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Paper Citation Record · LEDGER

Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations

As of 18 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 3 inbound Pith citation observations for arXiv:2405.14099.

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

pith.paper-citation-record.v1
2405.14099 v4

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 3 of 3 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T17:33:20.478422Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-02T00:16:23.914091Z

Reference resolution

0 of 0 outbound references displayed

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External citation measurements

No source-named external measurement is stored.

Outbound references

No outbound reference observations are available for this paper version.

Pith citing papers

Observation 345c5c56-6a28-41b0-a6be-2881ae8526ef · inbound

Learn Singularly Perturbed Solutions via Homotopy Dynamics cites this paper.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations

Reference 9

Resolution
unresolved
no resolver link, observed 2026-08-09T18:57:13.452489Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-09T18:57:13.452489Z digest=sha256:7974347023d8c2f7da9312c29759b4f2c5cfea5e6c164edfbe1562b9a1b95601

Observation 6c211c7b-52e9-4aac-b9da-83e109dfeec1 · inbound

Cosmology-informed Neural Networks to infer dark energy equation-of-state cites this paper.

Cosmology-informed Neural Networks to infer dark energy equation-of-state Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations

Reference 41

Resolution
unresolved
no resolver link, observed 2026-08-15T17:33:20.478422Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T17:33:20.478422Z digest=sha256:dc651a5102d8da0840f7e77b761a1e62e22bf7f6e92ea568a499f38e1c63d3fa

Observation 18474ef5-3014-47e6-9d43-ab05e4035ec2 · inbound

Neural Spectral Element Methods for stiff multiphysics PDEs with electrochemical transport benchmarks cites this paper.

Neural Spectral Element Methods for stiff multiphysics PDEs with electrochemical transport benchmarks Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations

Reference 30

Resolution
verified exact
arxiv_id, observed 2026-07-02T00:16:23.917114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-06-28T13:33:19.259276Z digest=sha256:125f5fd3b8ed8ffb9e24f6d302d79b6830db887ed08449a4a69caaea61a11abe