Paper Citation Record · LEDGER

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs

As of 12 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:2605.15754.

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

pith.paper-citation-record.v1
2605.15754 v1

Coverage vector

measured 41 of 41 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-19T18:55:55.093897Z

measured 41 of 41 standing notices

One-hop event checks from named stored sources.

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measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

41 of 41 outbound references displayed

verified exact30
verified fuzzy2
unresolved4
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External citation measurements

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Outbound references

Observation 3bdc58a6-a528-4e37-bff3-c4b75cc3baa9 · outbound

This paper cites an unresolved cited work.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Unresolved cited work

Reference 1

Resolution: verified exact; doi, observed 2026-05-19T18:57:43.106584Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 62432724-b3a5-4297-a4bd-6d4b37034c68 · outbound

This paper cites Kergrene, I.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Kergrene, I

Reference 2

Resolution: verified exact; doi, observed 2026-05-19T18:57:43.104539Z

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Observation a7d07e26-865f-4a93-b45f-c84f2d13edf6 · outbound

This paper cites Buchmüller, J.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Buchmüller, J

Reference 3

Resolution: verified exact; doi, observed 2026-05-19T18:57:43.116088Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e8a43119-4a95-47b9-8ea9-2d88edf01c6c · outbound

This paper cites Raissi, P.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Raissi, P

Reference 4

Resolution: verified exact; doi, observed 2026-05-19T18:57:43.114341Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation def2f601-9c54-4b59-a455-abaec3430b53 · outbound

This paper cites an unresolved cited work.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-05-19T18:57:43.391325Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1241a0d9-27fc-47a3-abce-67e86f5e875f · outbound

This paper cites an unresolved cited work.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Unresolved cited work

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-19T18:57:43.111904Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 0e665fbb-ee4c-4e8c-bec9-aacb02499006 · outbound

This paper cites Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

Reference 7

Resolution: verified exact; doi, observed 2026-05-19T18:57:43.109149Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 95869d0c-9a63-4972-9f51-3c4c25bcce21 · outbound

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

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Fourier Neural Operator for Parametric Partial Differential Equations

Reference 8

Resolution: verified exact; local_arxiv, observed 2026-05-19T18:57:43.164562Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d26eabb4-4982-4aff-bf78-c91cd7e6f43f · outbound

This paper cites Physics-Informed Neural Operator for Learning Partial Differential Equations.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-05-19T18:57:43.161744Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8375af4f-2c64-4959-a1bd-c0ca089fc807 · outbound

This paper cites Learning the solution operator of parametric partial differential equations with physics-informed DeepONets.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Learning the solution operator of parametric partial differential equations with physics-informed DeepONets

Reference 10

Resolution: verified exact; doi, observed 2026-05-19T18:57:43.081241Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 4b75cb31-5716-4530-be2a-3928c93fcf47 · outbound

This paper cites Multilingual Knowledge Graph Completion with Self-Supervised Adaptive Graph Alignment.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Multilingual Knowledge Graph Completion with Self-Supervised Adaptive Graph Alignment

Reference 11

Resolution: malformed identifier; doi_truncated, observed 2026-05-19T18:57:43.077548Z

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Observation 406605f9-9719-486c-9af6-4f41e14a5fd3 · outbound

This paper cites Arnold, F.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Arnold, F

Reference 12

Resolution: verified exact; doi, observed 2026-05-19T18:57:43.093117Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7d773e5b-54fd-4dc9-b471-ce6c43a0b8a8 · outbound

This paper cites Villadsen, W.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Villadsen, W

Reference 13

Resolution: verified exact; doi, observed 2026-05-19T18:57:43.102751Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation cc88e6f8-f1e8-4fbe-83e6-a59f1b8ac615 · outbound

This paper cites an unresolved cited work.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Unresolved cited work

Reference 14

Resolution: malformed identifier; arxiv_id, observed 2026-05-19T18:57:43.158978Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e2eb2bda-8e07-4542-93b1-d776d2a2bce7 · outbound

This paper cites MIONet: Learning Multiple-Input Operators via Tensor Product.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs MIONet: Learning Multiple-Input Operators via Tensor Product

Reference 15

Resolution: verified exact; doi, observed 2026-05-19T18:57:43.097839Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5be18cfb-fafa-447e-82d9-9c0e9230eb5a · outbound

This paper cites Temporal neural operator for modeling time-dependent physical phenomena.Scientific Reports, 15(1):32791.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Temporal neural operator for modeling time-dependent physical phenomena.Scientific Reports, 15(1):32791

Reference 16

Resolution: verified exact; doi, observed 2026-05-19T18:57:43.074803Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 11d1e2cc-46a7-428e-8e3b-01be32ff9f57 · outbound

This paper cites Neural Operator: Graph Kernel Network for Partial Differential Equations.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Neural Operator: Graph Kernel Network for Partial Differential Equations

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-05-19T18:57:43.147115Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 3276e05e-db21-4cc7-b771-7d42f473ba4f · outbound

This paper cites Convolutional Neural Operators for robust and accurate learning of PDEs.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Convolutional Neural Operators for robust and accurate learning of PDEs

Reference 18

Resolution: verified exact; arxiv_id, observed 2026-05-19T18:57:43.153386Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation af04570d-6a87-4523-ab96-5dd78e6f18fd · outbound

This paper cites Karumuri, L.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Karumuri, L

Reference 19

Resolution: verified exact; arxiv_id, observed 2026-05-19T18:57:43.084195Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 18da67ad-0dbf-4f26-b069-177d7619165d · outbound

This paper cites an unresolved cited work.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-05-19T18:57:43.397865Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 210d1587-2a92-4926-871b-013132252ef6 · outbound

This paper cites Koric, D.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Koric, D

Reference 21

Resolution: verified exact; arxiv_id, observed 2026-05-19T18:57:43.059725Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5e7a00c9-7ea5-46c7-8b06-37af7da92559 · outbound

This paper cites Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems

Reference 22

Resolution: verified exact; arxiv_id, observed 2026-05-19T18:57:43.150705Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c603ecc2-304d-4480-b63c-e6ce94d92b06 · outbound

This paper cites Khorasani, A.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Khorasani, A

Reference 23

Resolution: malformed identifier; doi_truncated, observed 2026-05-19T18:57:43.065343Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8ef6e18c-3702-4762-9839-1b826de759ad · outbound

This paper cites Long-time Integration of Nonlinear Wave Equations with Neural Operators.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Long-time Integration of Nonlinear Wave Equations with Neural Operators

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-05-19T18:57:43.137540Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a9a9dae4-7094-4c5b-b6e7-9a6b9db61af0 · outbound

This paper cites an unresolved cited work.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Unresolved cited work

Reference 25

Resolution: verified exact; arxiv_id, observed 2026-05-19T18:57:43.068689Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7e3ef8fe-a285-4ff0-8f7b-e350a51d7898 · outbound

This paper cites Nayak, S.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Nayak, S

Reference 26

Resolution: verified exact; arxiv_id, observed 2026-05-19T18:57:43.156328Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation cb1aaf21-53f2-4984-bdb7-d68ff10a3447 · outbound

This paper cites Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality

Reference 27

Resolution: verified exact; local_arxiv, observed 2026-05-19T18:57:43.134345Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1c5c965f-b12d-48c3-bad1-37139661278b · outbound

This paper cites State-space models are accurate and eﬀicient neural operators for dynamical systems.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs State-space models are accurate and eﬀicient neural operators for dynamical systems

Reference 28

Resolution: verified exact; arxiv_id, observed 2026-05-19T18:57:43.056463Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d5bb634e-e099-4595-8974-9f4fa7225ade · outbound

This paper cites an unresolved cited work.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-05-19T18:57:43.399470Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation b8599135-4e00-46e9-a3af-a1e7b9551667 · outbound

This paper cites Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling

Reference 30

Resolution: verified exact; local_arxiv, observed 2026-05-19T18:57:43.143998Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1a70ba5e-7ad8-4b9a-92b2-5adae9e46b8a · outbound

This paper cites Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting

Reference 31

Resolution: verified exact; arxiv_id, observed 2026-05-19T18:57:43.140792Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 189ad7f6-71ab-4975-a5f1-18ed39c9063b · outbound

This paper cites Buitrago, T.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Buitrago, T

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T18:57:43.392864Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation b466a602-9b02-496c-b5bf-28665bdd4d10 · outbound

This paper cites Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural Networks.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural Networks

Reference 33

Resolution: verified exact; arxiv_id, observed 2026-05-19T18:57:43.131229Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1cb1ef97-f4ac-4d5d-8db9-ee38ec480585 · outbound

This paper cites Deepomamba: state-space model for spatio-temporal PDE neural operator learning.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Deepomamba: state-space model for spatio-temporal PDE neural operator learning

Reference 34

Resolution: verified exact; arxiv_id, observed 2026-05-19T18:57:43.090687Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 6c24238f-6ad1-427c-837e-43848eab5157 · outbound

This paper cites , author Hakimzadeh, M.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs , author Hakimzadeh, M

Reference 35

Resolution: verified exact; arxiv_id, observed 2026-05-19T18:57:43.100656Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 16c34613-1b1a-4783-9245-f04cc402851b · outbound

This paper cites an unresolved cited work.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Unresolved cited work

Reference 36

Resolution: verified exact; arxiv_id, observed 2026-05-19T18:57:43.062428Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 3821de37-e0ec-4aaa-bcf5-e7941528d863 · outbound

This paper cites an unresolved cited work.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Unresolved cited work

Reference 37

Resolution: verified exact; arxiv_id, observed 2026-05-19T18:57:43.096041Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e4c1b682-7ada-40e1-9b24-fbd1019c1b16 · outbound

This paper cites an unresolved cited work.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-05-19T18:57:43.394424Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8b6df107-f781-4db2-9d2c-ff615e290b61 · outbound

This paper cites Rudin, Real and Complex Analysis, 3rd Edition, McGraw-Hill, New York.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Rudin, Real and Complex Analysis, 3rd Edition, McGraw-Hill, New York

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T18:57:43.396177Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 4e83abf6-f990-44fe-89a5-8915abf3014c · outbound

This paper cites Karin Dahmen and James P.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Karin Dahmen and James P

Reference 40

Resolution: metadata mismatch; doi, observed 2026-05-19T18:57:43.071403Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation bc690aaf-a2d5-4948-9a0b-09f6828f1a4d · outbound

This paper cites Abueidda, Panos Pantidis, and Mostafa E.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Abueidda, Panos Pantidis, and Mostafa E

Reference 41

Resolution: metadata mismatch; arxiv_id, observed 2026-05-19T18:57:43.087784Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

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