Paper Citation Record · LEDGER

Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning

As of 6 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 0 inbound Pith citation observations for arXiv:2410.06074.

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

pith.paper-citation-record.v1
2410.06074 v3

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-11T11:50:26.030339Z

measured 18 of 18 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-06T06:34:29.942622+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

18 of 18 outbound references displayed

verified exact6
verified fuzzy8
unresolved1
parse uncertain0
malformed identifier1
metadata mismatch2

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 8442d086-e108-4e46-9fcc-4e866c0affd3 · outbound

This paper cites A Mathematical Guide to Operator Learning.

Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning A Mathematical Guide to Operator Learning

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-05-23T19:33:22.114348Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation ae0025e1-58c7-43de-a822-b9676c83e083 · outbound

This paper cites an unresolved cited work.

Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-05-23T19:33:22.474285Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 902fac89-b9da-490f-9635-da971a5ee75e · outbound

This paper cites ODEFormer: Symbolic Regression of Dynamical Systems with Transformers.

Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning ODEFormer: Symbolic Regression of Dynamical Systems with Transformers

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-05-23T19:33:22.120695Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 366728d7-266e-4a14-a8fe-fb05c4940354 · outbound

This paper cites Ode- former: Symbolic regression of dynamical systems with transformers.

Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning Ode- former: Symbolic regression of dynamical systems with transformers

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T19:33:22.471042Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 58a8e5d4-2cac-4e65-8d34-fc36fc5abe79 · outbound

This paper cites 7, 18 11 Published as a conference paper at ICLR 2025 J.R.

Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning 7, 18 11 Published as a conference paper at ICLR 2025 J.R

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T19:33:22.466707Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 02cd93bc-7c90-435c-8ce0-44123aa8ca9f · outbound

This paper cites doi: https://doi.org/ 10.1016/0771-050X(80)90013-3.

Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning doi: https://doi.org/ 10.1016/0771-050X(80)90013-3

Reference 6

Resolution: verified exact; doi, observed 2026-05-23T19:33:21.770020Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 788ffdbf-dd51-41be-8f1d-291b5d24f87e · outbound

This paper cites Neural Operator: Graph Kernel Network for Partial Differential Equations.

Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning Neural Operator: Graph Kernel Network for Partial Differential Equations

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-05-23T19:33:22.127503Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 3fe25cb9-3974-4ecd-a664-3df71d115080 · outbound

This paper cites Mechanistic neural networks for scientific machine learning.

Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning Mechanistic neural networks for scientific machine learning

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T19:33:22.489863Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 892723e0-1582-4961-8c34-6f730c00a316 · outbound

This paper cites Universal Differential Equations for Scientific Machine Learning.

Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning Universal Differential Equations for Scientific Machine Learning

Reference 9

Resolution: metadata mismatch; local_arxiv, observed 2026-05-23T19:33:21.797995Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation bdeeb65c-30c7-4167-b235-89d81f6edc4d · outbound

This paper cites Universal Differential Equations for Scientific Machine Learning.

Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning Universal Differential Equations for Scientific Machine Learning

Reference 10

Resolution: verified exact; local_arxiv, observed 2026-05-23T19:33:22.133769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation e274a4b5-ba8a-4325-a7ed-dd824deb3ef7 · outbound

This paper cites Raissi, P.

Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning Raissi, P

Reference 11

Resolution: metadata mismatch; doi, observed 2026-05-23T19:33:21.785302Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 4d9798f3-8a7a-4511-868c-e2686a5f8f9b · outbound

This paper cites ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEs.

Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEs

Reference 12

Resolution: verified exact; arxiv_id, observed 2026-05-23T19:33:22.140774Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 9e117c62-e3e7-4995-bd9b-ea86fb3a86cc · outbound

This paper cites A, b, and W are only theoretical and they are not explicitly constructed during computation.

Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning A, b, and W are only theoretical and they are not explicitly constructed during computation

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T19:33:22.478500Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation eac38c14-fefe-43e9-adf2-7fa5ada4cace · outbound

This paper cites AutoDiff.

Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning AutoDiff

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T19:33:22.493425Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 589391ac-ef4e-4f97-b936-9130d675f542 · outbound

This paper cites u0 = y (0), u0 = y (0), u1 = y′ (0), u2 = y′′ (0) are initial values.

Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning u0 = y (0), u0 = y (0), u1 = y′ (0), u2 = y′′ (0) are initial values

Reference 15

Resolution: malformed identifier; raw_fallback, observed 2026-05-23T19:33:22.501133Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 64124193-8d95-4578-845e-c2e398e1cf6b · outbound

This paper cites Our modifications in S-MNN provide alterna- tive approximation methods that improve efficiency without sacrificing accuracy.

Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning Our modifications in S-MNN provide alterna- tive approximation methods that improve efficiency without sacrificing accuracy

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T19:33:22.486422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 04fd006c-4d3e-469c-8874-9afd40c7989b · outbound

This paper cites 54, 55, and 56): the approximation errors bounded by a slack variable ϵ ∈ R.

Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning 54, 55, and 56): the approximation errors bounded by a slack variable ϵ ∈ R

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T19:33:22.482314Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation c8990d40-5db5-4f5c-a978-111fc158b13d · outbound

This paper cites The square matrix in Eq.

Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning The square matrix in Eq

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T19:33:22.497379Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Pith citing papers

No inbound Pith citation observations are available.