Paper Citation Record · LEDGER

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups

As of 14 August 2026, this Paper Citation Record lists 42 of 42 outbound references and 0 inbound Pith citation observations for arXiv:2509.04265.

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pith.paper-citation-record.v1
2509.04265 v3

Coverage vector

measured 42 of 42 reference resolution

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Reference resolution

42 of 42 outbound references displayed

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Outbound references

Observation 69d793a7-34e8-4659-8eef-aa0ceafe4fcb · outbound

This paper cites Arnold.Mathematical methods of classical mechanics, volume 60.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Arnold.Mathematical methods of classical mechanics, volume 60

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:43.323326Z

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Observation 4dc3f410-db54-4aa5-b261-65babfc4f64c · outbound

This paper cites Batchelor.An introduction to fluid dynamics.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Batchelor.An introduction to fluid dynamics

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:43.308068Z

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Observation ae31addb-1591-4133-bdfb-72d9f28f4489 · outbound

This paper cites Athena scientific, 2012.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Athena scientific, 2012

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:43.293814Z

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Observation 27e6547c-8d4a-4304-8ede-13b07b7da21a · outbound

This paper cites Athena Scientific, 2008.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Athena Scientific, 2008

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:43.279245Z

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Observation 4c8a7947-b53d-47c8-a4a4-018b936756f3 · outbound

This paper cites Brunton and Nathan J.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Brunton and Nathan J

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:43.264440Z

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Observation 439b3e8f-0ff4-4598-b173-0f60523da9cc · outbound

This paper cites Brunton, Joshua L.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Brunton, Joshua L

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:43.249625Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 3bdd2999-b42c-480b-808a-1e6b811e3f82 · outbound

This paper cites Colbrook and Alex Townsend.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Colbrook and Alex Townsend

Reference 7

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Observation 81385606-811b-4e36-a5fe-67b2099b68dc · outbound

This paper cites an unresolved cited work.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Unresolved cited work

Reference 8

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Observation 46b421d0-0501-422c-a72e-8ac4de69bc0d · outbound

This paper cites Impulses and physiological states in theoretical models of nerve membrane.Biophysical journal, 1(6):445–466, 1961.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Impulses and physiological states in theoretical models of nerve membrane.Biophysical journal, 1(6):445–466, 1961

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:43.225485Z

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Observation 3762be78-92cd-4577-aeff-68ed29315b03 · outbound

This paper cites Springer Science & Business Media, 2013.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Springer Science & Business Media, 2013

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:43.211615Z

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Observation 83cc52e0-6805-4b79-b0cb-b2a339882c8e · outbound

This paper cites Hale.Ordinary differential equations.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Hale.Ordinary differential equations

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:43.197692Z

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Observation 4036d147-a313-4dbe-8d52-45d0d767d55c · outbound

This paper cites Hirsch, Stephen Smale, and Robert L.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Hirsch, Stephen Smale, and Robert L

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:43.182557Z

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Observation 9dd1d92c-85ff-4702-a606-df352c109c81 · outbound

This paper cites Cambridge university press, 2012.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Cambridge university press, 2012

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:43.167485Z

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Observation e8e760ae-f6e4-41c6-b7e5-c369f3dfff80 · outbound

This paper cites an unresolved cited work.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-05T10:20:43.152771Z

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Observation 71b32b6b-402a-4370-a50b-0cede0375069 · outbound

This paper cites Koopman operators with intrinsic observables in rigged reproducing kernel hilbert spaces.arXiv preprint arXiv:2403.02524, 2024.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Koopman operators with intrinsic observables in rigged reproducing kernel hilbert spaces.arXiv preprint arXiv:2403.02524, 2024

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-05T10:20:42.361609Z

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Unavailable: canonical work link unavailable.

Observation 3ee23459-678e-4674-bf1f-15470d9c3b77 · outbound

This paper cites Asymptotic phase and amplitude for classical and semiclassical stochastic oscillators via koopman operator theory.Mathematics, 9(18):2188, 2021.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Asymptotic phase and amplitude for classical and semiclassical stochastic oscillators via koopman operator theory.Mathematics, 9(18):2188, 2021

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:43.137961Z

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Observation 09aad655-2a31-4a27-be12-08d45d38ce26 · outbound

This paper cites Near-optimal reinforcement learning in polynomial time.Machine learning, 49(2):209–232, 2002.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Near-optimal reinforcement learning in polynomial time.Machine learning, 49(2):209–232, 2002

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:43.121786Z

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Observation 6720a8d7-4644-4f36-be27-f222e49d302c · outbound

This paper cites Data- driven approximation of the koopman generator: Model reduction, system identification, and control.Physica D: Nonlinear Phenomena, 406:132416, 2020.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Data- driven approximation of the koopman generator: Model reduction, system identification, and control.Physica D: Nonlinear Phenomena, 406:132416, 2020

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:43.106445Z

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Observation c7b609b5-7ecd-435b-b348-5908f3b7f3eb · outbound

This paper cites an unresolved cited work.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-05T10:20:43.092494Z

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Observation dfa64a37-efde-404c-9526-06a27db0cf5e · outbound

This paper cites Koopman and John von Neumann.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Koopman and John von Neumann

Reference 20

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Observation 127c7162-524a-4898-b3bf-73e574c0385f · outbound

This paper cites Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions

Reference 21

Resolution: verified exact; local_arxiv, observed 2026-08-05T10:20:42.612809Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a3bc76ce-d682-4463-abc9-9ba42b91f8b7 · outbound

This paper cites Kutz, Steven L.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Kutz, Steven L

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:43.076677Z

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Observation d3aa6ed0-dc4f-418e-b405-438fda8991bc · outbound

This paper cites an unresolved cited work.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-05T10:20:43.062296Z

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Observation 8e7af0de-23f9-46fb-bff3-ad004a891b63 · outbound

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

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Spectral properties of dynamical systems, model reduction and decompositions.Nonlinear Dynamics, 41:309–325, 2005

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:43.048706Z

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Observation 16609e9c-7558-4799-9c88-f4f5123c80b7 · outbound

This paper cites Playing Atari with Deep Reinforcement Learning.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Playing Atari with Deep Reinforcement Learning

Reference 25

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This paper cites Error bounds for approximate value iteration.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Error bounds for approximate value iteration

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-05T10:20:42.410752Z

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Observation e0f58c7a-f659-4879-aa9c-f7fb5612cb63 · outbound

This paper cites Murray.Mathematical biology: I.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Murray.Mathematical biology: I

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:43.024952Z

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Observation 8cbc7749-8a24-4ff0-9fa5-df4d1b34e650 · outbound

This paper cites An active pulse transmission line simulating nerve axon.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups An active pulse transmission line simulating nerve axon

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:43.011899Z

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Observation 9eb2602a-02df-4d2f-81b7-60028975a00e · outbound

This paper cites Pavliotis.Stochastic Processes and Applications: Diffusion Processes, the Fokker-Planck and Langevin Equations.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Pavliotis.Stochastic Processes and Applications: Diffusion Processes, the Fokker-Planck and Langevin Equations

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:42.997777Z

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Observation da00f610-dc6c-4713-bc1c-395a3f018e43 · outbound

This paper cites Applied Mathematical Sciences.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Applied Mathematical Sciences

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:42.983866Z

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Observation 619c67ef-a741-4398-82c0-daebe33814a2 · outbound

This paper cites Rowley, Igor Mezi´c, Shervin Bagheri, Philipp Schlatter, and Dan S.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Rowley, Igor Mezi´c, Shervin Bagheri, Philipp Schlatter, and Dan S

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:42.970193Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c845461a-a967-4890-8154-42617d713cba · outbound

This paper cites Proximal Policy Optimization Algorithms.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Proximal Policy Optimization Algorithms

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-05T10:20:42.436545Z

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Observation a40c1e36-31d0-4eca-b9b1-9c6a3f42e9f7 · outbound

This paper cites Introduction to multi-armed bandits.Foundations and Trends® in Machine Learning, 12 (1-2):1–286, 2019.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Introduction to multi-armed bandits.Foundations and Trends® in Machine Learning, 12 (1-2):1–286, 2019

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:42.955026Z

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Observation 06f0cfc7-c623-457f-9e4b-c894ce5d0a95 · outbound

This paper cites Strogatz.Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering (studies in nonlinearity), volume 1.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Strogatz.Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering (studies in nonlinearity), volume 1

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:42.940534Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 1bc379e5-b7d4-4a20-8529-8b6d18853fcb · outbound

This paper cites Sutton and Andrew G.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Sutton and Andrew G

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:42.924924Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4e88e091-cda1-486c-96ef-78b97c9bb858 · outbound

This paper cites Definition and data-driven reconstruction of asymptotic phase and amplitudes of stochastic oscillators via koopman operator theory.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Definition and data-driven reconstruction of asymptotic phase and amplitudes of stochastic oscillators via koopman operator theory

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:42.911204Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 2e89519c-a407-4da8-98c9-19a11f3936b5 · outbound

This paper cites Tu.Dynamic mode decomposition: Theory and applications.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Tu.Dynamic mode decomposition: Theory and applications

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:42.896929Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 21a9ee02-0488-4f4d-845e-3bbb8dc88241 · outbound

This paper cites Texts in Applied Mathematics.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Texts in Applied Mathematics

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-05T10:20:42.463145Z

Source-reported events for the cited work

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Observation 5a4c0d27-39ae-44dd-9846-966ebd500361 · outbound

This paper cites Williams, Ioannis G.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Williams, Ioannis G

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-05T10:20:42.467525Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c03011dd-af52-4ac7-a471-ed5f096ef6a6 · outbound

This paper cites Williams, Clarence W.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Williams, Clarence W

Reference 40

Resolution: malformed identifier; no resolver link, observed 2026-08-05T10:20:42.472179Z

Source-reported events for the cited work

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Observation 00f462e8-193f-4bfb-9a06-e6002f79162c · outbound

This paper cites A Data-Driven Framework for Koopman Semigroup Estimation in Stochastic Dynamical Systems.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups A Data-Driven Framework for Koopman Semigroup Estimation in Stochastic Dynamical Systems

Reference 41

Resolution: verified exact; local_arxiv, observed 2026-08-05T10:20:42.562421Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 6f15877f-c4fb-47eb-a497-0d096af7602d · outbound

This paper cites Reskoopnet: Learning koopman representations for complex dynamics with spectral residuals.

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups Reskoopnet: Learning koopman representations for complex dynamics with spectral residuals

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:20:42.883382Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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