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Paper Citation Record · LEDGER

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics

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.

pith.paper-citation-record.v1
2510.25306 v3

Coverage vector

measured 67 of 67 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T07:34:45.477143Z

measured 67 of 67 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

67 of 67 outbound references displayed

  • verified exact0
  • verified fuzzy0
  • unresolved67
  • parse uncertain0
  • malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 4b68c47a-18e3-4165-a155-bd3b75ef4acb · outbound

This paper cites an unresolved cited work.

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

This paper cites an unresolved cited work.

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

This paper cites an unresolved cited work.

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

This paper cites an unresolved cited work.

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

This paper cites an unresolved cited work.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work

Reference 5

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source=pdf_text observed=2026-08-04T07:34:38.932110Z digest=sha256:ca333c3d049d64ff5cd8a7d1dfcdf0bb6aa6451befe13094bc554a5f1e13812a

Observation 90b43786-77fa-4dfc-800d-122c032c91b1 · outbound

This paper cites & Frey, E.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Frey, E

Reference 6

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no resolver link, observed 2026-08-04T07:34:39.062421Z

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Observation 2b8c0392-e998-47cb-877b-904c176acbf2 · outbound

This paper cites an unresolved cited work.

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

This paper cites P-SV wave propagation in heterogeneous media: velocity-stress finite-difference method.

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

This paper cites & Vese, A.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Vese, A

Reference 9

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Observation d4b950d8-daee-4f43-889e-eda63e4eee1b · outbound

This paper cites B., Brantingham, P.

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

This paper cites an unresolved cited work.

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

This paper cites an unresolved cited work.

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

This paper cites an unresolved cited work.

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

This paper cites an unresolved cited work.

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

This paper cites an unresolved cited work.

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

This paper cites an unresolved cited work.

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

This paper cites Non-equilibrium statistical mechanics (Courier Dover Publications, 2017).

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

This paper cites an unresolved cited work.

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

This paper cites Lectures on phase transitions and the renormalization group (CRC Press, 2018).

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

This paper cites an unresolved cited work.

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

This paper cites an unresolved cited work.

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

This paper cites an unresolved cited work.

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

This paper cites an unresolved cited work.

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

This paper cites N., Brunton, S.

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

This paper cites an unresolved cited work.

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

This paper cites & Weinan, E.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Weinan, E

Reference 26

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Observation cc47a3b6-ccf7-4854-9a6a-9aef2811eb22 · outbound

This paper cites & Dong, B.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Dong, B

Reference 27

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Observation 0e00c47e-f9ca-4ea7-80fa-48afd3b872e8 · outbound

This paper cites & Brunton, S.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Brunton, S

Reference 28

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Observation ac8577c6-bebf-44c7-9f28-ae64e82b4d90 · outbound

This paper cites R., Siboni, N.

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

This paper cites L., Proctor, J.

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

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Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Karniadakis, G

Reference 31

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Observation 7db66a76-4b1e-4e70-8b6c-a37c082cc705 · outbound

This paper cites an unresolved cited work.

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

This paper cites an unresolved cited work.

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

This paper cites & Karniadakis, G.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Karniadakis, G

Reference 34

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Observation 78931107-e70f-4059-a563-b392073bdb8b · outbound

This paper cites & Luo , T.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Luo , T

Reference 35

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Observation 32dd3512-af12-4282-ad68-4aa67ba76833 · outbound

This paper cites an unresolved cited work.

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

This paper cites an unresolved cited work.

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

This paper cites an unresolved cited work.

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

This paper cites & Karniadakis, G.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Karniadakis, G

Reference 39

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Observation 3f1fbf50-8ff0-4cf8-85c6-e3838d155144 · outbound

This paper cites an unresolved cited work.

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

This paper cites an unresolved cited work.

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

This paper cites & Karniadakis, G.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Karniadakis, G

Reference 43

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Observation 1eba307f-f261-4764-a304-e94e901ee9aa · outbound

This paper cites & Karniadakis, G.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Karniadakis, G

Reference 44

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Observation b6af642e-ed85-42ca-a0e5-b0df2591d348 · outbound

This paper cites an unresolved cited work.

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

This paper cites an unresolved cited work.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work

Reference 46

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source=pdf_text observed=2026-08-04T07:34:43.742584Z digest=sha256:9bb59953bcb3cc7bc5cff9448cefc9c164df92b1d7a499ad064d599e2a2183fe

Observation aa058c47-f9dc-4562-8520-9dd0392304d8 · outbound

This paper cites Phase-field models in materials science.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Phase-field models in materials science

Reference 47

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source=pdf_text observed=2026-08-04T07:34:43.849462Z digest=sha256:cdaca9fefe3cb4c9f836f5b13c1d0520b2bc919baf99e0f89b33bff5dc6f5ff7

Observation f9d50d28-d65b-451b-bd1e-b051d6aa0ad7 · outbound

This paper cites A., Schulte, A., Allen, T.

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

This paper cites & Zhang, Y .-C.

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

This paper cites D., Braatz, R.

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

This paper cites an unresolved cited work.

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

This paper cites B., Loukas, A.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics B., Loukas, A

Reference 53

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source=pdf_text observed=2026-08-04T07:34:44.556476Z digest=sha256:0f03413eaa524af9346f54921b16dcde1232c36bafd83b5a26d1a3f09c612cbb

Observation 5f827a58-ce85-4cb8-ac77-87d607eefc26 · outbound

This paper cites an unresolved cited work.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work

Reference 54

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source=pdf_text observed=2026-08-04T07:34:44.669740Z digest=sha256:6f947f04c223a7c83b87f165a056384b87cfd72460e92dbede0537419b080dc3

Observation e0f067a3-5790-4c1f-b05d-79f448726dbd · outbound

This paper cites & Kutyniok, G.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Kutyniok, G

Reference 55

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Observation a81226d3-57a5-4beb-af82-56b4889e0b97 · outbound

This paper cites an unresolved cited work.

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

This paper cites H., Brunton, S.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics H., Brunton, S

Reference 57

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source=pdf_text observed=2026-08-04T07:34:44.920876Z digest=sha256:e9c1b1e165aa3696530ff3ad8c649aca3bdbbba22a27b2a95acc14b2a584dd8c

Observation e012b44e-1a33-41c1-b409-9d5bd798ebf9 · outbound

This paper cites & Pappu, R.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics & Pappu, R

Reference 58

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Observation a68eade2-c653-4ca6-8448-3e2c37fcbd6d · outbound

This paper cites an unresolved cited work.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work

Reference 59

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source=pdf_text observed=2026-08-04T07:34:45.002431Z digest=sha256:72a14c856a8ae809eef84545c7829a1931f511518a6ee2a579b552c5534332db

Observation 08e63263-37e4-43aa-b3bb-fcf2f0b5dd52 · outbound

This paper cites Furthermore, in the implementation of AFNO, the Fourier attention layer introduces some tricks.

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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source=pdf_text observed=2026-08-04T07:34:45.043694Z digest=sha256:e87aa8235a0fc1e0c1b7481bdbc1af73e5295e6a4ae46d45a15646c3ede5d58c

Observation 0cfbbaf1-06eb-457d-bfeb-e2b012239a0a · outbound

This paper cites Physics-encoded Recurrent Convolut ional Neural Network (PeRCNN).

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Physics-encoded Recurrent Convolut ional Neural Network (PeRCNN)

Reference 61

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source=pdf_text observed=2026-08-04T07:34:45.088854Z digest=sha256:490a2a1200fcf883bea8e9411453a1ef9bab7199a003c5b01eed6d313db2e4f9

Observation 7c33f490-7e72-4ec3-a2df-fadb6714d69f · outbound

This paper cites Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers

Reference 62

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source=pdf_text observed=2026-08-04T07:34:45.133380Z digest=sha256:b045cce7ab364ec67e4cf2b3ce93e9895d9651aa3953648f375bf5f05be1827c

Observation e2cc3128-c780-49a6-a53c-42a9478fe27c · outbound

This paper cites an unresolved cited work.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work

Reference 63

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source=pdf_text observed=2026-08-04T07:34:45.176185Z digest=sha256:3f909eabe146521b6760399f354db6c73255304c55942a46a6e0d5330ccf7ffb

Observation 04a5e46a-8ce0-4751-8663-420f90198b6e · outbound

This paper cites an unresolved cited work.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work

Reference 64

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source=pdf_text observed=2026-08-04T07:34:45.235946Z digest=sha256:c5899faf39a7a443d3aa0886a1afa03ee36b918e2ea91591ebeac9c3a1d46f92

Observation 0a274574-78b7-40ab-8fca-36e948fa722e · outbound

This paper cites an unresolved cited work.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work

Reference 65

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source=pdf_text observed=2026-08-04T07:34:45.283738Z digest=sha256:fac04271546921143138d327d8cbb8609a1d1e821d0a6132df40c49adbc4627d

Observation 888de41d-7673-4990-b4ce-30d60b366871 · outbound

This paper cites L., Proctor, J.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics L., Proctor, J

Reference 66

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source=pdf_text observed=2026-08-04T07:34:45.336283Z digest=sha256:2ddb61b5c82182826b54a88fc7d574394f1ccc79e5acf9db65da42f38c22c5f1

Observation 37ee228e-4dfb-4b68-a3b1-838d07bc7988 · outbound

This paper cites H., Brunton, S.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics H., Brunton, S

Reference 67

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source=pdf_text observed=2026-08-04T07:34:45.375442Z digest=sha256:84054b0c3f9d301bb44a1e73fca55ced47100976abe9a8ce7625775dac1602b7

Observation 279207c3-9a50-4da5-8c81-82f9354514c3 · outbound

This paper cites an unresolved cited work.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work

Reference 68

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source=pdf_text observed=2026-08-04T07:34:45.420385Z digest=sha256:dae7359a120d215a71bc5289b60898db5a29d2c2bcc4f8a5c3e6fa1a0109f4e7

Observation 7343ec24-a029-4354-9eeb-0bf3a6ead052 · outbound

This paper cites an unresolved cited work.

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics Unresolved cited work

Reference 69

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source=pdf_text observed=2026-08-04T07:34:45.477143Z digest=sha256:5065ef57bccdd0f928aa146a699d86815d6b943c87eeb924face93c18564d4a8

Pith citing papers

No inbound Pith citation observations are available.