Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T16:50:43.311167Z
Paper Citation Record · LEDGER
As of 17 August 2026, this Paper Citation Record lists 58 of 58 outbound references and 2 inbound Pith citation observations for arXiv:2508.20339.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T16:50:43.311167Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-05T10:20:42.389239Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-05T10:20:42.608102Z
58 of 58 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 7e07f813-1213-4043-8bb6-f38be951749a · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Barbara, T
Reference 1
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 d7d7064d-f916-4f6a-9667-29b8285a3423 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions An overview on deep learning-based approximation methods for partial differential equations
Reference 2
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c6f6b716-7dfb-441a-9b4a-3ffe45bbf116 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Unresolved cited work
Reference 3
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 5f6ef079-2948-4f24-9db9-2c9a57d709ab · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Unresolved cited work
Reference 4
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 7f0f0bff-0c93-40fe-a1a9-606c1ba79513 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Modern Koopman Theory for Dynamical Systems
Reference 5
Source-reported events for the cited work
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Observation 089764c1-6629-4ea6-a858-61ad6abeaa5a · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Budiˇsi´c, R
Reference 6
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 15a4a75b-fb90-4a76-ae65-bb701a798f8a · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Unresolved cited work
Reference 7
Source-reported events for the cited work
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Observation c6dd4711-2ec5-432e-8e2e-d44bef089a58 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Unresolved cited work
Reference 8
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 ed54fa82-13b2-4cd9-b404-b7b47d8679d4 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions ˇCrnjari´c-ˇZic, S
Reference 9
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 69b88272-782f-4cd5-b36b-0458b2fa0469 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Cuomo, V
Reference 10
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 8fc51163-67ca-42a1-9733-5f95be0f37c5 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions An efficient data-driven solver for Fokker-Planck equations: algorithm and analysis
Reference 11
Source-reported events for the cited work
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Observation 49e86bf3-2603-4097-9c10-36c08b0fea91 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Dobson, Y
Reference 12
Source-reported events for the cited work
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Observation d017d2b0-c9cf-4faf-ab39-bd0a38d32f20 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Unresolved cited work
Reference 13
Source-reported events for the cited work
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Observation a46c2845-1da8-4011-89c5-283c034c36b7 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Stationary Density Estimation of It\^o Diffusions Using Deep Learning
Reference 14
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 355480fb-8870-4b7f-96cc-4ff69460f335 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Han and J
Reference 15
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0676b3b6-7180-494f-82aa-6131e8ded735 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Unresolved cited work
Reference 16
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 c5fbe8b1-663e-44de-975b-983c099ce2d7 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Heinlein, A
Reference 17
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 d1b747f7-20ae-4ae4-b93d-3932937f6113 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Generalized dynamical phase reduction for stochastic oscillators
Reference 18
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 c65678f6-83be-438e-9f69-1ceddf23e5e7 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Hua and T
Reference 19
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 d2d5e0a0-91fb-4132-8443-150074ae0259 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Huang, M
Reference 20
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 fbbaa14a-4af0-4765-b192-b67b685cef6f · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Unresolved cited work
Reference 21
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 c4403ad3-ba1f-4e04-9a74-0d6a36740e1b · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Unresolved cited work
Reference 22
Source-reported events for the cited work
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Observation 50b45068-5094-4c84-ab0f-ffcb8164deb0 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Unresolved cited work
Reference 23
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 9a814150-42b4-4032-a564-fff676d1bd8d · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Unresolved cited work
Reference 24
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 389ceeb8-106b-45f3-9a0e-7150f9c810f7 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Adam: A Method for Stochastic Optimization
Reference 25
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 86c8d53d-d89a-4023-a933-e5cb849a84f4 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Korda and I
Reference 26
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 99327d01-ee49-4ec9-84a1-87d3f3aea6ce · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Korda and I
Reference 27
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 25fca51c-9f09-48b3-8af8-5e0ab8367799 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Korda, M
Reference 28
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 037e7118-8a2f-4b70-bfc5-d1dd50850a57 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions $Q$-functions, synchronization, and Arnold tongues for coupled stochastic oscillators
Reference 29
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 d5a7dcea-a639-4cee-a237-95415a74e2e0 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Laroche, The use of the matrix pencil method for the spectrum analysis of musical signals, The Journal of the Acoustical Society of America, 94 (1993), pp
Reference 30
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 d32c1182-58d9-4709-8d33-2e23ea5bb9df · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions A data-driven method for the steady state of randomly perturbed dynamics
Reference 31
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 09ccf415-7c73-43db-a50c-b580c69d3cd2 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Li and Y
Reference 32
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b4560fec-8218-4f3f-ab6d-1d32faaca0d8 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Unresolved cited work
Reference 33
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 daaf687c-a98d-4cb6-a756-77454658164e · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Melland and R
Reference 34
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 555416b8-1aea-492a-9ca1-2235fd604f13 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Mezi´c, Spectral properties of dynamical systems, model reduction and decompositions , Nonlinear Dy- namics, 41 (2005), pp
Reference 35
Source-reported events for the cited work
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Observation 24888e6f-261c-4202-8699-878c0ee2b447 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Mezi´c, Analysis of fluid flows via spectral properties of the koopman operator , Annual review of fluid mechanics, 45 (2013), pp
Reference 36
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 da401d81-5978-41d4-b51f-d5b926dbdd99 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Mezi´c, On numerical approximations of the koopman operator , Mathematics, 10 (2022), p
Reference 37
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 c6456684-1a93-47c2-ae30-5c8da5890205 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Unresolved cited work
Reference 38
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 9c13fd86-28a5-4ee0-a185-29404e84a8f7 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Unresolved cited work
Reference 39
Source-reported events for the cited work
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Observation 77dc0925-91eb-4aa3-8063-5018edb858a6 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions A Universal Description of Stochastic Oscillators
Reference 40
Source-reported events for the cited work
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Observation 6b310d54-741e-479c-ae91-16c1686d1cf5 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions P ´erez-Cervera, B
Reference 41
Source-reported events for the cited work
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Observation 94c052ec-1f66-4c3f-97fb-14d4fa1d1fd0 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Raissi, P
Reference 42
Source-reported events for the cited work
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Observation 365506da-d073-4dcd-b7fa-06a4614c56d7 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Risken and H
Reference 43
Source-reported events for the cited work
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Observation 1ffbdae4-e8b2-45cb-b254-fa3116457954 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Unresolved cited work
Reference 44
Source-reported events for the cited work
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Observation c575ce3b-ce6f-4b3e-b391-b627fe7e88e5 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Unresolved cited work
Reference 45
Source-reported events for the cited work
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Observation df24ed86-ae74-4f8e-9979-ff7d786e15cd · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Sch¨atzle, J
Reference 46
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 b2a7847c-f51b-46b9-a62b-9a0737473fbb · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Unresolved cited work
Reference 47
Source-reported events for the cited work
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Observation d6bd85d4-f61e-49ae-bdc4-0ceb7586ca55 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Unresolved cited work
Reference 48
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 d2e4cb5d-691a-4ea5-ae1d-845ec9ac712b · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Sirignano and K
Reference 49
Source-reported events for the cited work
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Observation 03547bad-e76d-4e0b-8902-a6d81d49687e · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Takahashi, Y
Reference 50
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 d3d067df-1d74-45d7-82b4-0a89797be21a · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Unresolved cited work
Reference 51
Source-reported events for the cited work
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Observation 8e0658e7-15a4-45ff-8e5d-f2529d3ddf83 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Unresolved cited work
Reference 52
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 c8e36b42-64f6-4f0f-b66e-a0cb083729d7 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Tsuchida, Control variate method for deep bsde solver using weak approximation , Asia-Pacific Finan- cial Markets, 30 (2023), pp
Reference 53
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 90168c2b-e40f-48e8-b4cb-b531012a3d01 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Weinan, J
Reference 54
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 f55b64d2-3b7e-40ce-94ef-1f73ad4d8500 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Unresolved cited work
Reference 55
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 25ea5f50-3970-40b9-bd90-e888af0213b7 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions A Data-Driven Framework for Koopman Semigroup Estimation in Stochastic Dynamical Systems
Reference 56
Source-reported events for the cited work
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Observation 58baec05-84a6-44ab-b583-4f43813d85da · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Unresolved cited work
Reference 57
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 8369ce25-1fdc-4895-94da-efdb0fe6eb60 · outbound
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions Zhao and L
Reference 58
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 127c7162-524a-4898-b3bf-73e574c0385f · inbound
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
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 10ba2764-a81c-4d1c-86e1-71c60438e593 · inbound
Robust topological oscillators govern a tunable phase transition to synchronized circadian rhythms Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions
Reference 24
Source-reported events for the cited work
Unavailable: canonical work link unavailable.