Paper Citation Record · LEDGER

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations

As of 22 July 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:2309.16131.

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

pith.paper-citation-record.v1
2309.16131 v1

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-24T06:52:30.657754Z

measured 34 of 34 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-07-21T06:31:05.380196+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

34 of 34 outbound references displayed

verified exact3
verified fuzzy31
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 375aa482-799b-45b2-9e05-9ae893f3d728 · outbound

This paper cites Unsupervised Deep Learning Algorithm for PDE-based Forward and Inverse Problems.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Unsupervised Deep Learning Algorithm for PDE-based Forward and Inverse Problems

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-05-24T06:54:03.209260Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 3eab91dd-2885-49b9-a72f-785d89ce76aa · outbound

This paper cites Hsieh, S.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Hsieh, S

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.141116Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation e2d84685-0613-4b75-8b55-bcae47cc0121 · outbound

This paper cites Ruthotto, E.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Ruthotto, E

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.123643Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation f58898e3-f17e-42da-a268-1ce533949064 · outbound

This paper cites Sirignano, J.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Sirignano, J

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.105491Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation c2be902a-9f89-47eb-abe3-2800002b726e · outbound

This paper cites Brandstetter, D.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Brandstetter, D

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.102080Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 887f196b-4b15-43d6-b27c-9bcb866e4256 · outbound

This paper cites an unresolved cited work.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Unresolved cited work

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.126495Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation bdcb2ca7-2d79-42a0-a6a0-87087f5b70f1 · outbound

This paper cites an unresolved cited work.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Unresolved cited work

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.113719Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 806fb45f-a303-43c0-b517-659425bdf683 · outbound

This paper cites an unresolved cited work.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Unresolved cited work

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.116818Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation b735cad5-1d44-45f7-81c2-ad658ab0526b · outbound

This paper cites an unresolved cited work.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Unresolved cited work

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.110890Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation c3030b15-1517-4991-a809-b0a01c420fdd · outbound

This paper cites an unresolved cited work.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Unresolved cited work

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.138073Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 9f42a79b-10c9-4d36-bf6c-4dc000b5a9a0 · outbound

This paper cites an unresolved cited work.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Unresolved cited work

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.135255Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 0f75c543-e018-4807-ae4a-5dbc88ef4787 · outbound

This paper cites Anandkumar, K.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Anandkumar, K

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.129201Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation a3046d8d-0642-479d-84d5-1abb6b4d5dcf · outbound

This paper cites an unresolved cited work.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Unresolved cited work

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.147110Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 94591cb7-c631-4857-a471-d34e4985eb4f · outbound

This paper cites Spectral Neural Operators.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Spectral Neural Operators

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-05-24T06:54:03.203678Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 454b3674-ccc2-428d-83db-5a989714c664 · outbound

This paper cites an unresolved cited work.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Unresolved cited work

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.144108Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation c01a6598-a5b1-44ca-84c5-d008e71a877f · outbound

This paper cites an unresolved cited work.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Unresolved cited work

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.126245Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation ca10e76f-19fe-4af5-9ced-30d57e2d19b8 · outbound

This paper cites Tang, The Hermite spectral method for Gaussian-type functions, SIAM Journal on Scientiﬁc Computing 14 (3) (1993) 594–606.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Tang, The Hermite spectral method for Gaussian-type functions, SIAM Journal on Scientiﬁc Computing 14 (3) (1993) 594–606

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.123422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation d97556b4-72d2-4460-86d4-eb02533b39f6 · outbound

This paper cites an unresolved cited work.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Unresolved cited work

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.064715Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation ef818b29-2d63-4d21-81ea-ca476071a4bd · outbound

This paper cites an unresolved cited work.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Unresolved cited work

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.110657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation a917a7b4-14e0-47f0-8d10-657fac13bde5 · outbound

This paper cites Shen, L.-L.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Shen, L.-L

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.113501Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation b21847fa-6886-4f8f-be1f-aa3409326ed5 · outbound

This paper cites an unresolved cited work.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Unresolved cited work

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.107237Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 1ea504b4-0991-410b-869d-4365051ee655 · outbound

This paper cites Bateman, Some recent researches on the motion of ﬂuid s, Monthly Weather Review 43 (4) (1915) 163–170.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Bateman, Some recent researches on the motion of ﬂuid s, Monthly Weather Review 43 (4) (1915) 163–170

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.065034Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 06c1e871-8632-439f-af99-6f48dea7b5ca · outbound

This paper cites Antoine, A.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Antoine, A

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.101393Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 8e64bf71-8789-4ac4-b0f8-8ea97e32dab4 · outbound

This paper cites an unresolved cited work.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Unresolved cited work

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.104422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 7cdf47d1-520a-46db-a3db-818986edc18f · outbound

This paper cites Improving neural networks by preventing co-adaptation of feature detectors.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Improving neural networks by preventing co-adaptation of feature detectors

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-05-24T06:54:03.198324Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 4db71f0c-a711-4ec1-a1a0-c38903358003 · outbound

This paper cites Srivastava, G.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Srivastava, G

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.116516Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation fb533240-8a0e-42d7-954c-09774e4450a3 · outbound

This paper cites an unresolved cited work.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Unresolved cited work

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.132241Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 817792ea-4292-408a-bbf4-6839a3262532 · outbound

This paper cites an unresolved cited work.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Unresolved cited work

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.098491Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 66511a9f-c61b-45e1-8cc4-49ad0b581aab · outbound

This paper cites Bungartz, M.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Bungartz, M

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.094677Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 806d796c-c9c9-456e-9e1d-0c4049d94326 · outbound

This paper cites Zenger, W.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Zenger, W

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.081892Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 301edcd6-5cca-487b-8ce8-d2f9d4809a92 · outbound

This paper cites Simonyan, A.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Simonyan, A

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.068606Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 52c79797-d03d-4b17-978c-0a083b3785f4 · outbound

This paper cites an unresolved cited work.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Unresolved cited work

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.098233Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation c84b2bfb-2dd2-403f-bc40-e0a078d9f36b · outbound

This paper cites an unresolved cited work.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Unresolved cited work

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.071862Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 31a3eedb-d649-4c48-9892-1ad0c493e3ca · outbound

This paper cites resolution-invariance.

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations resolution-invariance

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T06:56:03.076005Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Pith citing papers

No inbound Pith citation observations are available.