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Paper Citation Record · LEDGER

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates

As of 10 August 2026, this Paper Citation Record lists 81 of 81 outbound references and 1 inbound Pith citation observation for arXiv:2506.05513.

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

pith.paper-citation-record.v1
2506.05513 v1

Coverage vector

measured 81 of 81 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T10:30:13.789264Z

measured 82 of 82 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-30T16:23:26.962085Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

81 of 81 outbound references displayed

  • verified exact1
  • verified fuzzy57
  • unresolved23
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3a3099e3-cc1c-4cb7-b851-df712ee7d4b4 · outbound

This paper cites Computational design of the basic dynamical processes of the ucla general circulation model.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Computational design of the basic dynamical processes of the ucla general circulation model

Reference 1

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no resolver link, observed 2026-08-07T10:29:52.840817Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation baedcf3f-4c88-4a54-8cab-e58837a2c1de · outbound

This paper cites an unresolved cited work.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Unresolved cited work

Reference 2

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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.

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Observation 0bc6d075-38ef-4852-8d27-2b885d0c40c6 · outbound

This paper cites an unresolved cited work.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Unresolved cited work

Reference 3

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raw_fallback, observed 2026-08-07T10:30:14.786019Z

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

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Observation bc595ae4-b163-499d-8866-e302ea9315e2 · outbound

This paper cites M., Turner, R.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates M., Turner, R

Reference 4

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

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Observation 5882ec3b-4929-4f2e-8c5b-64b575ad0941 · outbound

This paper cites Enforcing analytic constraints in neural networks emulating physical systems.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Enforcing analytic constraints in neural networks emulating physical systems

Reference 5

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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.

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Observation e3f977b9-218d-4123-ae8c-022e682fe058 · outbound

This paper cites Spherical fourier neural operators: Learning stable dynamics on the sphere.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Spherical fourier neural operators: Learning stable dynamics on the sphere

Reference 6

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no resolver link, observed 2026-08-07T10:30:12.577173Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation 1db48b7d-1048-4bee-af21-b5e2f2806b2a · outbound

This paper cites J., and Welling, M.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates J., and Welling, M

Reference 7

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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.

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Observation 9b6fcb06-3ec0-4f3b-99af-c1b2268e5981 · outbound

This paper cites an unresolved cited work.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Unresolved cited work

Reference 8

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raw_fallback, observed 2026-08-07T10:30:14.726773Z

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.

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Observation 4dae8aec-7958-423e-8b10-1cc8e0dc7fc6 · outbound

This paper cites E., and Welling, M.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates E., and Welling, M

Reference 9

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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.

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Observation 5fceb3a1-c0af-49d2-8859-5466ddf49315 · outbound

This paper cites R., Gupta, R., Magee, A.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates R., Gupta, R., Magee, A

Reference 10

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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.

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Observation 157a03cc-1077-40db-9827-78ec4e1fcbeb · outbound

This paper cites A program to build e (n)-equivariant steerable cnns.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates A program to build e (n)-equivariant steerable cnns

Reference 11

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raw_fallback, observed 2026-08-07T10:30:14.686418Z

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.

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Observation dd1e76d5-4464-4254-8fd3-67fbf7b2e665 · outbound

This paper cites an unresolved cited work.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Unresolved cited work

Reference 12

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raw_fallback, observed 2026-08-07T10:30:14.675115Z

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.

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Observation 0789a90f-d324-455e-aaef-2316e99a8d93 · outbound

This paper cites N., and Ma, J.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates N., and Ma, J

Reference 13

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verified fuzzy
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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.

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Observation 9233dfc4-d90d-47f8-8841-fdf05b129299 · outbound

This paper cites and Welling, M.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates and Welling, M

Reference 14

Resolution
verified fuzzy
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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.

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Observation 79b5e36a-30cd-4b61-b342-7fc7d1c64764 · outbound

This paper cites Gauge equivariant convolutional networks and the icosahedral cnn.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Gauge equivariant convolutional networks and the icosahedral cnn

Reference 15

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no resolver link, observed 2026-08-07T10:30:12.637926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation 49224cd8-9ec6-4e68-bf09-bf97ac76cbc3 · outbound

This paper cites S., Geiger, M., K \"o hler, J., and Welling, M.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates S., Geiger, M., K \"o hler, J., and Welling, M

Reference 16

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no resolver link, observed 2026-08-07T10:30:12.644586Z

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Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-07T10:30:12.644586Z digest=sha256:0a42bada4ffb7fbb86e6af236d7221339d810edf7f2aaa609f6eb7b17b75755c

Observation a6534924-5a52-4df7-815e-bc8bbd1c2b40 · outbound

This paper cites Lagrangian Neural Networks.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Lagrangian Neural Networks

Reference 17

Resolution
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no resolver link, observed 2026-08-07T10:30:12.651390Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation 302277ff-dbdd-4055-85ac-70df8753ec33 · outbound

This paper cites Gauge equivariant mesh cnns: Anisotropic convolutions on geometric graphs.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Gauge equivariant mesh cnns: Anisotropic convolutions on geometric graphs

Reference 18

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

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Observation 8cc34532-9e4d-49fd-a39c-e59a7b365cb3 · outbound

This paper cites S., Manikin, G.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates S., Manikin, G

Reference 19

Resolution
verified fuzzy
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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.

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Observation 79beffc5-0d48-4582-8b3d-6dc91e862a75 · outbound

This paper cites Learning so (3) equivariant representations with spherical cnns.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Learning so (3) equivariant representations with spherical cnns

Reference 20

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

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Observation ee7b22e4-b7e0-48d7-bb45-320984fe9148 · outbound

This paper cites General covariance data augmentation for neural pde solvers.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates General covariance data augmentation for neural pde solvers

Reference 21

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

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Observation 201e37e3-d830-4da8-8190-dfc51c918ebf · outbound

This paper cites H., Peri \'c , M., and Street, R.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates H., Peri \'c , M., and Street, R

Reference 22

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

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Observation 201159a6-62e2-4d20-aa4a-9ae5a208c834 · outbound

This paper cites Directional message passing for molecular graphs.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Directional message passing for molecular graphs

Reference 23

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

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Observation 5a4d45a3-2bbb-4346-bace-0703df9948f7 · outbound

This paper cites Learning to optimize multigrid pde solvers.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Learning to optimize multigrid pde solvers

Reference 24

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

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Observation af341305-62d1-479c-adb1-fdc07e22de69 · outbound

This paper cites Hamiltonian neural networks.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Hamiltonian neural networks

Reference 25

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

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Observation dd1c92f8-956d-48cb-9c5d-8262be20bb53 · outbound

This paper cites an unresolved cited work.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Unresolved cited work

Reference 26

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raw_fallback, observed 2026-08-07T10:30:14.533132Z

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

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Observation 6ec65ab7-8c42-4786-9cc8-3f4cf7f5b3d6 · outbound

This paper cites Group equivariant fourier neural operators for partial differential equations.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Group equivariant fourier neural operators for partial differential equations

Reference 27

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raw_fallback, observed 2026-08-07T10:30:14.522089Z

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.

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Observation db7083c3-efa0-45e3-ac07-947c0daf7b64 · outbound

This paper cites and Thuerey, N.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates and Thuerey, N

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.510614Z

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.

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Observation 4d81f30c-282f-4223-9ad9-ce1a61c83908 · outbound

This paper cites and Mitsume, N.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates and Mitsume, N

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.499458Z

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.

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Observation 1c61652c-a6dd-4b26-a6a1-fef082c7ad0a · outbound

This paper cites Learning neural pde solvers with convergence guarantees.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Learning neural pde solvers with convergence guarantees

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.487778Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.741152Z digest=sha256:e3578c0e096f3cdaf3e786d5c213ea0b48247c1020f0b18e1a0c895b168575ef

Observation f62caf99-1564-4d97-9a9c-cd8111435032 · outbound

This paper cites and Greenberg, D.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates and Greenberg, D

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.475404Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.748372Z digest=sha256:2165a0e0f8d018561de4298898138c8eb2d1b112f339e7af649c5c3605c3123c

Observation fbf710a8-c9a8-4dca-a14e-43c1d9a0840d · outbound

This paper cites Openfoam: Open source cfd in research and industry.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Openfoam: Open source cfd in research and industry

Reference 32

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raw_fallback, observed 2026-08-07T10:30:14.464311Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.755264Z digest=sha256:43d6394e639bda4205bc0e4afeb6114a7b7341e5fd5537b4aa320a25c9681679

Observation 6434e390-ff90-4c7e-ac52-9e8483264202 · outbound

This paper cites u ggemann, N., Chegini, F., Cr \.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates u ggemann, N., Chegini, F., Cr \

Reference 33

Resolution
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raw_fallback, observed 2026-08-07T10:30:14.451899Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.762290Z digest=sha256:e13cd98c773fd3fcc7039edcc3cafe0bd3b455294313231f38ab8ff07e7f1b0f

Observation b72d73cd-de97-434c-9995-a70f4fa4bdfd · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Adam: A Method for Stochastic Optimization

Reference 34

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unresolved
no resolver link, observed 2026-08-07T10:30:12.769533Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-07T10:30:12.769533Z digest=sha256:35a66546455e1701b1ec21b995ca1edc479de838af4c537f117327f80d3a6e59

Observation cafa213c-a74f-44c1-8731-712491fea8e5 · outbound

This paper cites M., Wessels, D., Valperga, R., Papa, S., Sonke, J.-J., Bekkers, E.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates M., Wessels, D., Valperga, R., Papa, S., Sonke, J.-J., Bekkers, E

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.439333Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.776605Z digest=sha256:35035951cb4283e960a32b1707881ec8759c6306cac768d7e29f97910f71faef

Observation f4cacd03-fbb5-4938-8584-5fcd198f1417 · outbound

This paper cites A., Alieva, A., Wang, Q., Brenner, M.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates A., Alieva, A., Wang, Q., Brenner, M

Reference 36

Resolution
verified fuzzy
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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.

source=arxiv_source observed=2026-08-07T10:30:12.783782Z digest=sha256:7c269b1c979b70a16d6d4a4a7be82e74344e857bae2c9e394b1a568f7ba99405

Observation 6aac759d-3269-4186-bee5-040f32da4520 · outbound

This paper cites o wer, M., Lottes, J., Rasp, S., D \.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates o wer, M., Lottes, J., Rasp, S., D \

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.415723Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.790645Z digest=sha256:6b89270e11b10ce0a755d771c572587cb8587cb56ff5796404fde9e239c430d2

Observation efd7689a-017e-496b-bbd8-21abccf90689 · outbound

This paper cites Benchmarking autoregressive conditional diffusion models for turbulent flow simulation.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Benchmarking autoregressive conditional diffusion models for turbulent flow simulation

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.403737Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.797446Z digest=sha256:789b3dd0a15cab49004628ce26966d78728c5431ea7040b86ea82cc7475a51e7

Observation 0e9425c4-3eaf-4e48-b76d-2552a2abe19a · outbound

This paper cites H., Lorenz, S., Gutjahr, O., Haak, H., Linardakis, L., Mehlmann, C., Mikolajewicz, U., Notz, D., et al.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates H., Lorenz, S., Gutjahr, O., Haak, H., Linardakis, L., Mehlmann, C., Mikolajewicz, U., Notz, D., et al

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.392955Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.804499Z digest=sha256:704597dc03abc3de4238b42d43d8ae6b2e80be0d20e16573b79978a9d3022d91

Observation c97d56e0-b124-4aff-b0a7-dff10f7f451c · outbound

This paper cites B., Azizzadenesheli, K., Bhattacharya, K., Stuart, A., Anandkumar, A., et al.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates B., Azizzadenesheli, K., Bhattacharya, K., Stuart, A., Anandkumar, A., et al

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.380693Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.811674Z digest=sha256:38fb8ecf3f9e887b7cb9915d20218876639c8b175cf2f4d6942529a7698a92ca

Observation 70d784ae-727f-4b75-9cb9-7384e5d62343 · outbound

This paper cites Long-term predictions of turbulence by implicit u-net enhanced fourier neural operator.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Long-term predictions of turbulence by implicit u-net enhanced fourier neural operator

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.369013Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.818782Z digest=sha256:9f33852067593f4a402b89505cdeedcd6e4cfef47c4a88da26c30e8c274f6053

Observation 96466872-52d6-47d6-bd28-5072aedc4e29 · outbound

This paper cites A., and Cantwell, C.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates A., and Cantwell, C

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.355389Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.826095Z digest=sha256:5376934f2decebe10ffd0e961815782b76b01a5e5fa0cbfc9cc02dabbe14e555

Observation 81de23a2-aa46-4d8d-8ea0-23d4c48ce4b9 · outbound

This paper cites Pde-refiner: Achieving accurate long rollouts with neural pde solvers.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Pde-refiner: Achieving accurate long rollouts with neural pde solvers

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.342367Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.832882Z digest=sha256:c3c989d28ead6ea329041ba751f038f9577423daac8d39e8dd3df04e0fe53228

Observation abb759a6-8a71-498d-b90f-4d75ed664482 · outbound

This paper cites How temporal unrolling supports neural physics simulators.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates How temporal unrolling supports neural physics simulators

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.329750Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.843004Z digest=sha256:94941be68387f63a98d4588d3acc6ef20bae9bc5bc44f74b2c0830a8219d3e60

Observation 9aade8b4-dd6a-408a-afd8-a452c1d2baba · outbound

This paper cites Pde-net 2.0: Learning pdes from data with a numeric-symbolic hybrid deep network.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Pde-net 2.0: Learning pdes from data with a numeric-symbolic hybrid deep network

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.317791Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.849175Z digest=sha256:1ace40bf612d871bc697c8a928d312d6d3217ebcbbf04d5f1e6c1aa063f79767

Observation e36655e7-b2ad-4556-acb8-96411f702823 · outbound

This paper cites G., Paronuzzi, S., Peltier, M., Person, R., Rousset, C., Rynders, S., Samson, G., Téchené, S., Vancoppenolle, M., and Wilson, C.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates G., Paronuzzi, S., Peltier, M., Person, R., Rousset, C., Rynders, S., Samson, G., Téchené, S., Vancoppenolle, M., and Wilson, C

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.305054Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.856445Z digest=sha256:4a67a0377888fb6dd6edbb04e4752075dabb44c1bdfed2535b17bbc438654370

Observation e5705540-c000-43c9-b720-bdca29adb27d · outbound

This paper cites Nemo ocean engine reference manual.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Nemo ocean engine reference manual

Reference 47

Resolution
unresolved
no resolver link, observed 2026-08-07T10:30:12.863750Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-07T10:30:12.863750Z digest=sha256:4a770112a096b2a8a7551a024038deb43db90aedbf36f88edb7d77d5f05e70ec

Observation a8bbe180-16cd-40dd-afcc-645215a76516 · outbound

This paper cites Combining model and geostationary satellite data to reconstruct hourly sst field over the mediterranean sea.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Combining model and geostationary satellite data to reconstruct hourly sst field over the mediterranean sea

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.293945Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.870618Z digest=sha256:98d507c3687bda8bd13a747639952ae97e76fda0715baca21201d114d9f198c9

Observation 92cccf1c-690b-4963-8634-746b5bdb50f6 · outbound

This paper cites and Hakim, A.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates and Hakim, A

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.281747Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.877756Z digest=sha256:a51a17fe37501f3bdf7d166e16cc38ab94663ee6ff25ee7ebcaf6556285e4caa

Observation 6f454651-206d-418c-abb2-68b2dea69dc6 · outbound

This paper cites Physics-constrained Unsupervised Learning of Partial Differential Equations using Meshes.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Physics-constrained Unsupervised Learning of Partial Differential Equations using Meshes

Reference 50

Resolution
verified exact
local_arxiv, observed 2026-08-07T10:30:13.875291Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.884312Z digest=sha256:77e6a7b9441f949bada12156f31b26ed4de4eb16b57646dd79e10d649ce95866

Observation 5a848c93-e700-4006-9843-fb6459f9105b · outbound

This paper cites Embedding Hard Physical Constraints in Neural Network Coarse-Graining of 3D Turbulence.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Embedding Hard Physical Constraints in Neural Network Coarse-Graining of 3D Turbulence

Reference 51

Resolution
unresolved
no resolver link, observed 2026-08-07T10:30:12.891465Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-07T10:30:12.891465Z digest=sha256:dcebbef48e5acaebf7afb36e4a3ab6bb2f7ea88696e1a34fd9b413dd8b9e3199

Observation 9b9d1db5-eb43-4715-9129-343d32e4f599 · outbound

This paper cites K., and Grover, A.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates K., and Grover, A

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.271231Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.898766Z digest=sha256:ba60409b7d4046fee16cffe93a5dac755a819c3f3445dfc282a2afd872653a12

Observation 48416ddb-4d08-488e-af9f-ac29f03d9b40 · outbound

This paper cites Invariante variationsprobleme.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Invariante variationsprobleme

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.259941Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.905476Z digest=sha256:4ce5d8820ec328f34cb239a2fa3e577209b377514097ad29e770309930538756

Observation 9071cb97-2fc4-46ca-b5d2-97fb52edce08 · outbound

This paper cites an unresolved cited work.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Unresolved cited work

Reference 54

Resolution
unresolved
no resolver link, observed 2026-08-07T10:30:12.912396Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-07T10:30:12.912396Z digest=sha256:54f9b5088f67fbe2618f9fbbe0f1b35d6e12ce20bb8bddfb50079c53c0ef0871

Observation 009e5016-3a4f-4753-8e33-f6dc94a626ea · outbound

This paper cites Convolutional neural operators for robust and accurate learning of pdes.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Convolutional neural operators for robust and accurate learning of pdes

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.242441Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.919444Z digest=sha256:2eb82dd3c7b13d132f64c560802c20949a7357822ce4087a59c6012a2eb63610

Observation 60653113-7976-4041-bd8c-6015a4d90106 · outbound

This paper cites S., Jia, X., Willard, J., Appling, A.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates S., Jia, X., Willard, J., Appling, A

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.230250Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.926607Z digest=sha256:b94d9f71521fa93c4e1e414e1ed028fe9f76a4a0e6cf3394e834d24300546e9f

Observation 21ba133e-9340-4460-83e2-5241675498fc · outbound

This paper cites and Valiquette, F.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates and Valiquette, F

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.218322Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.933380Z digest=sha256:9b3dbc8d7767517e2df45e4733d51411ddb31109a1476c31c58865fb608b09a7

Observation 21554504-d1b1-43d1-8473-d6585788f0a6 · outbound

This paper cites an unresolved cited work.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Unresolved cited work

Reference 58

Resolution
unresolved
raw_fallback, observed 2026-08-07T10:30:14.205579Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.940531Z digest=sha256:67319b8537739923657aafb519f15da4b1e8291ed71aa72984e5cc71057b83ee

Observation 45301de0-1161-492e-8204-9993c2a89bfd · outbound

This paper cites U-net: Convolutional networks for biomedical image segmentation.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates U-net: Convolutional networks for biomedical image segmentation

Reference 59

Resolution
unresolved
no resolver link, observed 2026-08-07T10:30:12.947257Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-07T10:30:12.947257Z digest=sha256:d8dbd473808241758c8fc78be2aa9c7e43c3fd6b683e5181640b66906da5962e

Observation b83fa8b2-e553-47d5-b0e7-bcf38c580d30 · outbound

This paper cites Clifford group equivariant neural networks.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Clifford group equivariant neural networks

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.189199Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.954497Z digest=sha256:81dce7923b9f906c0ceb60ab6a13a6615486af73e84552b275e06c2a03e2165b

Observation 9bddb6d3-7e8a-4165-8b38-594c3d71987b · outbound

This paper cites Learning to simulate complex physics with graph networks.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Learning to simulate complex physics with graph networks

Reference 61

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.178796Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.961486Z digest=sha256:6ac1302c34e5c4d134df9618e3c503287fff82c4b18ed038fa44f6c8d031b852

Observation 185883a4-3c9c-46f3-b2fc-a4001b3c05af · outbound

This paper cites DySLIM: Dynamics Stable Learning by Invariant Measure for Chaotic Systems.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates DySLIM: Dynamics Stable Learning by Invariant Measure for Chaotic Systems

Reference 62

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unresolved
no resolver link, observed 2026-08-07T10:30:12.968735Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-07T10:30:12.968735Z digest=sha256:b43dba3d3b5ad3b903dc51b87da86617b9ae6eaca67ad569d07e86c9602317a3

Observation 53ab7782-02d8-416b-b3cb-7e95ac06b5cd · outbound

This paper cites M., Portegies, J., Bekkers, E.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates M., Portegies, J., Bekkers, E

Reference 63

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.167644Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.975365Z digest=sha256:05835a571fbd71676fd5e105ed8da886312cfd19f16b6c71cf7a9d9ae6ba1de8

Observation c1ab512a-8a92-4004-b517-f824004cee54 · outbound

This paper cites The shifted boundary method for hyperbolic systems: Embedded domain computations of linear waves and shallow water flows.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates The shifted boundary method for hyperbolic systems: Embedded domain computations of linear waves and shallow water flows

Reference 64

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.155725Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.982424Z digest=sha256:b712a6544eddb463ca7ab92ee17d364eead5a3be8bb03cfc273ff51f35382ab0

Observation b99d21f1-c84f-454f-9fc7-3c39b0fb4579 · outbound

This paper cites an unresolved cited work.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Unresolved cited work

Reference 65

Resolution
unresolved
raw_fallback, observed 2026-08-07T10:30:14.144211Z

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.

source=arxiv_source observed=2026-08-07T10:30:12.991023Z digest=sha256:c99787202d7df4ba86913bef2b4497c77572dfd8e97a7a36f10cddf71646074b

Observation e49a1064-0fec-47a4-8623-9305aaf36eca · outbound

This paper cites Learned Coarse Models for Efficient Turbulence Simulation.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Learned Coarse Models for Efficient Turbulence Simulation

Reference 66

Resolution
unresolved
no resolver link, observed 2026-08-07T10:30:12.998844Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-07T10:30:12.998844Z digest=sha256:81e48c96466e998c5712763b02acde757026715b25dea441b9a278e88170da8d

Observation 2788426b-8314-4eda-a961-673a59f1b286 · outbound

This paper cites M., Tomida, K., White, C.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates M., Tomida, K., White, C

Reference 67

Resolution
unresolved
no resolver link, observed 2026-08-07T10:30:13.082112Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-07T10:30:13.082112Z digest=sha256:5b75a5546ecce959353ffa9245d829c8246f5eecc94077c7b08b9258a356270e

Observation 8fbe54ae-4504-48f6-9c6d-6a8ebf170687 · outbound

This paper cites A neural pde solver with temporal stencil modeling.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates A neural pde solver with temporal stencil modeling

Reference 68

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.133280Z

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.

source=arxiv_source observed=2026-08-07T10:30:13.431644Z digest=sha256:a29103747dc64eabf0de722afc406f91f54918ec41a0d6e70996fd185f8999ba

Observation 796ac7ef-0137-46ca-8e09-af5dc239b684 · outbound

This paper cites Pdebench: An extensive benchmark for scientific machine learning.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Pdebench: An extensive benchmark for scientific machine learning

Reference 69

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.121448Z

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.

source=arxiv_source observed=2026-08-07T10:30:13.636162Z digest=sha256:161972d5e7bb8f8b2f9d7b13fd9f5dc8fde51af091fc07d5325bab4d3c12b558

Observation aec163db-22fa-48aa-b9ac-5e9e14d6c72f · outbound

This paper cites Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds

Reference 70

Resolution
unresolved
no resolver link, observed 2026-08-07T10:30:13.716882Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-07T10:30:13.716882Z digest=sha256:7e2e01c398b4ce2e5ce2c73f2a71c8a41c185f6bec758ca98506465dc06c5c89

Observation fdaa3761-f805-4229-bdf4-18b02829d585 · outbound

This paper cites Accelerating eulerian fluid simulation with convolutional networks.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Accelerating eulerian fluid simulation with convolutional networks

Reference 71

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.109421Z

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.

source=arxiv_source observed=2026-08-07T10:30:13.746131Z digest=sha256:21d96041580a0a9ce48ab032d1cba929c913b300e9c9207864737e6db47f13e5

Observation addcc71a-69a0-4736-94dd-88a875e56dad · outbound

This paper cites P., Galletti, G., Brandstetter, J., Adami, S., and Adams, N.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates P., Galletti, G., Brandstetter, J., Adami, S., and Adams, N

Reference 72

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.096813Z

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.

source=arxiv_source observed=2026-08-07T10:30:13.754535Z digest=sha256:b15b7fb0cb77fa3af2e02bc45f605842cbf3a8a803282c65e9cf7e236de1a50c

Observation 8d3a42b5-ff1a-4dba-8477-5528d6d863c2 · outbound

This paper cites an unresolved cited work.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Unresolved cited work

Reference 73

Resolution
unresolved
raw_fallback, observed 2026-08-07T10:30:14.085286Z

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.

source=arxiv_source observed=2026-08-07T10:30:13.757744Z digest=sha256:4d56fdac9ac1f6b411f110300ae8f5c3fd3731e915e83e7b21ca5f482b85beb5

Observation bf6babf0-8976-4440-a56e-4d10ededf875 · outbound

This paper cites and Chakraborty, S.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates and Chakraborty, S

Reference 74

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.073957Z

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.

source=arxiv_source observed=2026-08-07T10:30:13.760898Z digest=sha256:447bdbf17a79ba6d8537a6bd189eaf5e22c8bdabb324ee5375443adf757dc4ed

Observation 7f2387c8-189e-425a-b769-a7abd1266a09 · outbound

This paper cites R., Holl, P., and Thuerey, N.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates R., Holl, P., and Thuerey, N

Reference 75

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.063178Z

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.

source=arxiv_source observed=2026-08-07T10:30:13.764179Z digest=sha256:b2a153ec2e053be6a9abbc2445398214e565e12d18c8ba57bdccc8e4917cca01

Observation 4974ae35-9462-404e-9357-625c23bd2ae9 · outbound

This paper cites S., Linmans, J., Winkens, J., Cohen, T., and Welling, M.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates S., Linmans, J., Winkens, J., Cohen, T., and Welling, M

Reference 76

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.050706Z

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.

source=arxiv_source observed=2026-08-07T10:30:13.767903Z digest=sha256:a99b0771d9de50654fd0019b8cfd474f7744d75f68a363489614bee1f029aed5

Observation 63b06909-892d-434b-a07e-2aa0090bb2ca · outbound

This paper cites Learning incompressible fluid dynamics from scratch-towards fast, differentiable fluid models that generalize.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Learning incompressible fluid dynamics from scratch-towards fast, differentiable fluid models that generalize

Reference 77

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.037861Z

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.

source=arxiv_source observed=2026-08-07T10:30:13.772071Z digest=sha256:b393dd7962409d9c7d2c0bdc7d340e3013ea02134df91c91d20b7ec498810f38

Observation 2fbc5f7b-c7bd-4ce1-ba94-86c55d61f5fe · outbound

This paper cites Incorporating symmetry into deep dynamics models for improved generalization.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Incorporating symmetry into deep dynamics models for improved generalization

Reference 78

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.025637Z

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.

source=arxiv_source observed=2026-08-07T10:30:13.776492Z digest=sha256:3f69f802b78956d1abc7c5f476205b76ad2a19043e43e2cc34e4eee283719004

Observation 6fa6a7a7-bd58-404e-95b5-e8a729a5d6ba · outbound

This paper cites K., Henn, B., Duncan, J., Brenowitz, N.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates K., Henn, B., Duncan, J., Brenowitz, N

Reference 79

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.013693Z

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.

source=arxiv_source observed=2026-08-07T10:30:13.781071Z digest=sha256:e83a70fea2cc9d3fdfef420971572640d4dc2137af243ca071dd570521d70205

Observation 633fdb46-adaa-4e06-b1d6-55638a7c8fc9 · outbound

This paper cites and Cesa, G.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates and Cesa, G

Reference 80

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:30:14.000623Z

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.

source=arxiv_source observed=2026-08-07T10:30:13.785259Z digest=sha256:b4fec416888f80b5a9a2ab57c477c0350b9ada87402a60c4dd719b7050e42caa

Observation b1a008d6-9df6-46e6-bba5-c5e51129f771 · outbound

This paper cites write newline.

Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates write newline

Reference 81

Resolution
unresolved
no resolver link, observed 2026-08-07T10:30:13.789264Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-07T10:30:13.789264Z digest=sha256:f8a480ae2db3f5090ea18b267349f7af8d7c06f6e11fda9e3cf1c1fa2fd1e052

Pith citing papers

Observation 29c8536f-1f4f-4d50-a59e-e0f3dd713cba · inbound

No Free Lunch in Flow Surrogates under Time-Varying Boundary Conditions: A Two-Regime Study cites this paper.

No Free Lunch in Flow Surrogates under Time-Varying Boundary Conditions: A Two-Regime Study Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates

Reference 72

Resolution
unresolved
no resolver link, observed 2026-07-30T16:23:26.962085Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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