Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-04T07:34:45.477143Z
Paper Citation Record · LEDGER
As of 7 August 2026, this Paper Citation Record lists 67 of 67 outbound references and 0 inbound Pith citation observations for arXiv:2510.25306.
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 2026-08-04T07:34:45.477143Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
67 of 67 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 4b68c47a-18e3-4165-a155-bd3b75ef4acb · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 1
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Observation 8f47c0ad-c917-4728-b8a2-c9a70f1143a7 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 2
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Observation 5658fb36-55de-4db0-a41c-72cd99d160ef · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 3
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Observation 4bff545f-f71e-4e33-8a7f-5ee0ce1b7d86 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 4
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Observation 2b92c971-88d8-472e-8af8-1cd95b80dadf · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 5
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Observation 90b43786-77fa-4dfc-800d-122c032c91b1 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Frey, E
Reference 6
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Observation 2b8c0392-e998-47cb-877b-904c176acbf2 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 7
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Observation 61e7621f-de6b-4037-97fb-872ada6bb623 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics P-SV wave propagation in heterogeneous media: velocity-stress finite-difference method
Reference 8
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Observation d9545ea9-c493-4a3d-a5dc-f793b5277210 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Vese, A
Reference 9
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Observation d4b950d8-daee-4f43-889e-eda63e4eee1b · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics B., Brantingham, P
Reference 10
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Observation 095827d2-64e8-4e04-a5ab-41a26705c8a7 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 11
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Observation e0fb3c8d-4943-41e0-8c5c-b50afda34292 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 12
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Observation 31e3f784-c1b9-4f6f-9887-04a76233d4e0 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 13
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Observation 0efdac3e-78d2-40d6-a24a-df2aab8de18e · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 14
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Observation 3a45f1f1-aae6-4ef6-aecf-efbdb914513f · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 15
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Observation eb520099-b016-410f-8ab8-5f34e71bc154 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 16
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Observation e4aa57a4-c264-492a-b86b-0aded10fe66f · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Non-equilibrium statistical mechanics (Courier Dover Publications, 2017)
Reference 17
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Observation e4c634f0-10ab-40ae-a485-d30d3338c559 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 18
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Observation b2eb6c51-ed36-49da-8e4e-fe43c2cb9961 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Lectures on phase transitions and the renormalization group (CRC Press, 2018)
Reference 19
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Observation 4d81f198-9e23-43e8-ace7-5fdc751467d9 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 20
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Observation 57a905d1-e829-4e53-9bfc-1f72d01a5403 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 21
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Observation 1c1206ee-4729-4304-b404-2058f0e27e3b · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 22
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Observation 17e98fdc-f24a-4afd-8a5a-4b72ab07ba2c · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 23
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Observation 09aea0a5-9cc3-4750-967a-89142f9dd3d0 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics N., Brunton, S
Reference 24
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Observation 99c388f8-e31d-4e00-92ce-a73996e981f5 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 25
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Observation 2880a322-eb2f-4ac4-9d0b-d2b1a39a3df2 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Weinan, E
Reference 26
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Observation cc47a3b6-ccf7-4854-9a6a-9aef2811eb22 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Dong, B
Reference 27
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Observation 0e00c47e-f9ca-4ea7-80fa-48afd3b872e8 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Brunton, S
Reference 28
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Observation ac8577c6-bebf-44c7-9f28-ae64e82b4d90 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics R., Siboni, N
Reference 29
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Observation f4f0978d-e8d6-4989-8d2f-14d6e3f0bb8c · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics L., Proctor, J
Reference 30
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Observation ee32a284-6366-4f4b-b02a-1065cc4a41c6 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Karniadakis, G
Reference 31
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Observation 7db66a76-4b1e-4e70-8b6c-a37c082cc705 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 32
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Observation 3d7083eb-a2c5-402e-9177-5d7bcca1cdaa · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 33
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Observation bb92baac-3165-40a2-8374-dc7a20cfdcdc · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Karniadakis, G
Reference 34
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Observation 78931107-e70f-4059-a563-b392073bdb8b · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Luo , T
Reference 35
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Observation 32dd3512-af12-4282-ad68-4aa67ba76833 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 36
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Observation 465663c3-a625-4070-894a-658acfa048e6 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 37
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Observation ce9d495a-0731-40b9-a9e9-14fadf55b6c8 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 38
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Observation 1c0013b5-a37c-491d-8cc1-a6094e4dee26 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Karniadakis, G
Reference 39
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Observation 3f1fbf50-8ff0-4cf8-85c6-e3838d155144 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 41
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Observation 4d228b44-e05b-496f-ba9c-358f09332e55 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 42
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Observation ce954999-93bf-4120-8100-50d5581b780b · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Karniadakis, G
Reference 43
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Observation 1eba307f-f261-4764-a304-e94e901ee9aa · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Karniadakis, G
Reference 44
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Observation b6af642e-ed85-42ca-a0e5-b0df2591d348 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 45
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Observation f3503e1f-1897-4817-adb4-c090b4c00227 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 46
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Observation aa058c47-f9dc-4562-8520-9dd0392304d8 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Phase-field models in materials science
Reference 47
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Observation f9d50d28-d65b-451b-bd1e-b051d6aa0ad7 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics A., Schulte, A., Allen, T
Reference 49
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Observation 4e7e6904-cd10-4c59-959e-d0731676f858 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Zhang, Y .-C
Reference 50
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Observation ddaf28fe-a46f-401e-bb8c-977adfe9e7bd · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics D., Braatz, R
Reference 51
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Observation 521aab2c-ecfb-4899-9b1f-20721311e48c · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 52
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Observation 608af712-b9f1-439d-b284-7328052ee2fc · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics B., Loukas, A
Reference 53
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Observation 5f827a58-ce85-4cb8-ac77-87d607eefc26 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 54
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Observation e0f067a3-5790-4c1f-b05d-79f448726dbd · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Kutyniok, G
Reference 55
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Observation a81226d3-57a5-4beb-af82-56b4889e0b97 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 56
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Observation 65e534d9-0447-45dc-b249-dd3c6035932c · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics H., Brunton, S
Reference 57
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Observation e012b44e-1a33-41c1-b409-9d5bd798ebf9 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Pappu, R
Reference 58
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Observation a68eade2-c653-4ca6-8448-3e2c37fcbd6d · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 59
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Observation 08e63263-37e4-43aa-b3bb-fcf2f0b5dd52 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Furthermore, in the implementation of AFNO, the Fourier attention layer introduces some tricks
Reference 60
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Observation 0cfbbaf1-06eb-457d-bfeb-e2b012239a0a · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Physics-encoded Recurrent Convolut ional Neural Network (PeRCNN)
Reference 61
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Observation 7c33f490-7e72-4ec3-a2df-fadb6714d69f · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers
Reference 62
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Observation e2cc3128-c780-49a6-a53c-42a9478fe27c · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 63
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Observation 04a5e46a-8ce0-4751-8663-420f90198b6e · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 64
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Observation 0a274574-78b7-40ab-8fca-36e948fa722e · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 65
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Observation 888de41d-7673-4990-b4ce-30d60b366871 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics L., Proctor, J
Reference 66
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Observation 37ee228e-4dfb-4b68-a3b1-838d07bc7988 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics H., Brunton, S
Reference 67
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Observation 279207c3-9a50-4da5-8c81-82f9354514c3 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 68
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Observation 7343ec24-a029-4354-9eeb-0bf3a6ead052 · outbound
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work
Reference 69
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No inbound Pith citation observations are available.