Paper Citation Record · LEDGER

PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics

As of 11 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 15 inbound Pith citation observations for arXiv:2409.09811.

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

pith.paper-citation-record.v1
2409.09811 v1

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 15 of 15 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 15 of 15 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-09T21:55:52.608138Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-03T08:17:46.076628Z

Reference resolution

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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 27120485-e7d5-40d6-8382-632f6a16a1dd · inbound

BCAT: A Block Causal Transformer for PDE Foundation Models for Fluid Dynamics cites this paper.

BCAT: A Block Causal Transformer for PDE Foundation Models for Fluid Dynamics PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-09T21:55:52.608138Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 93cd4027-1140-47f5-a59a-18790646913d · inbound

A Multimodal PDE Foundation Model for Prediction and Scientific Text Descriptions cites this paper.

A Multimodal PDE Foundation Model for Prediction and Scientific Text Descriptions PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-08T17:02:12.776976Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5a1df786-3914-4563-bb75-fc0103931644 · inbound

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations cites this paper.

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T15:38:29.575921Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f37a56ef-5e11-4531-9d52-3f85b9c3d372 · inbound

Self-supervised neural operator for solving partial differential equations cites this paper.

Self-supervised neural operator for solving partial differential equations PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics

Reference 26

Resolution: verified exact; arxiv_id, observed 2026-05-21T22:10:42.363347Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 62bda610-a10a-43b9-81b3-1e146d838772 · inbound

Flow marching for a generative PDE foundation model cites this paper.

Flow marching for a generative PDE foundation model PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics

Reference 42

Resolution: verified exact; arxiv_id, observed 2026-05-18T13:51:25.630701Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 5d175c63-5ce2-48d9-9b52-bd36884bad3a · inbound

CompNO: A Novel Foundation Model approach for solving Partial Differential Equations cites this paper.

CompNO: A Novel Foundation Model approach for solving Partial Differential Equations PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics

Reference 25

Resolution: verified exact; arxiv_id, observed 2026-05-16T14:53:00.501748Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation fe10a0ce-037b-4aad-99ce-b6cf78aa3ac8 · inbound

OmniMol: Transferring Particle Physics Knowledge to Molecular Dynamics with Point-Edge Transformers cites this paper.

OmniMol: Transferring Particle Physics Knowledge to Molecular Dynamics with Point-Edge Transformers PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics

Reference 30

Resolution: verified exact; arxiv_id, observed 2026-05-16T13:20:58.057036Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 93ad568a-cc39-4efd-8203-4fa541286485 · inbound

MVNN: A Measure-Valued Neural Network for Learning McKean-Vlasov Dynamics from Particle Data cites this paper.

MVNN: A Measure-Valued Neural Network for Learning McKean-Vlasov Dynamics from Particle Data PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics

Reference 66

Resolution: verified exact; arxiv_id, observed 2026-05-13T22:48:23.009771Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f36b3c6c-57ac-42f1-ae84-190733241c40 · inbound

A Multimodal Vision Transformer-based Modeling Framework for Prediction of Fluid Flows in Energy Systems cites this paper.

A Multimodal Vision Transformer-based Modeling Framework for Prediction of Fluid Flows in Energy Systems PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics

Reference 5

Resolution: verified exact; arxiv_id, observed 2026-05-13T20:33:17.087118Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 371a03da-4cb6-4733-8445-f24bb99a010c · inbound

Compositional Neural Operators for Multi-Dimensional Fluid Dynamics cites this paper.

Compositional Neural Operators for Multi-Dimensional Fluid Dynamics PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-05-13T07:32:29.507957Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation fc4f9516-c72f-4e6a-bbc0-47e285eaba54 · inbound

Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospects cites this paper.

Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospects PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics

Reference 144

Resolution: verified exact; arxiv_id, observed 2026-05-19T20:32:45.616303Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 32a33cac-4695-4ec1-a798-61ebb6bc16e1 · inbound

ARC-STAR: Auditable Post-Hoc Correction for PDE Foundation Models cites this paper.

ARC-STAR: Auditable Post-Hoc Correction for PDE Foundation Models PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics

Reference 33

Resolution: verified exact; arxiv_id, observed 2026-05-22T07:14:42.383409Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation d5b1f637-487c-4096-997a-d9a11c971b7d · inbound

ARC-STAR: Auditable Post-Hoc Correction for PDE Foundation Models cites this paper.

ARC-STAR: Auditable Post-Hoc Correction for PDE Foundation Models PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics

Reference 33

Resolution: verified exact; arxiv_id, observed 2026-05-25T05:46:39.714438Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 7f3232b5-1c4b-4fc5-8ae4-d7fb5f14164c · inbound

ARC-STAR: Auditable Post-Hoc Correction for PDE Foundation Models cites this paper.

ARC-STAR: Auditable Post-Hoc Correction for PDE Foundation Models PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics

Reference 33

Resolution: verified exact; arxiv_id, observed 2026-06-30T17:44:57.779305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 2f4b506d-e046-4507-83a7-d44d36b4097c · inbound

Harness In-Context Operator Learning with Chain of Operators cites this paper.

Harness In-Context Operator Learning with Chain of Operators PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics

Reference 26

Resolution: verified exact; arxiv_id, observed 2026-07-03T08:17:46.078683Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.