Paper Citation Record · LEDGER

Neuro-Symbolic AI for Analytical Solutions of Differential Equations

As of 22 July 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2502.01476.

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

pith.paper-citation-record.v1
2502.01476 v4

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-23T03:33:09.370984Z

measured 21 of 21 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-07-20T06:30:07.809122+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

21 of 21 outbound references displayed

verified exact13
verified fuzzy3
unresolved0
parse uncertain0
malformed identifier3
metadata mismatch2

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7f29dd85-b467-4165-adfb-04a6d4d8b49f · outbound

This paper cites Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operators.

Neuro-Symbolic AI for Analytical Solutions of Differential Equations Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operators

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-05-23T03:35:21.208401Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-20T06:30:07.809122+00:00.

Observation 38b82215-71f4-4283-8754-576464aa5c45 · outbound

This paper cites doi: 10.11588/ ans.2015.100.20553.

Neuro-Symbolic AI for Analytical Solutions of Differential Equations doi: 10.11588/ ans.2015.100.20553

Reference 2

Resolution: malformed identifier; raw_fallback, observed 2026-05-23T03:35:22.676709Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-20T06:30:07.809122+00:00.

Observation df71280a-6568-4219-800d-6c534f938070 · outbound

This paper cites URLhttps://ojs.aaai.org/index.php/AAAI/ article/view/30050.

Neuro-Symbolic AI for Analytical Solutions of Differential Equations URLhttps://ojs.aaai.org/index.php/AAAI/ article/view/30050

Reference 3

Resolution: verified exact; doi, observed 2026-05-23T03:35:20.559704Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-20T06:30:07.809122+00:00.

Observation 01694dca-239c-4269-936e-74cadea708b1 · outbound

This paper cites Herbert Edelsbrunner and John Harer.Computational topology: an introduction.

Neuro-Symbolic AI for Analytical Solutions of Differential Equations Herbert Edelsbrunner and John Harer.Computational topology: an introduction

Reference 4

Resolution: verified exact; arxiv_id, observed 2026-05-23T03:35:20.555917Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-20T06:30:07.809122+00:00.

Observation 8fc3bc04-4795-4b26-8683-2666ed35fd21 · outbound

This paper cites DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training.

Neuro-Symbolic AI for Analytical Solutions of Differential Equations DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training

Reference 5

Resolution: verified exact; arxiv_id, observed 2026-05-23T03:35:21.232890Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-20T06:30:07.809122+00:00.

Observation 836b86fb-2581-4ca8-8be4-26a0c2fa063d · outbound

This paper cites Poseidon: Efficient Foundation Models for PDEs.

Neuro-Symbolic AI for Analytical Solutions of Differential Equations Poseidon: Efficient Foundation Models for PDEs

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-23T03:35:21.221718Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-20T06:30:07.809122+00:00.

Observation d420e12f-875f-4342-89fc-269e59dbe2b4 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Neuro-Symbolic AI for Analytical Solutions of Differential Equations Adam: A Method for Stochastic Optimization

Reference 7

Resolution: metadata mismatch; local_arxiv, observed 2026-05-23T03:35:21.238512Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-20T06:30:07.809122+00:00.

Observation 5ccc8eed-d028-47b3-a794-8c29a153f4de · outbound

This paper cites Grammar variational autoen- coder.

Neuro-Symbolic AI for Analytical Solutions of Differential Equations Grammar variational autoen- coder

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T03:35:22.659660Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-20T06:30:07.809122+00:00.

Observation 07252835-2c13-4f14-9dfb-5dbb2498b601 · outbound

This paper cites Deep Learning for Symbolic Mathematics.

Neuro-Symbolic AI for Analytical Solutions of Differential Equations Deep Learning for Symbolic Mathematics

Reference 9

Resolution: metadata mismatch; arxiv_id, observed 2026-05-23T03:35:21.186511Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-20T06:30:07.809122+00:00.

Observation 007485de-2e30-4063-9ac1-83877de09611 · outbound

This paper cites Generative AI for fast and accurate statistical computation of fluids.

Neuro-Symbolic AI for Analytical Solutions of Differential Equations Generative AI for fast and accurate statistical computation of fluids

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-05-23T03:35:21.208948Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-20T06:30:07.809122+00:00.

Observation d3e39dd0-1f4d-4372-90d6-4cc7f718e1d6 · outbound

This paper cites Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients.

Neuro-Symbolic AI for Analytical Solutions of Differential Equations Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-05-23T03:35:21.214265Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-20T06:30:07.809122+00:00.

Observation 86251982-fc36-44c6-8882-2a5e54a3d83d · outbound

This paper cites doi: 10.1038/s41586-023-06924-6.

Neuro-Symbolic AI for Analytical Solutions of Differential Equations doi: 10.1038/s41586-023-06924-6

Reference 12

Resolution: verified exact; doi, observed 2026-05-23T03:35:20.549640Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-20T06:30:07.809122+00:00.

Observation f5de78c4-129f-4d96-b978-c2dfb815f4dc · outbound

This paper cites Ups: Efficiently building foundation models for pde solving via cross-modal adaptation.

Neuro-Symbolic AI for Analytical Solutions of Differential Equations Ups: Efficiently building foundation models for pde solving via cross-modal adaptation

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T03:35:22.653568Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-20T06:30:07.809122+00:00.

Observation c6ec6256-ce6f-4d9f-855f-3da779e7a971 · outbound

This paper cites Towards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolation.

Neuro-Symbolic AI for Analytical Solutions of Differential Equations Towards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolation

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-05-23T03:35:21.197306Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-20T06:30:07.809122+00:00.

Observation 5e4ddfb6-f2ea-4c0d-b59c-4e28ff6b4bc1 · outbound

This paper cites SymFormer: End-to-end symbolic regression using transformer-based architecture.

Neuro-Symbolic AI for Analytical Solutions of Differential Equations SymFormer: End-to-end symbolic regression using transformer-based architecture

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-05-23T03:35:21.192010Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-20T06:30:07.809122+00:00.

Observation 8942bdfe-eec4-4bd5-858d-2f9a5f036600 · outbound

This paper cites Symbolic Regression is NP-hard.

Neuro-Symbolic AI for Analytical Solutions of Differential Equations Symbolic Regression is NP-hard

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-05-23T03:35:21.181138Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-20T06:30:07.809122+00:00.

Observation 74c458e5-81ba-4bbe-981f-8b4f0df775a6 · outbound

This paper cites Closed-form Solutions: A New Perspective on Solving Differential Equations.

Neuro-Symbolic AI for Analytical Solutions of Differential Equations Closed-form Solutions: A New Perspective on Solving Differential Equations

Reference 17

Resolution: verified exact; arxiv_id, observed 2026-05-23T03:35:21.191331Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-20T06:30:07.809122+00:00.

Observation 091dc681-a427-479b-bea7-13d701938c44 · outbound

This paper cites Grammar-based ordinary differential equation discovery.arXiv preprint arXiv:2504.02630.

Neuro-Symbolic AI for Analytical Solutions of Differential Equations Grammar-based ordinary differential equation discovery.arXiv preprint arXiv:2504.02630

Reference 18

Resolution: verified exact; arxiv_id, observed 2026-05-23T03:35:21.226710Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-20T06:30:07.809122+00:00.

Observation 8312f62a-c77a-4450-a7f2-53e6ccf3ec0d · outbound

This paper cites an unresolved cited work.

Neuro-Symbolic AI for Analytical Solutions of Differential Equations Unresolved cited work

Reference 19

Resolution: malformed identifier; raw_fallback, observed 2026-05-23T03:35:22.656629Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-20T06:30:07.809122+00:00.

Observation f1ab7509-ef45-4ef2-99bc-8e528ba80e89 · outbound

This paper cites IfL Hull = 0then everyz i lies in the an explicit convex enclosure of the frozen reservoir∩ D d=1{z: ⟨nm, z⟩ ≤h Rprev t }.

Neuro-Symbolic AI for Analytical Solutions of Differential Equations IfL Hull = 0then everyz i lies in the an explicit convex enclosure of the frozen reservoir∩ D d=1{z: ⟨nm, z⟩ ≤h Rprev t }

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T03:35:22.671075Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-20T06:30:07.809122+00:00.

Observation 7efb9753-c2ff-425c-a960-96fd6e65ccf8 · outbound

This paper cites 23 For evaluation on this problem, we rely on mesh convergence studies and physics-based consistency checks rather than direct error computation against an analytical reference.

Neuro-Symbolic AI for Analytical Solutions of Differential Equations 23 For evaluation on this problem, we rely on mesh convergence studies and physics-based consistency checks rather than direct error computation against an analytical reference

Reference 21

Resolution: malformed identifier; raw_fallback, observed 2026-05-23T03:35:22.663224Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-20T06:30:07.809122+00:00.

Pith citing papers

No inbound Pith citation observations are available.