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Paper Citation Record · LEDGER

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings

As of 17 August 2026, this Paper Citation Record lists 57 of 57 outbound references and 0 inbound Pith citation observations for arXiv:1909.00076.

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pith.paper-citation-record.v1
1909.00076 v1

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measured 57 of 57 reference resolution

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Reference resolution

57 of 57 outbound references displayed

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External citation measurements

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Outbound references

Observation 1464a6d5-9367-4f90-92e1-3f83ff7619c4 · outbound

This paper cites Deterministic nonperiodic flow,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Deterministic nonperiodic flow,

Reference 1

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This paper cites ˆU ∈ Rnq×r, ˆS ∈ Rr×r and ˆV∈ R(N−q)×r, and [X F]T = ˜U˜S˜V∗ with the truncation value selected as p, so that ˜U∈ R(n+n′)q×p, ˜S∈ Rp×p and ˜V∈ R(N−q)×p.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings ˆU ∈ Rnq×r, ˆS ∈ Rr×r and ˆV∈ R(N−q)×r, and [X F]T = ˜U˜S˜V∗ with the truncation value selected as p, so that ˜U∈ R(n+n′)q×p, ˜S∈ Rp×p and ˜V∈ R(N−q)×p

Reference 2

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A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Unresolved cited work

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Observation 45543326-3893-4c31-8b33-23e079894a85 · outbound

This paper cites Long-term research challenges in wind energy - A research agenda by the European academy of wind energy,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Long-term research challenges in wind energy - A research agenda by the European academy of wind energy,

Reference 4

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Observation af4cee4d-38ff-4f40-bdba-a59f42ceebdf · outbound

This paper cites Duriez, S.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Duriez, S

Reference 5

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Observation e402e289-edd5-45a9-bbfe-17a2bb47e5a3 · outbound

This paper cites Challenges in climate science and contemporary applied mathematics,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Challenges in climate science and contemporary applied mathematics,

Reference 6

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Observation dbaa2b51-63aa-4e80-97e8-70796f0c0a60 · outbound

This paper cites The quiet revolution of numerical weather prediction,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings The quiet revolution of numerical weather prediction,

Reference 7

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Observation 8f222c87-1188-46cd-92a1-de114696892a · outbound

This paper cites Model error, information barriers, state estimation and prediction in complex multiscale systems,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Model error, information barriers, state estimation and prediction in complex multiscale systems,

Reference 8

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Observation 17409448-ed8d-4361-bb7f-63eef77b25b4 · outbound

This paper cites A variational approach to probing extreme events in turbu- lent dynamical systems,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings A variational approach to probing extreme events in turbu- lent dynamical systems,

Reference 9

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Observation 3fa13e5d-6cf3-4311-8741-8bb17974b0c0 · outbound

This paper cites The interpretation of short climate records, with comments on the North Atlantic and Southern Oscillations,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings The interpretation of short climate records, with comments on the North Atlantic and Southern Oscillations,

Reference 10

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Observation f4865fdb-565e-4333-b890-88341df96b44 · outbound

This paper cites Van den Dool, Empirical methods in short-term climate prediction (Oxford University Press, 2007).

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Van den Dool, Empirical methods in short-term climate prediction (Oxford University Press, 2007)

Reference 11

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Observation de698f90-7fdb-4413-a05e-2ce6a3c37e58 · outbound

This paper cites The skill of atmospheric linear inverse models in hindcasting the Madden–Julian Oscillation,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings The skill of atmospheric linear inverse models in hindcasting the Madden–Julian Oscillation,

Reference 12

Resolution
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Observation be76a75e-88ae-4f8f-8808-bcb69fc36738 · outbound

This paper cites Data-driven spectral decomposition and forecasting of ergodic dynamical sys- tems,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Data-driven spectral decomposition and forecasting of ergodic dynamical sys- tems,

Reference 13

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Observation efab9e51-4136-4aea-82fd-4af6e0d7bd76 · outbound

This paper cites Data-driven prediction strategies for low-frequency patterns of North Pacific climate variability,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Data-driven prediction strategies for low-frequency patterns of North Pacific climate variability,

Reference 14

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Observation 047f3fca-b1d1-408c-922b-c5d0dda300e3 · outbound

This paper cites Data-driven reduced modelling of turbulent Rayleigh- B´ enard convection using dmd-enhanced fluctuation-dissipation theorem,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Data-driven reduced modelling of turbulent Rayleigh- B´ enard convection using dmd-enhanced fluctuation-dissipation theorem,

Reference 15

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Observation 37e78af1-3d2b-4d41-b575-e1c18a1bf725 · outbound

This paper cites An ensemble quadratic echo state network for non-linear spatio-temporal forecasting,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings An ensemble quadratic echo state network for non-linear spatio-temporal forecasting,

Reference 16

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Observation e36a1d65-2989-4d91-abbf-82c9001083af · outbound

This paper cites Long-term Forecasting using Higher Order Tensor RNNs.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Long-term Forecasting using Higher Order Tensor RNNs

Reference 17

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Observation 50a4ce34-6860-4641-b6cb-dc05f64080d2 · outbound

This paper cites Data-driven fore- casting of high-dimensional chaotic systems with long short-term memory networks,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Data-driven fore- casting of high-dimensional chaotic systems with long short-term memory networks,

Reference 18

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Observation 46a29765-79bc-41ac-8553-c2319ba33ecb · outbound

This paper cites Model-free prediction of large spatiotem- porally chaotic systems from data: A reservoir computing approach,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Model-free prediction of large spatiotem- porally chaotic systems from data: A reservoir computing approach,

Reference 19

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Observation 1c5c9fa6-0726-4dec-82d5-d4ed5fa018bc · outbound

This paper cites Physics-informed neural networks: A deep learning framework for learning forward and inverse problems involving nonlinear partial differential equations,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Physics-informed neural networks: A deep learning framework for learning forward and inverse problems involving nonlinear partial differential equations,

Reference 20

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Observation faa6b0c4-2b88-4a4d-9922-791e2ddfd389 · outbound

This paper cites Compressed Convolutional LSTM: An Efficient Deep Learning framework to Model High Fidelity 3D Turbulence.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Compressed Convolutional LSTM: An Efficient Deep Learning framework to Model High Fidelity 3D Turbulence

Reference 21

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Observation 118e00e6-163b-4371-96c4-5c04fd71075f · outbound

This paper cites Deep state networks with uncertainty quantification for spatio-temporal forecasting,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Deep state networks with uncertainty quantification for spatio-temporal forecasting,

Reference 22

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Observation a2d4b553-d67b-4683-a39d-4cbe92cbe797 · outbound

This paper cites Data-driven prediction of a multi-scale Lorenz 96 chaotic system using deep learning methods: Reservoir computing, ANN, and RNN-LSTM.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Data-driven prediction of a multi-scale Lorenz 96 chaotic system using deep learning methods: Reservoir computing, ANN, and RNN-LSTM

Reference 23

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This paper cites Hamiltonian systems and transformation in Hilbert space,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Hamiltonian systems and transformation in Hilbert space,

Reference 24

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This paper cites Spectral properties of dynamical systems, model reduction and decompositions,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Spectral properties of dynamical systems, model reduction and decompositions,

Reference 25

Resolution
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This paper cites Analysis of fluid flows via spectral properties of the Koopman operator,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Analysis of fluid flows via spectral properties of the Koopman operator,

Reference 26

Resolution
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This paper cites Dynamic mode decomposition of numerical and experimental data,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Dynamic mode decomposition of numerical and experimental data,

Reference 27

Resolution
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This paper cites Spectral analysis of nonlinear flows,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Spectral analysis of nonlinear flows,

Reference 28

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This paper cites On dynamic mode decomposition: Theory and applications,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings On dynamic mode decomposition: Theory and applications,

Reference 29

Resolution
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Observation 56e437a4-2cef-4a5b-9df1-c09738811fa4 · outbound

This paper cites A data–driven approximation of the Koopman operator: Extending dynamic mode decomposition,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings A data–driven approximation of the Koopman operator: Extending dynamic mode decomposition,

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Resolution
verified fuzzy
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Observation 3bc46067-19ec-425c-8ec3-d50a7f40a36a · outbound

This paper cites Ergodic theory, dynamic mode decomposition, and computation of spectral properties of the Koopman operator,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Ergodic theory, dynamic mode decomposition, and computation of spectral properties of the Koopman operator,

Reference 31

Resolution
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Observation eaf0a33a-278e-40a9-a64a-5273aa2e9cf3 · outbound

This paper cites Study of dynamics in post-transient flows using Koopman mode decomposition,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Study of dynamics in post-transient flows using Koopman mode decomposition,

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T10:07:35.203005Z

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.

source=pdf_text observed=2026-08-14T10:07:34.575313Z digest=sha256:cabec273ee0ec139be3f9b21d530df85282f062ea75274ac78ab89ad35d69743

Observation f6d0da0a-113d-4848-8d60-f6156247cbb1 · outbound

This paper cites On convergence of extended dynamic mode decomposition to the Koopman operator,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings On convergence of extended dynamic mode decomposition to the Koopman operator,

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T10:07:35.187758Z

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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Observation 302bce05-1bbf-49be-bdc2-32956f356774 · outbound

This paper cites Model reduction for flow analysis and control,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Model reduction for flow analysis and control,

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T10:07:35.171820Z

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.

source=pdf_text observed=2026-08-14T10:07:34.584337Z digest=sha256:e333a3e7b4abf9619f85ebdd14fdde4bab71d5feafac84334c98489ad7a25ce5

Observation 93cd01d4-c435-4f00-b6bc-a1d6ddd79b9b · outbound

This paper cites Detecting strange attractors in turbulence,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Detecting strange attractors in turbulence,

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T10:07:35.156298Z

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.

source=pdf_text observed=2026-08-14T10:07:34.588836Z digest=sha256:0c03690e7443f686e741ae1718ad8dcf94365fc8033f976adc3539a92f99f083

Observation 7c5acbb1-34d7-48a0-9e60-4c54d2f457ee · outbound

This paper cites Linear predictors for nonlinear dynamical systems: Koopman oper- ator meets model predictive control,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Linear predictors for nonlinear dynamical systems: Koopman oper- ator meets model predictive control,

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T10:07:35.140034Z

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.

source=pdf_text observed=2026-08-14T10:07:34.593691Z digest=sha256:485952b0e7c25593d362e15efeaa7e45247ce42503ca12411d8ae5ddcfa26982

Observation 06e5b2b4-74aa-42e5-9c67-0e6d490e64b5 · outbound

This paper cites A data-driven Koopman model predictive control framework for nonlinear flows.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings A data-driven Koopman model predictive control framework for nonlinear flows

Reference 37

Resolution
unresolved
no resolver link, observed 2026-08-14T10:07:34.598352Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T10:07:34.598352Z digest=sha256:3db40a5b2afdc9afb092370578b4f6fe68a0ed34779eebd69a83fe7aa4499d86

Observation dada5588-3ec0-45e2-b109-6385cbbf5fb2 · outbound

This paper cites Nonlinear laplacian spectral analysis for time series with intermittency and low-frequency variability,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Nonlinear laplacian spectral analysis for time series with intermittency and low-frequency variability,

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T10:07:35.125160Z

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.

source=pdf_text observed=2026-08-14T10:07:34.603540Z digest=sha256:51cab3401782d7d8b16972fdaa94e8535b1d91af750a9dcc5818b326ade01eb4

Observation 11348528-818a-41a6-8116-856efa31bcec · outbound

This paper cites Chaos as an intermittently forced linear system,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Chaos as an intermittently forced linear system,

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T10:07:35.110721Z

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.

source=pdf_text observed=2026-08-14T10:07:34.608285Z digest=sha256:36222f4ecec184cb432e691212f3a4ec3ea0b46d4b1063a0ab6220d0db39565c

Observation 1970b96a-351f-474c-a2c5-0805dee18080 · outbound

This paper cites Discovering governing equations from data by sparse identification of nonlinear dynamical systems,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Discovering governing equations from data by sparse identification of nonlinear dynamical systems,

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T10:07:35.095136Z

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.

source=pdf_text observed=2026-08-14T10:07:34.613011Z digest=sha256:7b5ae9d163c1d052c6ef008e65e779bc988841f06eda774c4d7a3d2b9234ed48

Observation 9f72c4b6-7785-4927-a3ed-593c8c1d0adc · outbound

This paper cites Matrix pencils in time and frequency domain system identification,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Matrix pencils in time and frequency domain system identification,

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T10:07:35.079844Z

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.

source=pdf_text observed=2026-08-14T10:07:34.617614Z digest=sha256:18e48860a7121b181eec9c72190fdfb3dadd640aaada0453ef06899847a706d2

Observation 4605c522-75b9-45f8-a5c9-7530e1fb9ec6 · outbound

This paper cites Model reduction of bilinear systems in the Loewner framework,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Model reduction of bilinear systems in the Loewner framework,

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T10:07:35.064966Z

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.

source=pdf_text observed=2026-08-14T10:07:34.622248Z digest=sha256:2facbd3aaa4aaf885f65c7ff95ab84642f8dbf3c63ba7253379a8cabd5794bc4

Observation b8de00cf-c9c9-4aeb-8509-57ea054d97f8 · outbound

This paper cites On the Loewner framework for model reduction of Burgers’ equation,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings On the Loewner framework for model reduction of Burgers’ equation,

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T10:07:35.050012Z

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.

source=pdf_text observed=2026-08-14T10:07:34.627165Z digest=sha256:284d2bd0560b5c197fcb2cb6abd26f39091fa9623e0d961f651dcf6d2874b8e3

Observation c14729d0-589c-4194-a336-32dc74743e37 · outbound

This paper cites Gugercin, C.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Gugercin, C

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T10:07:35.034720Z

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.

source=pdf_text observed=2026-08-14T10:07:34.631971Z digest=sha256:106732d263ba5851cf5b5da794aa481162a11e0a0625627063076a0333585803

Observation 815335be-2c43-4fda-9b83-f6151e10578e · outbound

This paper cites Clustering of Series via Dynamic Mode Decomposition and the Matrix Pencil Method.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Clustering of Series via Dynamic Mode Decomposition and the Matrix Pencil Method

Reference 45

Resolution
verified exact
local_arxiv, observed 2026-08-14T10:07:34.757258Z

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.

source=pdf_text observed=2026-08-14T10:07:34.636609Z digest=sha256:f4981078cb47734bf49bc8c6ca0082ccb1ca75e73bc24be3fdd54852ecf06d40

Observation 07f55ee1-9775-4dd0-a87c-955b5091d71f · outbound

This paper cites Dynamic mode decomposition with control,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Dynamic mode decomposition with control,

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T10:07:35.019039Z

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.

source=pdf_text observed=2026-08-14T10:07:34.642350Z digest=sha256:4c5d54fdfa56ad17d84bcdb239d4de53ee26a4efc805698b227a0c5f948b80a7

Observation c187e978-d49b-4b21-a725-b8dfe93d145b · outbound

This paper cites Determining Lyapunov exponents from a time series,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Determining Lyapunov exponents from a time series,

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T10:07:35.003310Z

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.

source=pdf_text observed=2026-08-14T10:07:34.647460Z digest=sha256:6d91d579e33039b531df8b2252ecf80cd2b2431514d01caa6c07bc6485f4f136

Observation 2a27c3b0-dac2-403c-8f12-143a86124e1b · outbound

This paper cites Statistically accurate low-order models for uncertainty quantifi- cation in turbulent dynamical systems,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Statistically accurate low-order models for uncertainty quantifi- cation in turbulent dynamical systems,

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T10:07:34.987646Z

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.

source=pdf_text observed=2026-08-14T10:07:34.651888Z digest=sha256:7bf4f6656a7236f40b414ed0dcc656334835c3d2c8877e042363a619e4c01c1b

Observation af49bcaa-5e34-4f11-941b-c468b2cd0e75 · outbound

This paper cites Introduction to turbulent dynamical systems for complex systems,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Introduction to turbulent dynamical systems for complex systems,

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T10:07:34.971461Z

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.

source=pdf_text observed=2026-08-14T10:07:34.656497Z digest=sha256:67905ab4b73009be46f388cabbad5fac020cbb5db518747cf6c1023a54a5c5b4

Observation 0a6ad61e-627f-427a-b62c-4ac2062f59c2 · outbound

This paper cites Low-dimensional reduced-order models for statistical response and uncertainty quantification: Two-layer baroclinic turbulence,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Low-dimensional reduced-order models for statistical response and uncertainty quantification: Two-layer baroclinic turbulence,

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T10:07:34.954974Z

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.

source=pdf_text observed=2026-08-14T10:07:34.661268Z digest=sha256:4717d9335a1da1256f6c2a7975fab30e61b4e210f2f2af0a65b2019010b7f86a

Observation b4aa50c1-0b4e-4bad-9b63-a96d6af4142c · outbound

This paper cites an unresolved cited work.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Unresolved cited work

Reference 51

Resolution
unresolved
raw_fallback, observed 2026-08-14T10:07:34.937347Z

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.

source=pdf_text observed=2026-08-14T10:07:34.666122Z digest=sha256:32f63df79fed0353a04f9c2ddfb01e286e0320c0d20c1cf0215deda69cfe0a9e

Observation 9a06f893-115c-47b1-a945-b2d988ef8192 · outbound

This paper cites Predictability - a problem partly solved,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Predictability - a problem partly solved,

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T10:07:34.920071Z

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.

source=pdf_text observed=2026-08-14T10:07:34.670942Z digest=sha256:f1b61dd4b2967c40a222cd16d60758ec9a5b233a160ad33468a65d11d749b2f0

Observation 5173e43a-43c1-4799-9e99-f17439fb3a88 · outbound

This paper cites High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method,

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T10:07:34.902781Z

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.

source=pdf_text observed=2026-08-14T10:07:34.675477Z digest=sha256:37bba2be2a10a673dc228bfa7c3b028c7d06e46237c871aa38381bb63561c78d

Observation 1ae8c3c2-0b11-490d-b959-ccfb277afafd · outbound

This paper cites Driven cavity flows by efficient numerical techniques,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Driven cavity flows by efficient numerical techniques,

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T10:07:34.884988Z

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.

source=pdf_text observed=2026-08-14T10:07:34.680227Z digest=sha256:93f4d09177e5eea8ae70bdc7a952fcade8dd0c94ac1fb1b5bed93d0956dc4103

Observation 17f3f084-9cf6-4ee1-a456-8b552462e2c4 · outbound

This paper cites A novel fully implicit finite volume method applied to the lid- driven cavity problempart I: High Reynolds number fow calculations,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings A novel fully implicit finite volume method applied to the lid- driven cavity problempart I: High Reynolds number fow calculations,

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T10:07:34.870118Z

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.

source=pdf_text observed=2026-08-14T10:07:34.684998Z digest=sha256:313b93044588696b03c2c53b0cf7ee1f8b57bcb5e6e98e9f598bed985d4f683d

Observation 22e9ed92-736e-4f4f-996f-1b9daf2038fa · outbound

This paper cites Linearly recurrent autoencoder networks for learning dynamics,.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Linearly recurrent autoencoder networks for learning dynamics,

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T10:07:34.855063Z

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.

source=pdf_text observed=2026-08-14T10:07:34.689738Z digest=sha256:f5370eb9ac9e2ff146614f260291c33112c9697cd87e2206934b4c2ebde5edab

Observation d3c9cc89-c3c1-41e0-9ace-88b94efb7918 · outbound

This paper cites Singular Value Decomposition (svd) and Principal Component Analysis (PCA),.

A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings Singular Value Decomposition (svd) and Principal Component Analysis (PCA),

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T10:07:34.839687Z

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.

source=pdf_text observed=2026-08-14T10:07:34.694488Z digest=sha256:a351f3f8dfb679e7cf746e6ee2797ca3f325b2bf89dd680d57880bbea6258cc3

Pith citing papers

No inbound Pith citation observations are available.