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Paper Citation Record · LEDGER

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model

As of 9 August 2026, this Paper Citation Record lists 53 of 53 outbound references and 2 inbound Pith citation observations for arXiv:2509.01293.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2509.01293 v3

Coverage vector

measured 53 of 53 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T12:48:34.698218Z

measured 55 of 55 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-13T08:47:34.631129Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-11T00:20:51.556917Z

Reference resolution

53 of 53 outbound references displayed

  • verified exact3
  • verified fuzzy36
  • unresolved14
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f67b93d3-00f7-43cc-8385-a4add1b5eaa9 · outbound

This paper cites Anderson, G.B.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Anderson, G.B

Reference 1

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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Observation d8ea54ea-9097-45e2-a44d-5a3e945cf158 · outbound

This paper cites an unresolved cited work.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Unresolved cited work

Reference 2

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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Observation f9ad1f7a-099e-4cdb-974f-1fb08e68f922 · outbound

This paper cites Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks

Reference 3

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source=pdf_text observed=2026-08-05T12:48:25.569319Z digest=sha256:d3573d764ddd440130e94f8d0da3cb71a6c965ea88cd367823f2a2135ddb4c85

Observation f1b8d73f-b8b2-41d3-aca0-ab29e8a1021c · outbound

This paper cites an unresolved cited work.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Unresolved cited work

Reference 4

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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Observation 5b13bc19-8a08-4159-bc34-e74d2656f35e · outbound

This paper cites Cahn and J.E.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Cahn and J.E

Reference 5

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Observation f47c928c-9ffa-45df-9d09-aa73dc5d9ac2 · outbound

This paper cites Gurtin, D.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Gurtin, D

Reference 6

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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Observation 7265d98e-b76c-4ee3-93f7-ab9bb23cd0db · outbound

This paper cites Lowengrub and L.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Lowengrub and L

Reference 7

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Observation ae719275-ac3f-41d3-8e7c-bbcfadab4c6b · outbound

This paper cites ten Eikelder, K.G.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model ten Eikelder, K.G

Reference 8

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source=pdf_text observed=2026-08-05T12:48:26.510329Z digest=sha256:f1b3f72b413dfe2380f736c43e63c866f9eca90df0c99080a138e0742becbc72

Observation 753cb57e-6448-4995-b28a-d9793d9e6bd3 · outbound

This paper cites Abels, H.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Abels, H

Reference 9

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:26.711750Z digest=sha256:00655b6e0d87603c5f1ac412cb25be67b92fcbaf9955c2cef545384b10ed8edb

Observation 1397c44a-58f0-40eb-a2b1-09b8bc485ee9 · outbound

This paper cites AunifiedframeworkforN-phaseNavier–StokesCahn–HilliardAllen–Cahnmixture models with non-matching densities.Journal of Fluid Mechanics, 1013:A26, 2025.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model AunifiedframeworkforN-phaseNavier–StokesCahn–HilliardAllen–Cahnmixture models with non-matching densities.Journal of Fluid Mechanics, 1013:A26, 2025

Reference 10

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Observation 8dd42cf5-99ca-4063-8838-45df348fd602 · outbound

This paper cites A Thermodynamically Consistent Free Boundary Model for Two-Phase Flows in an Evolving Domain with Bulk-Surface Interaction.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model A Thermodynamically Consistent Free Boundary Model for Two-Phase Flows in an Evolving Domain with Bulk-Surface Interaction

Reference 11

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local_arxiv, observed 2026-08-05T12:48:35.713797Z

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source=pdf_text observed=2026-08-05T12:48:27.089614Z digest=sha256:ced5c6a4d8a1820a3ee5e01d388b2043d92629ccacdc4438beb49f0f9b384e9b

Observation 123bcad3-15b8-4508-aa83-ec5bee696881 · outbound

This paper cites Compressible N-phase fluid mixture models.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Compressible N-phase fluid mixture models

Reference 12

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Source-reported events for the cited work

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source=pdf_text observed=2026-08-05T12:48:27.242069Z digest=sha256:e04dc19186abbc9f7e5850e32c35dc6338bb0fb909112acf8f609ef331209834

Observation 4b7784b6-41b0-41ba-b6d2-a4a4eb1696f2 · outbound

This paper cites Kay and R.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Kay and R

Reference 13

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:27.402413Z digest=sha256:771e4de28e970688d1397a976b25fa5bab1b5a525597109d372aaf49e09aea20

Observation e7dd942f-8d6d-486c-ace6-e0c8703b35c7 · outbound

This paper cites Minjeaud.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Minjeaud

Reference 14

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:27.627845Z digest=sha256:32185a45b9020748bfc09d2f96d8bab21832579d9c116d40c0a90676591ba94b

Observation 6b25536b-731f-43b2-9976-c42ee74194c6 · outbound

This paper cites ten Eikelder and D.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model ten Eikelder and D

Reference 15

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raw_fallback, observed 2026-08-05T12:48:44.586211Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:27.833541Z digest=sha256:00c1899fbaa2149c2443676ddacf5d6d11d5e6ec91fae209db67c14f1164c2a8

Observation ce40a024-5926-472d-9c96-86bc70e97ed6 · outbound

This paper cites Garcke and S.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Garcke and S

Reference 16

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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Observation b225edfc-8fc4-49fe-a339-5e8d7537c875 · outbound

This paper cites Ebenbeck and H.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Ebenbeck and H

Reference 17

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:28.204054Z digest=sha256:7aae4855a589ee2292eb1361ef12f774e7a75b1ea7e9b550b891729b08b98314

Observation 94cca9d3-1e4b-4ed4-bf90-c3e9d35268b3 · outbound

This paper cites Bertozzi, S.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Bertozzi, S

Reference 18

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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Observation 9f3c3b8b-28f1-4a09-959f-1cfae4a78a11 · outbound

This paper cites Khain and L.M.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Khain and L.M

Reference 19

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:28.578495Z digest=sha256:24104c2a661661f1aaaddd1ea8709e1d0afc2f4442a230bcfeb496a5621ad726

Observation 5a9e26cb-9f53-4626-abfa-12d9d3beebc3 · outbound

This paper cites Elson, E.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Elson, E

Reference 20

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:28.764619Z digest=sha256:8e63a71802c5cd355ef9d08e1fe3c4b3dbf769e2f60598addd3440e2db276511

Observation 9f8a4b66-76ff-4328-9e26-cc0bb09352a9 · outbound

This paper cites Berry, C.P.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Berry, C.P

Reference 21

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Observation 74ea4108-5227-448c-b400-a5fd32224e14 · outbound

This paper cites Brown, B.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Brown, B

Reference 22

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source=pdf_text observed=2026-08-05T12:48:29.140277Z digest=sha256:8b96f23e4e8c58862221054bc278cb065f25b732d8bd93308ad02fc1df01f056

Observation ba098b36-3cd7-4f8b-80a1-b8bc22055260 · outbound

This paper cites Voulodimos, N.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Voulodimos, N

Reference 23

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:29.273464Z digest=sha256:5dae1a69829745a0191b008dae357d858a863b2e7de8dc9d59a49bb4777f6b4c

Observation fb1a18d8-a17c-4d3c-a5fa-245e1881e1cb · outbound

This paper cites Ding.Data-driven design of fault diagnosis and fault-tolerant control systems.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Ding.Data-driven design of fault diagnosis and fault-tolerant control systems

Reference 24

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source=pdf_text observed=2026-08-05T12:48:29.398351Z digest=sha256:05d2edf257b57942e32ea22652aee06d6582a3486741a5909e47872efbbf6390

Observation a3c1b4c1-0454-410b-b29d-bf4515b49c5e · outbound

This paper cites Brunton, B.R.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Brunton, B.R

Reference 25

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source=pdf_text observed=2026-08-05T12:48:29.580983Z digest=sha256:0e6468668742292137dc1afe46aa7dfd544a2f8bef6cdeede92a64a2f346351c

Observation 242eacce-bbad-4457-a6ec-3d0b39f785fb · outbound

This paper cites Karniadakis, I.G.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Karniadakis, I.G

Reference 26

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:29.822042Z digest=sha256:f1b891bc34c7ec5e09901b0881622fb02d7da5eeba207deb712531d61bde30f3

Observation f3c543af-3920-4773-aa1d-2afd02c56a24 · outbound

This paper cites Cheng, M.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Cheng, M

Reference 27

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source=pdf_text observed=2026-08-05T12:48:29.997787Z digest=sha256:d9ab929625a57446e04d862e8aedd61cdd597cd3053417a05b00b9c66f3de61b

Observation ae72998c-6827-419d-aa7b-37f25c9de35a · outbound

This paper cites Quantum-Informed Machine Learning for Predicting Spatiotemporal Chaos with Practical Quantum Advantage.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Quantum-Informed Machine Learning for Predicting Spatiotemporal Chaos with Practical Quantum Advantage

Reference 28

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local_arxiv, observed 2026-08-05T12:48:35.304782Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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Observation 88926a09-ae18-4c74-a27e-fb61fa7f9e73 · outbound

This paper cites Fukami, Y.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Fukami, Y

Reference 29

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raw_fallback, observed 2026-08-05T12:48:42.872778Z

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source=pdf_text observed=2026-08-05T12:48:30.203839Z digest=sha256:2a39715f4b8a4e6a17f1d0944a015679fec048060b40c649d10370a5d827b0a4

Observation 73431e09-d46e-4b44-8747-f6f75311c9e4 · outbound

This paper cites Xue, H.-D.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Xue, H.-D

Reference 30

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raw_fallback, observed 2026-08-05T12:48:42.701514Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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Observation 45749cfb-9e62-422d-93d2-f0c56bede874 · outbound

This paper cites an unresolved cited work.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Unresolved cited work

Reference 31

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raw_fallback, observed 2026-08-05T12:48:42.513303Z

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Observation 80bf934f-3b74-4067-914b-4c95fd290cdb · outbound

This paper cites an unresolved cited work.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Unresolved cited work

Reference 32

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raw_fallback, observed 2026-08-05T12:48:42.231361Z

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source=pdf_text observed=2026-08-05T12:48:30.722278Z digest=sha256:406de87a00ae4b7b8bda08750c6df4e57dfd06e80beea57ab1eed58e5fc108ff

Observation 7d6e9afe-640f-4215-9f2f-a92b8bf7264a · outbound

This paper cites Cheng, F.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Cheng, F

Reference 33

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raw_fallback, observed 2026-08-05T12:48:41.932716Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:30.905684Z digest=sha256:27d8647d333756eb6f062a48d6780f1583e5a1b019cfb2e47f27d2640ff6c7da

Observation c5cd1b54-2e09-4128-a3ed-ff107c0f3827 · outbound

This paper cites an unresolved cited work.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Unresolved cited work

Reference 35

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raw_fallback, observed 2026-08-05T12:48:41.616988Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:31.277471Z digest=sha256:a217f713b80fc98d7c639f44ea7ba7dbcd0244e17756c8e5608f14c3f2e480d3

Observation e17a21ef-a4db-467b-af25-bd681439a145 · outbound

This paper cites an unresolved cited work.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Unresolved cited work

Reference 36

Resolution
unresolved
raw_fallback, observed 2026-08-05T12:48:41.312447Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:31.441694Z digest=sha256:fdc0a42e496e3eade71f8f14ba05290ee7b7f58a0aa1ead211f4a070315d13ff

Observation f083d83c-b0f1-4357-a104-2291fae6c4a6 · outbound

This paper cites Shen, J.-J.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Shen, J.-J

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T12:48:41.000062Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:31.647009Z digest=sha256:76ec3467baa78de3a0ca055ed0037fa39a327da4a058b2e936d0096cfa3c0fae

Observation 6cd419b3-0541-4d5e-b2fd-0fdd521769fb · outbound

This paper cites an unresolved cited work.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Unresolved cited work

Reference 38

Resolution
unresolved
raw_fallback, observed 2026-08-05T12:48:40.588701Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:31.793797Z digest=sha256:026e4f1fda441b3118c8c34d28817739eca33b576b93a0afbd94994e559ae41f

Observation 7c48df84-0b2f-4c81-8888-399841a9dee9 · outbound

This paper cites Teichert, A.R.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Teichert, A.R

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T12:48:40.274235Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:31.950137Z digest=sha256:8f6a9ca5be441529c1420870a95f10da959d335bd2ea10093de2f5519dde6f2f

Observation f6c3c5d7-4599-4840-a283-c9eebf00f33a · outbound

This paper cites Oommen, K.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Oommen, K

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T12:48:39.957625Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:32.128281Z digest=sha256:ef63109cdc0c69c07db03d3f784a93472d2df58aaf8531dd7caefb6241bd66ca

Observation bd2cfa5f-7153-4ada-8d4d-064cadadeb74 · outbound

This paper cites Cohen and M.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Cohen and M

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T12:48:39.496898Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:32.380557Z digest=sha256:cb32fcd297232f8ec506db16dbe4132f8cec19ec99c40797ac0c50f0a9e167f1

Observation 4861859c-ede4-4fb9-84a9-b768368ab89f · outbound

This paper cites Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds

Reference 42

Resolution
unresolved
no resolver link, observed 2026-08-05T12:48:32.614372Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-05T12:48:32.614372Z digest=sha256:89c2faa036c1086a33bc4446932c6585f7df0efdf3c99219596c4b3d30931b3d

Observation 4986a902-066c-4722-b035-265a176ba45a · outbound

This paper cites Schütt, O.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Schütt, O

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T12:48:39.066100Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:32.815621Z digest=sha256:2cfe619504eea39411cef7b3ced7207dc5b6751966d8581687c8abade6cd2661

Observation 9bea5b38-1e8c-4365-9093-849e4db3fee6 · outbound

This paper cites Novick-Cohen.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Novick-Cohen

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T12:48:38.716409Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:32.997873Z digest=sha256:6fda10688fa318dcf0397b55189854725f4905ce65a45b41f14c5f72ce708684

Observation 893b6e77-311d-4930-8cb8-04058ad4671b · outbound

This paper cites Kovachki, Z.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Kovachki, Z

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T12:48:38.418709Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:33.178691Z digest=sha256:d0f423b9a2aae0cb92358c23e669ede34043566743747630b4613f95b5b33cb8

Observation 22dc69ec-cd7c-4233-b43e-c4d952fb6378 · outbound

This paper cites Evans.Partial differential equations, volume 19.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Evans.Partial differential equations, volume 19

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T12:48:38.119746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:33.377270Z digest=sha256:aab6f9522fe237de1b7d1f5b801129c1ae812c4fdfc2a0957e79c8c787561ccf

Observation 71d6254c-2694-44b8-b59e-741783dd23f3 · outbound

This paper cites Fourier Neural Operator for Parametric Partial Differential Equations.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Fourier Neural Operator for Parametric Partial Differential Equations

Reference 47

Resolution
unresolved
no resolver link, observed 2026-08-05T12:48:33.546012Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-05T12:48:33.546012Z digest=sha256:35d9573ddcc31b02bb910b4d24c26258b37a7f08c7947197a5539a8485877228

Observation 618a5d3d-34f3-48bc-b4b9-6649bf27cf22 · outbound

This paper cites an unresolved cited work.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Unresolved cited work

Reference 48

Resolution
unresolved
raw_fallback, observed 2026-08-05T12:48:37.806295Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:33.731505Z digest=sha256:3c7e7a82b78b374b3eb2de31c613dece6468a06d8f3d62665fb3b14b827701a6

Observation f56c4c2e-a7e7-4d67-8d41-e82c7a699d4f · outbound

This paper cites Multi-componentCahn–Hilliardsystemwithdifferentboundaryconditions in complex domains.Journal of Computational Physics, 323:1–16, 2016.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Multi-componentCahn–Hilliardsystemwithdifferentboundaryconditions in complex domains.Journal of Computational Physics, 323:1–16, 2016

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T12:48:37.450931Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:33.870688Z digest=sha256:47f47de1239ba9659ca595de2ba3f042e75c23bea285127ebdc80fdbc822ac80

Observation 4a684a4c-5dae-4684-8efa-675bf1ce728c · outbound

This paper cites ten Eikelder, K.G.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model ten Eikelder, K.G

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T12:48:37.156669Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:34.015328Z digest=sha256:24670c15ea3465139f85d2484a728461696bbe427cbfb2cd9a9e1cb3dad3e124

Observation d4b26926-8ec5-45d9-9d8e-1de671e379b7 · outbound

This paper cites an unresolved cited work.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Unresolved cited work

Reference 51

Resolution
unresolved
raw_fallback, observed 2026-08-05T12:48:36.758257Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:34.167674Z digest=sha256:88a01014a02dd8064b9ba717bb29a0201aa96cc54f2a55345291c7de6a1b4f30

Observation b9b31c82-5801-41e1-be74-aafd4bb90e32 · outbound

This paper cites Phase-field modeling of elastic microphase separation.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Phase-field modeling of elastic microphase separation

Reference 52

Resolution
verified exact
local_arxiv, observed 2026-08-05T12:48:34.988738Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:34.320774Z digest=sha256:65cc5dde40b4b1e02f26de09a33cd898be3190b51c63492e42ab297e321b4c30

Observation 1a48f3b7-095f-4ad7-ae73-55664325fc55 · outbound

This paper cites Golovin, S.H.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Golovin, S.H

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T12:48:36.386753Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:34.525099Z digest=sha256:9b81feeaf3cca7969d6fc54d0ac3f4832e2eec157bb7e9c66a8c186fe6f1e248

Observation d3e0a9b4-2d1c-48af-8429-83ee521247af · outbound

This paper cites Balakrishna and W.C.

Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Balakrishna and W.C

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T12:48:36.098392Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-05T12:48:34.698218Z digest=sha256:f1b6665cd045253223a1408107315024c4acfee4082f3ec916bb2d41c7f52405

Pith citing papers

Observation 276f193e-f885-4c4e-858f-3938b0d6af5f · inbound

MENO: MeanFlow-Enhanced Neural Operators for Dynamical Systems cites this paper.

MENO: MeanFlow-Enhanced Neural Operators for Dynamical Systems Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model

Reference 15

Resolution
verified exact
arxiv_id, observed 2026-05-11T00:20:51.560037Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T18:36:38.674342Z digest=sha256:edbc26952b93e875a36d900e1e9943393de897384f33b8cf0487910e47f157b4

Observation 5b9d301e-df5f-484c-a005-170d7180515c · inbound

MENO: MeanFlow-Enhanced Neural Operators for Dynamical Systems cites this paper.

MENO: MeanFlow-Enhanced Neural Operators for Dynamical Systems Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model

Reference 28

Resolution
unresolved
no resolver link, observed 2026-07-13T08:47:34.631129Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-07-13T08:47:34.631129Z digest=sha256:c7c4e7c42e457252ad208ae7556d048c31fab76647e30300214d7805dd91d991