378, 2013.

Finding Koopman Invariant Subspaces via Personalized PageRank Analysis of fluid flows via spectral properties of the Koopman operator.Annual Review of Fluid Mechanics, 45(V olume 45, 2013):357–378, 2013

Reference 6

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Finding Koopman Invariant Subspaces via Personalized PageRank Unresolved cited work

Reference 7

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Observation 20a7c0b1-91e5-42c6-8226-488964cffb3e · outbound

This paper cites Brunton, Marko Budiši ´c, Eurika Kaiser, and J.

Finding Koopman Invariant Subspaces via Personalized PageRank Brunton, Marko Budiši ´c, Eurika Kaiser, and J

Reference 8

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This paper cites Colbrook.

Finding Koopman Invariant Subspaces via Personalized PageRank Colbrook

Reference 9

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This paper cites Springer Basel, Basel, 2026.

Finding Koopman Invariant Subspaces via Personalized PageRank Springer Basel, Basel, 2026

Reference 10

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Observation 4ca6bcc9-7ed6-42f1-b0c6-1025e7fee24a · outbound

This paper cites Brunton, Joshua L.

Finding Koopman Invariant Subspaces via Personalized PageRank Brunton, Joshua L

Reference 11

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Observation 8237fde8-0c3d-4d9c-9e4e-d5bf6f31dd61 · outbound

This paper cites Brunton, Lise A.

Finding Koopman Invariant Subspaces via Personalized PageRank Brunton, Lise A

Reference 12

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Observation 8171e577-8e75-444f-8f0b-81e4815c7be7 · outbound

This paper cites Variational Koopman models: Slow collective variables and molecular kinetics from short off-equilibrium simulations.The Journal of Chemical Physics, 146(15):154104, 2017.

Finding Koopman Invariant Subspaces via Personalized PageRank Variational Koopman models: Slow collective variables and molecular kinetics from short off-equilibrium simulations.The Journal of Chemical Physics, 146(15):154104, 2017

Reference 13

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Observation dfebfbc7-5dbb-44b8-a685-215ae310dba9 · outbound

This paper cites A data-driven approximation of the Koopman operator: Extending dynamic mode decomposition.Journal of Nonlinear Science, 25(6):1307–1346, 2015.

Finding Koopman Invariant Subspaces via Personalized PageRank A data-driven approximation of the Koopman operator: Extending dynamic mode decomposition.Journal of Nonlinear Science, 25(6):1307–1346, 2015

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.676016Z

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Observation 9317c658-6697-4030-964e-c86c79d5bb17 · outbound

This paper cites On convergence of extended dynamic mode decomposition to the Koopman operator.Journal of Nonlinear Science, 28(2):687–710, 2018.

Finding Koopman Invariant Subspaces via Personalized PageRank On convergence of extended dynamic mode decomposition to the Koopman operator.Journal of Nonlinear Science, 28(2):687–710, 2018

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.587055Z

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This paper cites Sharp spectral rates for Koopman operator learning.Advances in Neural Information Processing Systems, 36:32328–32339, 2023.

Finding Koopman Invariant Subspaces via Personalized PageRank Sharp spectral rates for Koopman operator learning.Advances in Neural Information Processing Systems, 36:32328–32339, 2023

Reference 16

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This paper cites Finite-data error bounds for Koopman-based prediction and control.Journal of Nonlinear Science, 33(1):14, 2023.

Finding Koopman Invariant Subspaces via Personalized PageRank Finite-data error bounds for Koopman-based prediction and control.Journal of Nonlinear Science, 33(1):14, 2023

Reference 17

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Observation 05d0f7bd-bb2f-4bd5-9753-fef53f957a33 · outbound

This paper cites Colbrook and Alex Townsend.

Finding Koopman Invariant Subspaces via Personalized PageRank Colbrook and Alex Townsend

Reference 18

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Observation 9ff6c9c2-3e29-4719-9b23-a4d9bc6e950a · outbound

This paper cites Koopman operators for estimation and control of dynamical systems.Annual Review of Control, Robotics, and Autonomous Systems, 4(1):59–87, 2021.

Finding Koopman Invariant Subspaces via Personalized PageRank Koopman operators for estimation and control of dynamical systems.Annual Review of Control, Robotics, and Autonomous Systems, 4(1):59–87, 2021

Reference 19

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Observation 7433dea7-e3c7-4908-829a-d3d0ce95878f · outbound

This paper cites Dynamic mode decomposition with reproducing kernels for Koopman spectral analysis.Advances in neural information processing systems, 29, 2016.

Finding Koopman Invariant Subspaces via Personalized PageRank Dynamic mode decomposition with reproducing kernels for Koopman spectral analysis.Advances in neural information processing systems, 29, 2016

Reference 20

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This paper cites Ergodic theory, dynamic mode decomposition, and computation of spectral properties of the Koopman operator.SIAM Journal on Applied Dynamical Systems, 16(4):2096–2126, 2017.

Finding Koopman Invariant Subspaces via Personalized PageRank Ergodic theory, dynamic mode decomposition, and computation of spectral properties of the Koopman operator.SIAM Journal on Applied Dynamical Systems, 16(4):2096–2126, 2017

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.706249Z

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This paper cites Deep learning enhanced dynamic mode decomposition.Chaos: An Interdisciplinary Journal of Nonlinear Science, 32(3):033116, 2022.

Finding Koopman Invariant Subspaces via Personalized PageRank Deep learning enhanced dynamic mode decomposition.Chaos: An Interdisciplinary Journal of Nonlinear Science, 32(3):033116, 2022

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.670551Z

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Observation b1a2eb6c-9d4b-4f92-ba4f-59d635af63aa · outbound

This paper cites Learning Koopman invariant subspaces for dynamic mode decomposition.Advances in neural information processing systems, 30, 2017.

Finding Koopman Invariant Subspaces via Personalized PageRank Learning Koopman invariant subspaces for dynamic mode decomposition.Advances in neural information processing systems, 30, 2017

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.673278Z

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Observation 66dfac56-b792-4c61-863b-d25470b8eb86 · outbound

This paper cites Extended dynamic mode decomposi- tion with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator.

Finding Koopman Invariant Subspaces via Personalized PageRank Extended dynamic mode decomposi- tion with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.599145Z

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Observation 0cd588ec-2263-4b42-b5f3-635f8334b52a · outbound

This paper cites Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics.The Journal of chemical physics, 148(24):241703, 2018.

Finding Koopman Invariant Subspaces via Personalized PageRank Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics.The Journal of chemical physics, 148(24):241703, 2018

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.656598Z

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Observation c3e35f5f-00b8-4640-a43a-7217ea2931ae · outbound

This paper cites Koopman operator learning using invertible neural networks.

Finding Koopman Invariant Subspaces via Personalized PageRank Koopman operator learning using invertible neural networks

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.694272Z

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Observation 116c6a50-6d18-4df1-ba7c-e3c719a9b179 · outbound

This paper cites Learning deep neural network representations for Koopman operators of nonlinear dynamical systems.

Finding Koopman Invariant Subspaces via Personalized PageRank Learning deep neural network representations for Koopman operators of nonlinear dynamical systems

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.685756Z

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Observation d12efac8-9890-4ee6-8edd-3cc3566f1aaf · outbound

This paper cites Brunton, and Matthew J.

Finding Koopman Invariant Subspaces via Personalized PageRank Brunton, and Matthew J

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.696601Z

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Observation eb23aba2-27de-4ddd-b120-7f1725df9d7b · outbound

This paper cites Learning Koopman eigenfunctions and invariant subspaces from data: Symmetric subspace decomposition.IEEE Transactions on Automatic Control, 67(7):3442–3457, 2021.

Finding Koopman Invariant Subspaces via Personalized PageRank Learning Koopman eigenfunctions and invariant subspaces from data: Symmetric subspace decomposition.IEEE Transactions on Automatic Control, 67(7):3442–3457, 2021

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.703943Z

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Observation a90a3d3b-658b-4267-be3b-5c05c4bdd199 · outbound

This paper cites Generalizing dynamic mode decomposition: Balancing accuracy and expressiveness in Koopman approximations.Automatica, 153:111001, 2023.

Finding Koopman Invariant Subspaces via Personalized PageRank Generalizing dynamic mode decomposition: Balancing accuracy and expressiveness in Koopman approximations.Automatica, 153:111001, 2023

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.719152Z

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Observation 2b929588-f0a7-4580-ac87-a13ca757f3b4 · outbound

This paper cites Courier Corporation, 2004.

Finding Koopman Invariant Subspaces via Personalized PageRank Courier Corporation, 2004

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.721922Z

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Observation 0e269a57-afee-4bfd-8959-e01c3b5346cf · outbound

This paper cites Finite approximation for the Frobenius-Perron operator.

Finding Koopman Invariant Subspaces via Personalized PageRank Finite approximation for the Frobenius-Perron operator

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.716129Z

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Observation ef8043ac-c891-4222-8383-ebe97f63eb24 · outbound

This paper cites On the numerical approximation of the Perron-Frobenius and Koopman operator.Journal of Computational Dynamics, 3(1):51–79, 2016.

Finding Koopman Invariant Subspaces via Personalized PageRank On the numerical approximation of the Perron-Frobenius and Koopman operator.Journal of Computational Dynamics, 3(1):51–79, 2016

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.689077Z

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Observation 12532d88-ecd5-43c1-9029-803891b7b60b · outbound

This paper cites The anatomy of a large-scale hypertextual web search engine.Computer Networks and ISDN Systems, 30(1):107–117, 1998.

Finding Koopman Invariant Subspaces via Personalized PageRank The anatomy of a large-scale hypertextual web search engine.Computer Networks and ISDN Systems, 30(1):107–117, 1998

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.622052Z

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Observation 0fabf3b1-b40a-4196-8e8d-f69d42b0d6df · outbound

This paper cites Deeper inside PageRank.Internet Mathematics, 1(3):335–380, 2004.

Finding Koopman Invariant Subspaces via Personalized PageRank Deeper inside PageRank.Internet Mathematics, 1(3):335–380, 2004

Reference 35

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Observation d72aa33e-0566-4081-8dd2-47153eec4dd5 · outbound

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Finding Koopman Invariant Subspaces via Personalized PageRank Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-07-09T08:16:06.651665Z

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Finding Koopman Invariant Subspaces via Personalized PageRank Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-07-09T08:16:06.649482Z

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Observation cea995c7-9613-4d48-9759-68e066f6adf2 · outbound

This paper cites Simon and Albert Ando.

Finding Koopman Invariant Subspaces via Personalized PageRank Simon and Albert Ando

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.578937Z

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Observation df7e432b-910c-4057-a377-d27a65b52379 · outbound

This paper cites New York : Academic Press, New York (State), United States, 1977.

Finding Koopman Invariant Subspaces via Personalized PageRank New York : Academic Press, New York (State), United States, 1977

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.662402Z

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Observation 3fd9c477-0d60-4928-a7f8-e66e7d70c77e · outbound

This paper cites Haveliwala.

Finding Koopman Invariant Subspaces via Personalized PageRank Haveliwala

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.710983Z

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Observation 3df93ff6-c382-4111-aebd-7c4cf814ceb3 · outbound

This paper cites Local graph partitioning using PageRank vectors.

Finding Koopman Invariant Subspaces via Personalized PageRank Local graph partitioning using PageRank vectors

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.713530Z

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Observation c14b2a61-c223-48b7-9fb6-d0086b7c70d0 · outbound

This paper cites A tutorial on spectral clustering.Statistics and Computing, 17(4):395–416.

Finding Koopman Invariant Subspaces via Personalized PageRank A tutorial on spectral clustering.Statistics and Computing, 17(4):395–416

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.667604Z

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Observation 98407369-29c5-47ca-a6cd-caff439674ce · outbound

This paper cites Community detection in graphs.Physics Reports, 486(3):75–174, 2010.

Finding Koopman Invariant Subspaces via Personalized PageRank Community detection in graphs.Physics Reports, 486(3):75–174, 2010

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.642579Z

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Observation f4511c1a-45b2-4b1c-b2fd-4d166ea50f28 · outbound

This paper cites Robust Perron cluster analysis in conformation dynamics.Linear Algebra and its Applications, 398:161–184, 2005.

Finding Koopman Invariant Subspaces via Personalized PageRank Robust Perron cluster analysis in conformation dynamics.Linear Algebra and its Applications, 398:161–184, 2005

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.654060Z

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Observation 0f192cd0-cc96-41bd-874b-f2a301f1c3e5 · outbound

This paper cites Fuzzy spectral clustering by PCCA+: application to Markov state models and data classification.Advances in Data Analysis and Classification, 7(2):147–179, 2013.

Finding Koopman Invariant Subspaces via Personalized PageRank Fuzzy spectral clustering by PCCA+: application to Markov state models and data classification.Advances in Data Analysis and Classification, 7(2):147–179, 2013

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.724791Z

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Observation bf23162c-d19e-46c3-b33c-468ee902196d · outbound

This paper cites Finding communities in directed networks by pager- ank random walk induced network embedding.Physica A: Statistical Mechanics and its Applications, 389(12):2443–2454, 2010.

Finding Koopman Invariant Subspaces via Personalized PageRank Finding communities in directed networks by pager- ank random walk induced network embedding.Physica A: Statistical Mechanics and its Applications, 389(12):2443–2454, 2010

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.594212Z

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Observation 1abfaa4f-8d69-4269-8224-f4c2a28befb2 · outbound

This paper cites Golub and Charles F.

Finding Koopman Invariant Subspaces via Personalized PageRank Golub and Charles F

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.576513Z

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Finding Koopman Invariant Subspaces via Personalized PageRank Unresolved cited work

Reference 48

Resolution: unresolved; raw_fallback, observed 2026-07-09T08:16:06.708521Z

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Observation 3e2ceee9-e779-429f-8950-b60e3171d4c8 · outbound

This paper cites Koopman operator, geometry, and learning of dynamical systems.Notices of the American Mathematical Society, 68(7):1087–1105, 2021.

Finding Koopman Invariant Subspaces via Personalized PageRank Koopman operator, geometry, and learning of dynamical systems.Notices of the American Mathematical Society, 68(7):1087–1105, 2021

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.632711Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation daf86968-6aa2-45a0-88f2-e282325f5e71 · outbound

This paper cites Ramachandran, C.

Finding Koopman Invariant Subspaces via Personalized PageRank Ramachandran, C

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.635421Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 0b73632b-fb80-4a32-a3bc-55eb09f22b1c · outbound

This paper cites Identification of slow molecular order parameters for Markov model construction.The Journal of Chemical Physics, 139(1):015102, 2013.

Finding Koopman Invariant Subspaces via Personalized PageRank Identification of slow molecular order parameters for Markov model construction.The Journal of Chemical Physics, 139(1):015102, 2013

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.618007Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 585626f0-9dfb-4131-8eda-26fe23a367a8 · outbound

This paper cites Data-driven approximation of Koopman operators and generators: Convergence rates and error bounds, 2024.

Finding Koopman Invariant Subspaces via Personalized PageRank Data-driven approximation of Koopman operators and generators: Convergence rates and error bounds, 2024

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.611904Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 89ab7c2c-036d-40a1-9481-4d048cb7197b · outbound

This paper cites Beyond expectations: residual dynamic mode decomposition and variance for stochastic dynamical systems.Nonlinear Dynamics, 112(3):2037– 2061, 2024.

Finding Koopman Invariant Subspaces via Personalized PageRank Beyond expectations: residual dynamic mode decomposition and variance for stochastic dynamical systems.Nonlinear Dynamics, 112(3):2037– 2061, 2024

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.683516Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 754b8362-6f8c-4593-9c32-e3cbf14e0689 · outbound

This paper cites Dynamic mode decomposition of numerical and experimental data.Journal of Fluid Mechanics, 656:5–28.

Finding Koopman Invariant Subspaces via Personalized PageRank Dynamic mode decomposition of numerical and experimental data.Journal of Fluid Mechanics, 656:5–28

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.606210Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation eb7898b1-be7d-4d38-ab8c-dc320b6b766f · outbound

This paper cites Spectral analysis of nonlinear flows.Journal of Fluid Mechanics, 641:115–127, 2009.

Finding Koopman Invariant Subspaces via Personalized PageRank Spectral analysis of nonlinear flows.Journal of Fluid Mechanics, 641:115–127, 2009

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.664829Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 72b9694e-99d0-4a45-858b-ff43eb5763c4 · outbound

This paper cites Society for Industrial and Applied Mathematics, Philadelphia, PA, 2016.

Finding Koopman Invariant Subspaces via Personalized PageRank Society for Industrial and Applied Mathematics, Philadelphia, PA, 2016

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.691879Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 32d755f8-4cf8-4144-839b-a358b38fdfc1 · outbound

This paper cites A kernel-based method for data-driven Koopman spectral analysis.Journal of Computational Dynamics, 2(2):247–265, 2016.

Finding Koopman Invariant Subspaces via Personalized PageRank A kernel-based method for data-driven Koopman spectral analysis.Journal of Computational Dynamics, 2(2):247–265, 2016

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.626181Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 5ffb8d11-0b92-4165-878f-c1cda87ba790 · outbound

This paper cites A quantitative analysis of Koopman operator methods for system identification and predictions.Comptes Rendus.

Finding Koopman Invariant Subspaces via Personalized PageRank A quantitative analysis of Koopman operator methods for system identification and predictions.Comptes Rendus

Reference 58

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.629793Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 212bd898-d9ed-4ea3-9ffd-32f155d90b09 · outbound

This paper cites an unresolved cited work.

Finding Koopman Invariant Subspaces via Personalized PageRank Unresolved cited work

Reference 59

Resolution: unresolved; raw_fallback, observed 2026-07-09T08:16:06.602991Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation b4d0dd7c-0eeb-4931-9314-36e28a436a7c · outbound

This paper cites an unresolved cited work.

Finding Koopman Invariant Subspaces via Personalized PageRank Unresolved cited work

Reference 60

Resolution: unresolved; raw_fallback, observed 2026-07-09T08:16:06.647420Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 5e7bd38b-8830-4604-9810-099a287644ae · outbound

This paper cites Brunton, Bingni W.

Finding Koopman Invariant Subspaces via Personalized PageRank Brunton, Bingni W

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.701259Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 5a23848b-0d9d-45dc-91ef-4cdb495accb2 · outbound

This paper cites A prony approximation of Koopman mode decomposition.

Finding Koopman Invariant Subspaces via Personalized PageRank A prony approximation of Koopman mode decomposition

Reference 62

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.596554Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 03598c80-d067-4260-a377-0322363c4a88 · outbound

This paper cites (Kψ1)(x(k)) (Kψ2)(x(k)) (Kψ3)(x(k)) #⊺ =.

Finding Koopman Invariant Subspaces via Personalized PageRank (Kψ1)(x(k)) (Kψ2)(x(k)) (Kψ3)(x(k)) #⊺ =

Reference 63

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.699154Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 802db1dc-9437-4a62-8a36-77c5d8bb5582 · outbound

This paper cites does not requireαnear1.

Finding Koopman Invariant Subspaces via Personalized PageRank does not requireαnear1

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T08:16:06.609200Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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