Paper Citation Record · LEDGER

Missing Physics Discovery through Fully Differentiable Finite Element-Based Machine Learning

As of 9 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 1 inbound Pith citation observation for arXiv:2507.15787.

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

pith.paper-citation-record.v1
2507.15787 v3

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T15:30:27.057692Z

measured 19 of 19 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-28T01:45:05.606735Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-02T12:56:56.951361Z

Reference resolution

18 of 18 outbound references displayed

verified exact3
verified fuzzy4
unresolved9
parse uncertain0
malformed identifier1
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e37f44c4-4ee1-4ba4-bb1e-133d03c73a40 · outbound

This paper cites Differentiable programming across the PDE and Machine Learning barrier.

Missing Physics Discovery through Fully Differentiable Finite Element-Based Machine Learning Differentiable programming across the PDE and Machine Learning barrier

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T15:30:27.002207Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 29f4aae2-aa9f-46b7-bf0a-6f6db8a96eb8 · outbound

This paper cites & Regazzoni, F.

Missing Physics Discovery through Fully Differentiable Finite Element-Based Machine Learning & Regazzoni, F

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T15:30:27.006536Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a873744a-43dc-42f5-af82-55a884538faf · outbound

This paper cites Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction.

Missing Physics Discovery through Fully Differentiable Finite Element-Based Machine Learning Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-08-06T15:30:27.151219Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 71549dbe-c1dc-4455-b9d6-f6bc619808db · outbound

This paper cites Physics-driven machine learning models coupling PyTorch and Firedrake.

Missing Physics Discovery through Fully Differentiable Finite Element-Based Machine Learning Physics-driven machine learning models coupling PyTorch and Firedrake

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-06T15:30:27.013534Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1e2c98ee-7d79-4074-bc97-97bd392bc670 · outbound

This paper cites & Bouziani, N.

Missing Physics Discovery through Fully Differentiable Finite Element-Based Machine Learning & Bouziani, N

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:30:27.312969Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 28344086-ab74-46f5-a563-cea1ad8492af · outbound

This paper cites InInternational Conference on Learning Representations(2021).

Missing Physics Discovery through Fully Differentiable Finite Element-Based Machine Learning InInternational Conference on Learning Representations(2021)

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:30:27.303590Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ef7446d0-ddcf-4da5-95c6-c375b07f8f1b · outbound

This paper cites Physics-Informed Neural Operator for Learning Partial Differential Equations.

Missing Physics Discovery through Fully Differentiable Finite Element-Based Machine Learning Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-06T15:30:27.024022Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 90d368d4-6b9c-4540-9962-968d5292e51f · outbound

This paper cites Structure-Preserving Operator Learning.

Missing Physics Discovery through Fully Differentiable Finite Element-Based Machine Learning Structure-Preserving Operator Learning

Reference 9

Resolution: malformed identifier; no resolver link, observed 2026-08-06T15:30:27.027119Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 20cbd25d-14fa-44a7-9cea-0b63d4021531 · outbound

This paper cites an unresolved cited work.

Missing Physics Discovery through Fully Differentiable Finite Element-Based Machine Learning Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-06T15:30:27.030167Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c86dbb4b-1c27-4907-91e8-254494044b20 · outbound

This paper cites Escaping the abstraction: a foreign function interface for the Unified Form Language [UFL].

Missing Physics Discovery through Fully Differentiable Finite Element-Based Machine Learning Escaping the abstraction: a foreign function interface for the Unified Form Language [UFL]

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-06T15:30:27.118434Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1b93bbb9-f219-4f8a-8b92-b71a60fa4bbd · outbound

This paper cites InAdvances in Neural Information Processing Systems, vol.

Missing Physics Discovery through Fully Differentiable Finite Element-Based Machine Learning InAdvances in Neural Information Processing Systems, vol

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:30:27.294782Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 53299a0e-6fd2-4949-a152-45db4b1133d8 · outbound

This paper cites http://github.com/google/jax (2018).

Missing Physics Discovery through Fully Differentiable Finite Element-Based Machine Learning http://github.com/google/jax (2018)

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:30:27.285237Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 78c9b3e2-7fa5-4142-8260-d4c9fda5ef42 · outbound

This paper cites & Salehipour, H.

Missing Physics Discovery through Fully Differentiable Finite Element-Based Machine Learning & Salehipour, H

Reference 15

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T15:30:27.251544Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 186cb9f4-6a5b-4f6e-ab8b-11658909ca7f · outbound

This paper cites Learning to Control PDEs with Differentiable Physics.

Missing Physics Discovery through Fully Differentiable Finite Element-Based Machine Learning Learning to Control PDEs with Differentiable Physics

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-06T15:30:27.044492Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d2b6ac7a-926e-42fc-ad54-9ba305dd8847 · outbound

This paper cites an unresolved cited work.

Missing Physics Discovery through Fully Differentiable Finite Element-Based Machine Learning Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-06T15:30:27.048376Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b27a177e-9658-4892-9d42-b5d54809273d · outbound

This paper cites Universal Differential Equations for Scientific Machine Learning.

Missing Physics Discovery through Fully Differentiable Finite Element-Based Machine Learning Universal Differential Equations for Scientific Machine Learning

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-06T15:30:27.051243Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 784654b7-3ad9-45e2-9010-39ff6cce31b9 · outbound

This paper cites an unresolved cited work.

Missing Physics Discovery through Fully Differentiable Finite Element-Based Machine Learning Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:30:27.276350Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 46077744-dabf-4281-b51e-c1da22135762 · outbound

This paper cites Reports7, 46190, DOI: 10.1038/srep46190 (2017).

Missing Physics Discovery through Fully Differentiable Finite Element-Based Machine Learning Reports7, 46190, DOI: 10.1038/srep46190 (2017)

Reference 20

Resolution: verified exact; doi, observed 2026-08-06T15:30:27.083910Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Pith citing papers

Observation 42acede7-99ae-4b9e-900e-5d85fd593116 · inbound

Integrating Mechanistic and Data-Driven Models for Neurological Disorders through Differentiable Programming cites this paper.

Integrating Mechanistic and Data-Driven Models for Neurological Disorders through Differentiable Programming Missing Physics Discovery through Fully Differentiable Finite Element-Based Machine Learning

Reference 42

Resolution: verified exact; arxiv_id, observed 2026-07-20T01:18:18.179451Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.