Paper Citation Record · LEDGER

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space

As of 14 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:2501.12116.

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

pith.paper-citation-record.v1
2501.12116 v2

Coverage vector

measured 41 of 41 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T17:34:33.593186Z

measured 41 of 41 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+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

41 of 41 outbound references displayed

verified exact5
verified fuzzy2
unresolved27
parse uncertain0
malformed identifier4
metadata mismatch3

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5477b084-ac35-4dba-ac23-5200ba561eb4 · outbound

This paper cites an unresolved cited work.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Unresolved cited work

Reference 1

Resolution: verified exact; doi, observed 2026-08-10T17:34:33.956490Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 95b25f41-b046-4e19-9603-8f91db419187 · outbound

This paper cites Mathematical Problems in Engineering 2014, 1–1 (2014) https://doi.org/10.1155/2014/787412.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Mathematical Problems in Engineering 2014, 1–1 (2014) https://doi.org/10.1155/2014/787412

Reference 2

Resolution: verified exact; doi, observed 2026-08-10T17:34:33.942696Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 259fc866-8e79-4c92-bf1f-8b3aaed64a2b · outbound

This paper cites Pure & Applied Mathematics S.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Pure & Applied Mathematics S

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:34:34.520791Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4fa4405d-e00c-456e-882f-48b8866aba35 · outbound

This paper cites https://doi.org/10.48550/arXiv.2006.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space https://doi.org/10.48550/arXiv.2006

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.446233Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 54c8949e-da2f-407a-a94d-221d517dd438 · outbound

This paper cites Journal of Open Source Software 5(46), 1931 (2020) https: //doi.org/10.21105/joss.01931.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Journal of Open Source Software 5(46), 1931 (2020) https: //doi.org/10.21105/joss.01931

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.450832Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dfe0a461-9556-46a0-bda1-3edee6df63c7 · outbound

This paper cites SIAM Review 63, 208–228 (2021) https://doi.org/ 10.1137/19M1274067.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space SIAM Review 63, 208–228 (2021) https://doi.org/ 10.1137/19M1274067

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.455149Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7e84f03e-ae93-47f1-ad63-9f7120f2854e · outbound

This paper cites Nature Reviews Physics 3(6), 422–440 (2021) https://doi.org/10.1038/s42254-021-00314-5.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Nature Reviews Physics 3(6), 422–440 (2021) https://doi.org/10.1038/s42254-021-00314-5

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.459722Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c909cd97-63d3-4e3b-8bc9-7c262d54e26e · outbound

This paper cites Nature Machine Intelligence 3(3), 218–229 (2021) https://doi.org/10.1038/ s42256-021-00302-5.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Nature Machine Intelligence 3(3), 218–229 (2021) https://doi.org/10.1038/ s42256-021-00302-5

Reference 8

Resolution: malformed identifier; raw_fallback, observed 2026-08-10T17:34:34.509135Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 0ad9a846-c258-4ebb-8dbb-6b02e9103f17 · outbound

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

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Fourier Neural Operator for Parametric Partial Differential Equations

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.467491Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 01ace104-d911-45e4-a68b-3584749f6876 · outbound

This paper cites Stiff and Differential-Algebraic Problems vol.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Stiff and Differential-Algebraic Problems vol

Reference 10

Resolution: malformed identifier; raw_fallback, observed 2026-08-10T17:34:34.497482Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 85d6cbab-9cd1-428f-99de-a8c56c1bb73b · outbound

This paper cites Stiff Transfer Learning for Physics-Informed Neural Networks.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Stiff Transfer Learning for Physics-Informed Neural Networks

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.475897Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9673d3cd-4202-464a-af8c-3278b5e013fa · outbound

This paper cites John Wiley & Sons, Inc., USA (1991).

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space John Wiley & Sons, Inc., USA (1991)

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:34:34.486237Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation bac76e2c-e808-4111-b3f4-9fad38c58f1a · outbound

This paper cites Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 33.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 33

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.483668Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 46a94aad-7436-4b7b-9911-7ca5a3d6e199 · outbound

This paper cites IEEE Trans- actions on Neural Networks and Learning Systems 31(4), 1410–1416 (2020) https://doi.org/10.1109/TNNLS.2019.2919705.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space IEEE Trans- actions on Neural Networks and Learning Systems 31(4), 1410–1416 (2020) https://doi.org/10.1109/TNNLS.2019.2919705

Reference 14

Resolution: metadata mismatch; raw_fallback, observed 2026-08-10T17:34:34.471467Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 9a460a43-374b-4f2d-afde-e6c52a6c764f · outbound

This paper cites Thoughts on the Consistency between Ricci Flow and Neural Network Behavior.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Thoughts on the Consistency between Ricci Flow and Neural Network Behavior

Reference 15

Resolution: metadata mismatch; local_arxiv, observed 2026-08-10T17:34:33.873214Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 9bd6ff87-591e-4337-9061-cce4cdcc7b6a · outbound

This paper cites RicciNets: Curvature-guided Pruning of High-performance Neural Networks Using Ricci Flow.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space RicciNets: Curvature-guided Pruning of High-performance Neural Networks Using Ricci Flow

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-10T17:34:33.857544Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ab3aff2b-b4ae-46af-a54b-3e83cf082dbd · outbound

This paper cites 558–567 (2023).

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space 558–567 (2023)

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.499176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 220b14aa-b6f6-48f6-9e0d-226b8d5d46cf · outbound

This paper cites Invariant Physics-Informed Neural Networks for Ordinary Differential Equations.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Invariant Physics-Informed Neural Networks for Ordinary Differential Equations

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.502789Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f137108e-7931-4c2c-8e28-e40201234fcb · outbound

This paper cites Engineering Applications of Artificial Intelligence 127, 107324 (2024) https://doi.org/10.1016/j.engappai.2023.107324.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Engineering Applications of Artificial Intelligence 127, 107324 (2024) https://doi.org/10.1016/j.engappai.2023.107324

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.506892Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b8882882-88f9-42d7-90bd-6237ddb0269a · outbound

This paper cites Neural Networks 181, 106826 (2025) https://doi.org/10.1016/j.neunet.2024.106826.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Neural Networks 181, 106826 (2025) https://doi.org/10.1016/j.neunet.2024.106826

Reference 20

Resolution: metadata mismatch; raw_fallback, observed 2026-08-10T17:34:34.255209Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 89efc8ef-a31c-48a0-ba7f-67cfb2b350df · outbound

This paper cites https://doi.org/10.48550/arXiv.2301.02152.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space https://doi.org/10.48550/arXiv.2301.02152

Reference 21

Resolution: verified exact; doi, observed 2026-08-10T17:34:33.828354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 12908c46-6840-436d-a4a1-5766bb5049e7 · outbound

This paper cites One-Shot Transfer Learning of Physics-Informed Neural Networks.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space One-Shot Transfer Learning of Physics-Informed Neural Networks

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.519044Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a0497dce-bfe1-4eae-94ea-18fcaabbe90b · outbound

This paper cites Data-Guided Physics-Informed Neural Networks for Solving Inverse Problems in Partial Differential Equations.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Data-Guided Physics-Informed Neural Networks for Solving Inverse Problems in Partial Differential Equations

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.523311Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 098f60e2-d551-4912-9d16-25c6e8235ba0 · outbound

This paper cites Computer Methods in Applied Mechanics and Engineering 435, 117628 (2025) https://doi.org/10.1016/j.cma.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Computer Methods in Applied Mechanics and Engineering 435, 117628 (2025) https://doi.org/10.1016/j.cma

Reference 24

Resolution: malformed identifier; no resolver link, observed 2026-08-10T17:34:33.527410Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9fd354cb-d55b-4487-9bfa-380928aeca96 · outbound

This paper cites arXiv e-prints, 2311–14931 (2023) https://doi.org/10.48550/arXiv.2311.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space arXiv e-prints, 2311–14931 (2023) https://doi.org/10.48550/arXiv.2311

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.531007Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 76298255-34e1-4bc5-86cf-bb96837cddcd · outbound

This paper cites Transfer Learning with Physics-Informed Neural Networks for Efficient Simulation of Branched Flows.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Transfer Learning with Physics-Informed Neural Networks for Efficient Simulation of Branched Flows

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.534694Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 10cf5498-1150-405f-95d8-fbe884f9365c · outbound

This paper cites IEEE Transactions on Magnetics 59(2), 1–5 (2023) https://doi.org/10.1109/CEFC55061.2022.9940890.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space IEEE Transactions on Magnetics 59(2), 1–5 (2023) https://doi.org/10.1109/CEFC55061.2022.9940890

Reference 27

Resolution: verified exact; raw_fallback, observed 2026-08-10T17:34:34.100566Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 3c5ca669-e53c-4a3a-892b-611d45412e26 · outbound

This paper cites communications in Numerical Methods in Engineering 10(3), 195–201 (1994) https://doi.org/10.1002/cnm.1640100303.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space communications in Numerical Methods in Engineering 10(3), 195–201 (1994) https://doi.org/10.1002/cnm.1640100303

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.542792Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f8e04f58-7663-48d4-9b4c-f84f6429505f · outbound

This paper cites IEEE Transactions on Neural Networks 11(5), 1041–1049 (2000) https://doi.org/10.1109/72.870037.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space IEEE Transactions on Neural Networks 11(5), 1041–1049 (2000) https://doi.org/10.1109/72.870037

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.546796Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4493a376-99cb-436b-a722-919909803274 · outbound

This paper cites an unresolved cited work.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Unresolved cited work

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.550761Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 68d4b9e3-58e3-4d42-bc52-cb7609cba994 · outbound

This paper cites Journal of Computational Physics 375, 1339–1364 (2018) https://doi.org/10.1016/j.jcp.2018.08.029.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Journal of Computational Physics 375, 1339–1364 (2018) https://doi.org/10.1016/j.jcp.2018.08.029

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.554768Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 21a6a627-ccfe-446b-87eb-25c98cf8071c · outbound

This paper cites Journal of Computational Physics 394, 56–81 (2019) https://doi.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Journal of Computational Physics 394, 56–81 (2019) https://doi

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.558531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3f36e586-87e0-48aa-9e0e-32f13bf46f5a · outbound

This paper cites Physics enhanced neural networks predict order and chaos.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Physics enhanced neural networks predict order and chaos

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.562149Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4a5950e7-1496-4911-bd32-c4c5f697a3ae · outbound

This paper cites Forecasting Hamiltonian dynamics without canonical coordinates.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Forecasting Hamiltonian dynamics without canonical coordinates

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.565844Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ff4b078a-fd9d-4e2d-884e-6a8aee3aaafd · outbound

This paper cites Hamiltonian Neural Networks.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Hamiltonian Neural Networks

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.570110Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fed020ae-339c-455a-b445-5da168fceb3e · outbound

This paper cites https: //doi.org/10.1007/978-981-19-3079-9 15-1.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space https: //doi.org/10.1007/978-981-19-3079-9 15-1

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.574242Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5f2f6ddb-89ec-4098-8903-6a25f4043cfb · outbound

This paper cites Unimodular Gravity vs General Relativity: A status report.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Unimodular Gravity vs General Relativity: A status report

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.577940Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f4c33521-4396-4b35-88f6-984458cb248a · outbound

This paper cites Robust Learning with Jacobian Regularization.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Robust Learning with Jacobian Regularization

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.581660Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 00b57e2f-5ad7-4b98-a19e-b1ebe58df669 · outbound

This paper cites Gravitational Duals from Equations of State.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Gravitational Duals from Equations of State

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.585548Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 648de69f-16c2-4183-8f95-3f6c8b432514 · outbound

This paper cites Heating up Exotic RG Flows with Holography.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Heating up Exotic RG Flows with Holography

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-10T17:34:33.589252Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6fd7f60f-7a3d-4771-b18d-331a830cf54d · outbound

This paper cites Mimicking the QCD equation of state with a dual black hole.

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space Mimicking the QCD equation of state with a dual black hole

Reference 41

Resolution: malformed identifier; no resolver link, observed 2026-08-10T17:34:33.593186Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.