Paper Citation Record · LEDGER

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations

As of 20 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 2 inbound Pith citation observations for arXiv:2506.10636.

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

pith.paper-citation-record.v1
2506.10636 v1

Coverage vector

measured 41 of 41 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T04:30:54.459009Z

measured 43 of 43 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-29T06:01:03.987717Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-10T12:15:01.137692Z

Reference resolution

41 of 41 outbound references displayed

verified exact1
verified fuzzy23
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0ef43cdd-ffe0-466a-b60c-d8849ba99ccb · outbound

This paper cites Ayi and E.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Ayi and E

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:30:55.083237Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0a73bca1-d116-4ed2-ba37-e9658a09073d · outbound

This paper cites Bertaglia, C.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Bertaglia, C

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:30:55.068918Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation eb16549e-afd1-4b29-aa7e-3a7a63a4fd8d · outbound

This paper cites an unresolved cited work.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:30:55.054100Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 11533d45-b7d8-4b0c-8101-e19f807cd8aa · outbound

This paper cites an unresolved cited work.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:30:55.040996Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 944f1c71-ea76-4a8c-8da0-9e8391d30a0c · outbound

This paper cites Cercignani , The Boltzmann Equation and Its Applications , Springer-Verlag Inc., New York, 1988.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Cercignani , The Boltzmann Equation and Its Applications , Springer-Verlag Inc., New York, 1988

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:30:55.026790Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 742b46a4-4789-4e87-8c71-d25ca3147a55 · outbound

This paper cites Dimarco and L.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Dimarco and L

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:30:55.012765Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation bd7d65e3-41e3-474e-9d7b-dd906c45df9c · outbound

This paper cites Dimarco and L.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Dimarco and L

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:30:54.997925Z

Source-reported events for the cited work

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Observation 08505290-a48b-41c2-8f70-5feaca5e91c6 · outbound

This paper cites Dimarco and L.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Dimarco and L

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:30:54.983648Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 7dd7ebe3-88be-45e3-85aa-030d928f3e3f · outbound

This paper cites an unresolved cited work.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:30:54.969091Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 621162b3-4a1d-4198-b874-ef073ab4fe7f · outbound

This paper cites an unresolved cited work.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:30:54.955031Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 79725881-a1b2-42ac-9b73-191a06106269 · outbound

This paper cites Hu and S.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Hu and S

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:30:54.939769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0c770b70-6a1c-46c0-80e3-102355091ff6 · outbound

This paper cites an unresolved cited work.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:30:54.923676Z

Source-reported events for the cited work

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Observation efb250c4-28a5-40c9-b7ef-9e4c9af373bd · outbound

This paper cites Jin , Asymptotic-preserving schemes for multiscale physical problems , Acta Numer., 31 (2022), pp.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Jin , Asymptotic-preserving schemes for multiscale physical problems , Acta Numer., 31 (2022), pp

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:30:54.909352Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d1059c2d-72a0-4d48-ba5c-a35b1b870dcf · outbound

This paper cites an unresolved cited work.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:30:54.894869Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1f43c4dc-0e8a-4d4b-a690-bc3ae80a25a1 · outbound

This paper cites an unresolved cited work.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:30:54.880356Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c71b3312-750f-4d79-8034-1c8778479c60 · outbound

This paper cites Jin and B.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Jin and B

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:30:54.864798Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2e98c28d-66bb-457d-bda9-74a159270610 · outbound

This paper cites an unresolved cited work.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Unresolved cited work

Reference 17

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 69aa4879-26cc-4918-aff8-a61ec6944043 · outbound

This paper cites an unresolved cited work.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:30:54.838516Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4c7ca3ec-c1a8-4470-9941-0d83c3b1cf09 · outbound

This paper cites an unresolved cited work.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:30:54.822672Z

Source-reported events for the cited work

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Observation 1c7e170c-d321-4ea5-a676-31c02c25c7d7 · outbound

This paper cites Liu and K.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Liu and K

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:30:54.807994Z

Source-reported events for the cited work

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Observation 88baec8c-452a-4f8f-9a83-02834a4f0391 · outbound

This paper cites an unresolved cited work.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:30:54.794472Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4ced5d17-4d4f-4af1-9317-6fef7e5d3bb3 · outbound

This paper cites Liu and X.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Liu and X

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:30:54.780062Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 6a9151b7-e2a2-44b8-9f38-6613228a6241 · outbound

This paper cites Medaglia, L.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Medaglia, L

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:30:54.765529Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3b021e81-8b2d-4b7b-856a-674deb3d83af · outbound

This paper cites Mishra and C.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Mishra and C

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:30:54.750940Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation cfc3256e-2397-45d7-a230-b47281982d49 · outbound

This paper cites Mishra, C.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Mishra, C

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:30:54.735998Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0c8ca943-48c1-4711-9123-7faa5b067999 · outbound

This paper cites Mouhot and L.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Mouhot and L

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:30:54.721125Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e2a78b80-535b-4672-a7c9-6517c3f546a2 · outbound

This paper cites Peherstorfer, M.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Peherstorfer, M

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:30:54.705107Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1c0e5aec-1438-4adf-bd7d-f2e6b0cec446 · outbound

This paper cites Peherstorfer, K.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Peherstorfer, K

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:30:54.690505Z

Source-reported events for the cited work

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Observation a4c7bff2-ec7b-4f19-9f88-86fd5b27c207 · outbound

This paper cites Perthame and M.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Perthame and M

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:30:54.674928Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation cddf1fb9-e1e2-4526-a449-577b54ea35d3 · outbound

This paper cites Raissi, P.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Raissi, P

Reference 30

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 220b9585-971b-46b0-a840-4c25d2856ec5 · outbound

This paper cites Schotth\"ofer, M.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Schotth\"ofer, M

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:30:54.650106Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 6d53697b-6ce8-4df7-92b4-8c2c0fa7a018 · outbound

This paper cites an unresolved cited work.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:30:54.635250Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ecf30feb-2b06-4d98-8ed9-35522dadd139 · outbound

This paper cites Villani , A review of mathematical topics in collisional kinetic theory , Handbook of Mathematical Fluid Dynamics, 1 (2002), pp.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Villani , A review of mathematical topics in collisional kinetic theory , Handbook of Mathematical Fluid Dynamics, 1 (2002), pp

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:30:54.620233Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4d1b4057-5c50-473e-bcce-53a430e0f9bc · outbound

This paper cites Error estimates of asymptotic-preserving neural networks in approximating stochastic linearized Boltzmann equation.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Error estimates of asymptotic-preserving neural networks in approximating stochastic linearized Boltzmann equation

Reference 34

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:30:54.500199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f1b0e8a7-16b1-40e8-9c2f-37343ac9bebb · outbound

This paper cites an unresolved cited work.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:30:54.605224Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 799d3785-4b43-43f6-8058-6b36f07b2124 · outbound

This paper cites an unresolved cited work.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:30:54.588750Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8444e2dd-c2c5-446d-a01c-e7a432034ff0 · outbound

This paper cites Xiao and M.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Xiao and M

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:30:54.573282Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 26afedbb-b1f3-4df8-96cd-aedf2b03bdf3 · outbound

This paper cites Xiao and M.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Xiao and M

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:30:54.559315Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ff832b12-8637-46e5-92e7-a8618254da2b · outbound

This paper cites an unresolved cited work.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:30:54.543282Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f71367e5-d26d-46ed-a4ef-4c6784f8407a · outbound

This paper cites Xiu , Numerical Methods for Stochastic Computations , Princeton University Press, 2010.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Xiu , Numerical Methods for Stochastic Computations , Princeton University Press, 2010

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:30:54.527180Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c94b451e-dd51-4ddd-bb4a-9d64e6f4b682 · outbound

This paper cites write newline.

Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations write newline

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-07T04:30:54.459009Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 63de18e1-110f-4abe-95dc-af7b9d1fd012 · inbound

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks cites this paper.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-06-29T06:03:07.781777Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8b183493-841a-4d8b-8eb2-fde844576a85 · inbound

A Dynamical Low-rank Multilevel Monte Carlo Estimator for High-Dimensional Kinetic Equations cites this paper.

A Dynamical Low-rank Multilevel Monte Carlo Estimator for High-Dimensional Kinetic Equations Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-07-01T17:25:52.015369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.