Paper Citation Record · LEDGER

A deformation-based framework for learning solution mappings of PDEs defined on varying domains

As of 13 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 1 inbound Pith citation observation for arXiv:2412.01379.

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

pith.paper-citation-record.v1
2412.01379 v2

Coverage vector

measured 43 of 43 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T04:31:53.134335Z

measured 44 of 44 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-13T11:26:17.627449Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

43 of 43 outbound references displayed

verified exact0
verified fuzzy13
unresolved30
parse uncertain0
malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d9354685-e760-4e90-ae6e-b4e1d41cc229 · outbound

This paper cites an unresolved cited work.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-12T04:31:53.655554Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation c32c0a53-0bac-4f61-ac85-0993ceac5497 · outbound

This paper cites an unresolved cited work.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-12T04:31:53.643194Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 10b4e2eb-1eed-47af-90c9-a7cd69d262f6 · outbound

This paper cites Dugundji.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Dugundji

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:31:53.632288Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d829c541-b6b1-48f5-b90e-ce3fb3bb8280 · outbound

This paper cites The Barron Space and the Flow-induced Function Spaces for Neural Network Models.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains The Barron Space and the Flow-induced Function Spaces for Neural Network Models

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-12T04:31:52.969744Z

Source-reported events for the cited work

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Observation 1602c820-03c4-46fb-9956-b0f0c3824d38 · outbound

This paper cites an unresolved cited work.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-12T04:31:52.974057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ed9c9b43-0306-4f70-a503-5ec88e696264 · outbound

This paper cites Gonz´ alez.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Gonz´ alez

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:31:53.613820Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 9c13bbfd-cc43-47a1-849a-9e0200b659ca · outbound

This paper cites Goswami, K.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Goswami, K

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:31:53.602723Z

Source-reported events for the cited work

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Observation fa87b6a1-af94-4525-b58f-4f09b769f47e · outbound

This paper cites Gupta, X.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Gupta, X

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:31:53.591123Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation e5a7e9a2-0fef-42e9-a317-7209662d7d97 · outbound

This paper cites an unresolved cited work.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-12T04:31:53.576994Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation c57de896-7ed7-4c39-91d2-5896d52f38d3 · outbound

This paper cites an unresolved cited work.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-12T04:31:53.563762Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 5758ad22-d8ef-4e17-9da2-a299ee5f7811 · outbound

This paper cites MgNO: Efficient Parameterization of Linear Operators via Multigrid.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains MgNO: Efficient Parameterization of Linear Operators via Multigrid

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-12T04:31:52.999441Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8a164daf-f250-4665-8618-322679e74953 · outbound

This paper cites Hornik, M.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Hornik, M

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-12T04:31:53.003477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b4ed347e-d228-4686-a0b9-f59386813f79 · outbound

This paper cites Hornik, M.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Hornik, M

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:31:53.547901Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 0dc9e06e-26f2-4da2-910e-8a555c051b9f · outbound

This paper cites A hybrid iterative method based on MIONet for PDEs: Theory and numerical examples.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains A hybrid iterative method based on MIONet for PDEs: Theory and numerical examples

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-12T04:31:53.010963Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1652afb1-179c-4461-90d9-232bb03227ed · outbound

This paper cites an unresolved cited work.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-12T04:31:53.536827Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 8fdc3ed2-3014-425e-820a-f6765bbd6259 · outbound

This paper cites Kalmykov and L.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Kalmykov and L

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:31:53.525719Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 6f4a2578-153f-4f55-a792-0a222c0c6436 · outbound

This paper cites an unresolved cited work.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-12T04:31:53.513924Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 90d54348-890d-4e3b-8597-e84dacf15c71 · outbound

This paper cites an unresolved cited work.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-12T04:31:53.500764Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ba3c5564-ea14-42e6-95f4-0ab8eff23ee8 · outbound

This paper cites Fourier Neural Operator with Learned Deformations for PDEs on General Geometries.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Fourier Neural Operator with Learned Deformations for PDEs on General Geometries

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-12T04:31:53.032456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 619756d5-9323-4aa5-9ac2-6a4a5d01f898 · outbound

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

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Fourier Neural Operator for Parametric Partial Differential Equations

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-12T04:31:53.040096Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 54c54362-33f2-46c9-b6d2-da4938f49a46 · outbound

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

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Neural Operator: Graph Kernel Network for Partial Differential Equations

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-12T04:31:53.044534Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4d640a27-13fe-4c45-ad5e-2c539d6ed31f · outbound

This paper cites DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-12T04:31:53.049197Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 033a4d37-808d-4aa3-8189-3c3934194aa8 · outbound

This paper cites an unresolved cited work.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-12T04:31:53.488291Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation c7dd0627-dfcf-4cc8-8ac3-a942d0ec0ed5 · outbound

This paper cites an unresolved cited work.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-12T04:31:53.474427Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation a6eb42ba-f9cb-413b-b6b6-067bb56f1e2c · outbound

This paper cites an unresolved cited work.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-12T04:31:53.060923Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b2fe65f0-85b5-492c-8728-237ee4053de1 · outbound

This paper cites an unresolved cited work.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-12T04:31:53.453633Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation a1749267-5d1a-4c99-b771-87eea5cfa464 · outbound

This paper cites an unresolved cited work.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Unresolved cited work

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-12T04:31:53.069448Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ae4b85ee-6166-459c-955b-eb931dda5e4a · outbound

This paper cites an unresolved cited work.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-12T04:31:53.436629Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 39a0e7e0-aa4b-4005-940e-ef1930e73270 · outbound

This paper cites U-NO: U-shaped Neural Operators.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains U-NO: U-shaped Neural Operators

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-12T04:31:53.082503Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 20c1eb98-00e5-4e5c-9cff-d85cad2e3d49 · outbound

This paper cites Raissi, P.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Raissi, P

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:31:53.426551Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 755a1f95-d41c-47b6-bbd2-385f84a88870 · outbound

This paper cites Raonic, R.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Raonic, R

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:31:53.416307Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation c4cc1552-8eda-473d-93f5-a230e82b565a · outbound

This paper cites an unresolved cited work.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-12T04:31:53.406479Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation e425a1eb-1e69-4f73-b867-7afe25756566 · outbound

This paper cites Serrano, L.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Serrano, L

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:31:53.395434Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation dc265f1d-e70d-4b5d-ae96-65ed27e9ea55 · outbound

This paper cites an unresolved cited work.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-12T04:31:53.384406Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 02ea06ef-d9e5-49e1-8238-9a86496ff071 · outbound

This paper cites Sirignano and K.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Sirignano and K

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:31:53.369789Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 37fa2ffd-05b8-4099-b1b3-d209b5862c7a · outbound

This paper cites Sitzmann, J.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Sitzmann, J

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:31:53.352173Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation a27f4cc4-6e8a-4e55-abe9-8a323e3b7242 · outbound

This paper cites Swinbank and R.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Swinbank and R

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:31:53.338553Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 916aa055-0c84-47a6-befc-137dac14c6da · outbound

This paper cites an unresolved cited work.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-12T04:31:53.323666Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ec28f40b-e130-4cd8-bd45-847c9c3cf025 · outbound

This paper cites Solving High-Dimensional PDEs with Latent Spectral Models.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Solving High-Dimensional PDEs with Latent Spectral Models

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-12T04:31:53.120297Z

Source-reported events for the cited work

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Observation 50378469-3c65-4624-b2e9-45522e65d685 · outbound

This paper cites Learning solution operators of PDEs defined on varying domains via MIONet.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Learning solution operators of PDEs defined on varying domains via MIONet

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-12T04:31:53.123755Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4527e295-bc7a-4de1-b636-542014640544 · outbound

This paper cites DIMON: Learning Solution Operators of Partial Differential Equations on a Diffeomorphic Family of Domains.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains DIMON: Learning Solution Operators of Partial Differential Equations on a Diffeomorphic Family of Domains

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-12T04:31:53.127182Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f162d7e3-1737-4c44-91e2-22d80a213114 · outbound

This paper cites an unresolved cited work.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Unresolved cited work

Reference 42

Resolution: unresolved; raw_fallback, observed 2026-08-12T04:31:53.310775Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d6170365-3832-4a27-8fb4-dca5db1f94ca · outbound

This paper cites Zheng, X.

A deformation-based framework for learning solution mappings of PDEs defined on varying domains Zheng, X

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:31:53.296618Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Pith citing papers

Observation d58b79b9-c2b5-478b-890d-d4b871b12f2f · inbound

A Geometry-Aware Operator Learning Framework for Interface Problems on Varying Domains cites this paper.

A Geometry-Aware Operator Learning Framework for Interface Problems on Varying Domains A deformation-based framework for learning solution mappings of PDEs defined on varying domains

Reference 24

Resolution: unresolved; no resolver link, observed 2026-07-13T11:26:17.627449Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.