Paper Citation Record · LEDGER

Observations on Recurrent Loss in the Neural Network Model of a Partial Differential Equation: the Advection-Diffusion Equation

As of 7 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:2503.19036.

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

pith.paper-citation-record.v1
2503.19036 v2

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-22T22:28:57.369468Z

measured 23 of 23 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+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

23 of 23 outbound references displayed

verified exact0
verified fuzzy16
unresolved7
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b720d893-a54d-45bc-9fc4-a41dca12f252 · outbound

This paper cites A First Course in the Numerical Analysis of Differential Equations.

Observations on Recurrent Loss in the Neural Network Model of a Partial Differential Equation: the Advection-Diffusion Equation A First Course in the Numerical Analysis of Differential Equations

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T22:37:14.108297Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c37c29ee-0592-4966-8c30-8d49e9b9e4bd · outbound

This paper cites Bar-Sinai, S.

Observations on Recurrent Loss in the Neural Network Model of a Partial Differential Equation: the Advection-Diffusion Equation Bar-Sinai, S

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T22:37:14.111845Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 4881544a-99b7-4166-a322-7e416e733104 · outbound

This paper cites an unresolved cited work.

Observations on Recurrent Loss in the Neural Network Model of a Partial Differential Equation: the Advection-Diffusion Equation Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-05-22T22:37:14.105416Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 96e52b7d-92c3-45e0-81ee-eec6150364bc · outbound

This paper cites Akers and Kristina O.

Observations on Recurrent Loss in the Neural Network Model of a Partial Differential Equation: the Advection-Diffusion Equation Akers and Kristina O

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T22:37:14.118141Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 74fbde36-c65c-4d05-87c1-48557d93c51d · outbound

This paper cites PDE-net: Learning PDEs from data.

Observations on Recurrent Loss in the Neural Network Model of a Partial Differential Equation: the Advection-Diffusion Equation PDE-net: Learning PDEs from data

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T22:37:14.115226Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation ac07a52c-63c1-4a8a-b04e-e5592a45d60c · outbound

This paper cites an unresolved cited work.

Observations on Recurrent Loss in the Neural Network Model of a Partial Differential Equation: the Advection-Diffusion Equation Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-05-22T22:37:14.102308Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 3072e315-3eeb-4e97-a112-5dddda87a487 · outbound

This paper cites Deep hidden physics models: deep learning of nonlinear partial differential equations.

Observations on Recurrent Loss in the Neural Network Model of a Partial Differential Equation: the Advection-Diffusion Equation Deep hidden physics models: deep learning of nonlinear partial differential equations

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T22:37:14.065833Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 40aa8bfb-1337-498d-a070-3ad3bea26d39 · outbound

This paper cites Raissi, P.

Observations on Recurrent Loss in the Neural Network Model of a Partial Differential Equation: the Advection-Diffusion Equation Raissi, P

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T22:37:14.075223Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f0e61065-d3bc-415c-8c90-a26fe1d9a02f · outbound

This paper cites Pde-net 2.0: Learning pdes from data with a numeric-symbolic hybrid deep network.

Observations on Recurrent Loss in the Neural Network Model of a Partial Differential Equation: the Advection-Diffusion Equation Pde-net 2.0: Learning pdes from data with a numeric-symbolic hybrid deep network

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T22:37:14.099206Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d0bdf082-e8ca-476a-b5eb-e9f293328107 · outbound

This paper cites Neural network enhanced computations on coarse grids.

Observations on Recurrent Loss in the Neural Network Model of a Partial Differential Equation: the Advection-Diffusion Equation Neural network enhanced computations on coarse grids

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T22:37:14.068746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation be456ded-8a7c-439c-898f-20d208e8a462 · outbound

This paper cites A logical calculus of ideas immanent in nervous activity.

Observations on Recurrent Loss in the Neural Network Model of a Partial Differential Equation: the Advection-Diffusion Equation A logical calculus of ideas immanent in nervous activity

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T22:37:14.078443Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 7a49a43b-0c0a-4a8e-92f0-3af702a7212a · outbound

This paper cites an unresolved cited work.

Observations on Recurrent Loss in the Neural Network Model of a Partial Differential Equation: the Advection-Diffusion Equation Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-05-22T22:37:14.087248Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d5378cff-8e39-4e9d-8d08-f1af65a6a5b8 · outbound

This paper cites Ode-ru: a dynamical system view on recurrent neural networks.

Observations on Recurrent Loss in the Neural Network Model of a Partial Differential Equation: the Advection-Diffusion Equation Ode-ru: a dynamical system view on recurrent neural networks

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T22:37:14.062294Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6ccd9451-65c1-4b70-b143-9fa68d514899 · outbound

This paper cites an unresolved cited work.

Observations on Recurrent Loss in the Neural Network Model of a Partial Differential Equation: the Advection-Diffusion Equation Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-05-22T22:37:14.089572Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 9737a952-286c-41e9-8ce3-74ce6539d8f7 · outbound

This paper cites IMEXnet a forward stable deep neural network.

Observations on Recurrent Loss in the Neural Network Model of a Partial Differential Equation: the Advection-Diffusion Equation IMEXnet a forward stable deep neural network

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T22:37:14.055224Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 1f5cee3f-7959-405f-9e99-e442b8b450df · outbound

This paper cites Haber and L.

Observations on Recurrent Loss in the Neural Network Model of a Partial Differential Equation: the Advection-Diffusion Equation Haber and L

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T22:37:14.058430Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2b670f2c-c80a-4d24-8914-cea07631f5e3 · outbound

This paper cites an unresolved cited work.

Observations on Recurrent Loss in the Neural Network Model of a Partial Differential Equation: the Advection-Diffusion Equation Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-05-22T22:37:14.092101Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2ca9af86-5a96-46c9-9c39-5dec57fb310d · outbound

This paper cites Hunter and B.

Observations on Recurrent Loss in the Neural Network Model of a Partial Differential Equation: the Advection-Diffusion Equation Hunter and B

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T22:37:14.084555Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 510a90a4-05dd-425f-8468-2aea0c1bff67 · outbound

This paper cites an unresolved cited work.

Observations on Recurrent Loss in the Neural Network Model of a Partial Differential Equation: the Advection-Diffusion Equation Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-05-22T22:37:14.095804Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation de68811c-7ef1-41d7-ba79-b5f8bc8997cb · outbound

This paper cites an unresolved cited work.

Observations on Recurrent Loss in the Neural Network Model of a Partial Differential Equation: the Advection-Diffusion Equation Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-05-22T22:37:14.081426Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 5cd34d7e-50c4-4976-a8fa-aa249c181147 · outbound

This paper cites Stability ordinates of adams predictor-corrector methods.

Observations on Recurrent Loss in the Neural Network Model of a Partial Differential Equation: the Advection-Diffusion Equation Stability ordinates of adams predictor-corrector methods

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T22:37:14.048765Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 3a6d7bc1-1b52-4158-b202-b07c44c0ea83 · outbound

This paper cites Nocedal and S.

Observations on Recurrent Loss in the Neural Network Model of a Partial Differential Equation: the Advection-Diffusion Equation Nocedal and S

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T22:37:14.052058Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation b962d861-2265-4089-9077-eee9d8e3a6ab · outbound

This paper cites Long short-term memory.Neu- ral Computation, 9:1735–1780, 11 1997.

Observations on Recurrent Loss in the Neural Network Model of a Partial Differential Equation: the Advection-Diffusion Equation Long short-term memory.Neu- ral Computation, 9:1735–1780, 11 1997

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T22:37:14.072305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Pith citing papers

No inbound Pith citation observations are available.