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Paper Citation Record · LEDGER

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems

As of 22 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 0 inbound Pith citation observations for arXiv:2608.12286.

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

pith.paper-citation-record.v1
2608.12286 v1

Coverage vector

measured 49 of 49 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T00:16:22.821206Z

measured 49 of 49 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+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

49 of 49 outbound references displayed

  • verified exact2
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  • unresolved20
  • parse uncertain0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a1dad3b7-bc47-4f93-95cf-0a899893f1d1 · outbound

This paper cites an unresolved cited work.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Unresolved cited work

Reference 1

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation 3d64623f-36cb-488d-8bb4-2d26cd1d1223 · outbound

This paper cites Gray and S.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Gray and S

Reference 2

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation accf33e8-7216-4511-9a64-6b6ca6a553df · outbound

This paper cites an unresolved cited work.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Unresolved cited work

Reference 3

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation 6079e29a-7a4c-4a1c-b2a7-b799e6a69305 · outbound

This paper cites an unresolved cited work.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Unresolved cited work

Reference 4

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation afd5eb55-3ae4-42f8-b24a-2d544fae6d9c · outbound

This paper cites Gierer and H.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Gierer and H

Reference 5

Resolution
unresolved
no resolver link, observed 2026-08-16T00:16:22.628230Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-16T00:16:22.628230Z digest=sha256:ae202c662060c77cac2fbf45208a804d5d670ec890bcc8cbd29844ad89c29a0e

Observation 972b747f-1c59-4548-b7e2-b1b9c8175e94 · outbound

This paper cites Solution landscape of reaction-diffusion systems reveals a nonlinear mechanism and spatial robustness of pattern formation.Fundamental Research, 2025.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Solution landscape of reaction-diffusion systems reveals a nonlinear mechanism and spatial robustness of pattern formation.Fundamental Research, 2025

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:16:23.637602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.633077Z digest=sha256:0c36ea81cc18042b12ac5b6a16a184454901ed6d5c4d6b87cddc64f0e56732e3

Observation 9261e871-9dd5-4137-af17-71095b24457d · outbound

This paper cites Spatial pattern formation in reaction–diffusion models: a computational approach.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Spatial pattern formation in reaction–diffusion models: a computational approach

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:16:23.624656Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.637466Z digest=sha256:d9cb98a547095003fd7b7ae32b2fd9a03fc51462338337e9520d93e0e2288c66

Observation fe4400a3-64ae-45c9-80b9-89ac02e5ba91 · outbound

This paper cites Matrix-oriented discretization methods for reaction–diffusion PDEs: comparisons and applications.Computers and Mathematics with Applications, 79: 2067–2085, 2020.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Matrix-oriented discretization methods for reaction–diffusion PDEs: comparisons and applications.Computers and Mathematics with Applications, 79: 2067–2085, 2020

Reference 8

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation 179a2e97-2db0-4e86-9bd9-1651734fabf9 · outbound

This paper cites an unresolved cited work.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Unresolved cited work

Reference 9

Resolution
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.646276Z digest=sha256:9bb153b5f520657bae8517bc41c728de2714143f0055071481fdb940990fc515

Observation b837ec4c-9009-4059-9d7a-4947aa7a5248 · outbound

This paper cites A homotopy method based on weno schemes for solving steady state problems of hyperbolic conservation laws.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems A homotopy method based on weno schemes for solving steady state problems of hyperbolic conservation laws

Reference 10

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.651579Z digest=sha256:c83cc84f0340fcf1d7d1e462c573c61c354840c580e3b0e71c5b0d80dbe04d02

Observation 026426ee-5a87-4315-8a41-02210c308677 · outbound

This paper cites A bootstrapping approach for computing multiple solutions of differential equations.Journal of Computational and Applied Mathematics, 258:181–190, 2014.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems A bootstrapping approach for computing multiple solutions of differential equations.Journal of Computational and Applied Mathematics, 258:181–190, 2014

Reference 11

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation bb04ad5b-6224-4112-addc-12d8d66d15fe · outbound

This paper cites an unresolved cited work.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Unresolved cited work

Reference 12

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation d35e687a-d584-482d-a506-042aceea4693 · outbound

This paper cites an unresolved cited work.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Unresolved cited work

Reference 13

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation b4aa90d7-db19-4776-881e-476c78a4b82e · outbound

This paper cites an unresolved cited work.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Unresolved cited work

Reference 14

Resolution
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation 7bb89543-4a1e-496b-8156-9dd83089bd1b · outbound

This paper cites an unresolved cited work.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Unresolved cited work

Reference 15

Resolution
unresolved
no resolver link, observed 2026-08-16T00:16:22.672755Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-16T00:16:22.672755Z digest=sha256:e4bdf61e5a49c43f1fe80b8cb66f117e7a7d5e7261fa09fbbca9a3403d8e8876

Observation 751d5f72-8c05-48e1-8adf-8b7d5217bf75 · outbound

This paper cites an unresolved cited work.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Unresolved cited work

Reference 16

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.677456Z digest=sha256:cf7556ea2ef8ad486be6e9f95a2d6e2c3e05c88ea8467938a1436417ff301eb8

Observation bb11d9c2-1e09-44d9-8061-50652efee23b · outbound

This paper cites Raissi, P.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Raissi, P

Reference 17

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.681749Z digest=sha256:696f31b3450889a272adcd0dc493921dadd39955dee305c42352085520610391

Observation 7c9f7e68-66cf-43b0-8da5-8ded96c8b7c8 · outbound

This paper cites Giampaolo, M.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Giampaolo, M

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:16:23.486970Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation cb196e2c-e105-422b-89e7-f8a5804be879 · outbound

This paper cites an unresolved cited work.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Unresolved cited work

Reference 19

Resolution
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.689911Z digest=sha256:17f1bad9dabf09620d560d33437f266adc149de06f0da70b046a4f603d1dc7f8

Observation a8384aff-f089-4f94-af12-d44c66527cb3 · outbound

This paper cites When and why PINNs fail to train: a neural tangent kernel perspective.Journal of Computational Physics, 449:110768, 2022.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems When and why PINNs fail to train: a neural tangent kernel perspective.Journal of Computational Physics, 449:110768, 2022

Reference 20

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.693669Z digest=sha256:62fd92e6ed7b0ec3e41b8ab384b8243f3202d2a314c4cefdd815672104fd2f65

Observation effcb032-e050-44af-86fa-d23ededc3c2b · outbound

This paper cites Stiff-PINN: physics-informed neural network for stiff chemical kinetics.The Journal of Physical Chemistry A, 125(36):8098–8106, 2021.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Stiff-PINN: physics-informed neural network for stiff chemical kinetics.The Journal of Physical Chemistry A, 125(36):8098–8106, 2021

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:16:23.447011Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.698352Z digest=sha256:7f6bd93ff5b53cbf13957ef651dbbfd20f6466c50b28cc737c593a76f33ecee8

Observation 895763ce-b520-491c-bb75-6f7c8e9b7dc4 · outbound

This paper cites an unresolved cited work.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Unresolved cited work

Reference 22

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.703594Z digest=sha256:07c19672ef2feb9fb6bcbafd87c04d176d88eb33a6e5f5b6d377a5336b149459

Observation 030c2407-9a58-41ac-bf10-ce5cef5835b8 · outbound

This paper cites Geometry-informed neural networks.Proceedings of the International Conference on Machine Learning (ICML), 2025.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Geometry-informed neural networks.Proceedings of the International Conference on Machine Learning (ICML), 2025

Reference 23

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.707991Z digest=sha256:a1d8e8e978fa6bec80b0c0908fa162895da3fafb696ae89f7e460b06c2aec944

Observation cc198c5a-121d-429d-9dce-5cb7cb7686e4 · outbound

This paper cites Newton informed neural operator for computing multiple solutions of nonlinear partial differential equations.Advances in Neural Information Processing Systems (NeurIPS), 2024.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Newton informed neural operator for computing multiple solutions of nonlinear partial differential equations.Advances in Neural Information Processing Systems (NeurIPS), 2024

Reference 24

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.712491Z digest=sha256:11a8ecd964e3daa6bcc3e732072ecc308eac85bc018944140622d6a8cc4b5c10

Observation 4ea15d86-9b66-4f22-a090-dd1fc3476ff0 · outbound

This paper cites A neural network kernel decomposition for learning multiple steady states in parameterized dynamical systems.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems A neural network kernel decomposition for learning multiple steady states in parameterized dynamical systems

Reference 25

Resolution
verified exact
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation 418c771f-ebcd-4a01-b845-c7672cd4d2b2 · outbound

This paper cites Wang and W.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Wang and W

Reference 26

Resolution
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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-16T00:16:22.721218Z digest=sha256:416dbc0438bc0f4bee9548c34be8a5749a8c02eda8f631bc2d88543f02a8836f

Observation 0f1d4ff5-0f6c-4c76-8ddd-f796b635b045 · outbound

This paper cites an unresolved cited work.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-16T00:16:23.387158Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation 011aa354-86dc-4b56-98fe-4bf29b5de8f4 · outbound

This paper cites an unresolved cited work.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Unresolved cited work

Reference 28

Resolution
unresolved
raw_fallback, observed 2026-08-16T00:16:23.369217Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.729963Z digest=sha256:40c7340b7050db5eb03f56076327c0fe9c4e9538ffe26351b9fc8fcc6ffefec9

Observation 1151404d-42d6-42fb-8563-56a3bdec7ab0 · outbound

This paper cites Andersson, Andrew El-Kadi, Dominic Masters, Timo Ewalds, Jacklynn Stott, Shakir Mohamed, Peter Battaglia, Remi Lam, and Matthew Willson.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Andersson, Andrew El-Kadi, Dominic Masters, Timo Ewalds, Jacklynn Stott, Shakir Mohamed, Peter Battaglia, Remi Lam, and Matthew Willson

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:16:23.353055Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.735585Z digest=sha256:254d0b662304cdf9ef444086b04913abfcc7250cb9b0ddf0389913fb93d9be08

Observation 46f5e0f1-db05-4da2-a12c-051f6c0467b0 · outbound

This paper cites Pawan Kumar, Emilien Dupont, Francisco J.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Pawan Kumar, Emilien Dupont, Francisco J

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:16:23.336012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.739669Z digest=sha256:cd1fcd564585f5fe14b59827aadef40a080b93041ad6ae86503a98a9b781f01f

Observation cd803664-15ff-475d-a6b2-73102fe31887 · outbound

This paper cites an unresolved cited work.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Unresolved cited work

Reference 31

Resolution
unresolved
raw_fallback, observed 2026-08-16T00:16:23.321464Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.743524Z digest=sha256:738d5fe5365e4546d1d524dc6fa9e5cc3ca9bc151cbe783ebda5cffb35199cf3

Observation 74f4efe5-1285-4c56-95c6-09b9607108fd · outbound

This paper cites Fine-Tune Language Models as Multi-Modal Differential Equation Solvers.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Fine-Tune Language Models as Multi-Modal Differential Equation Solvers

Reference 32

Resolution
unresolved
no resolver link, observed 2026-08-16T00:16:22.747502Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-16T00:16:22.747502Z digest=sha256:e1473c40f59c8cc40523435e4d0987d9fbdca4a0e422952f3ef0a13e7007d2d4

Observation b87a7d12-23ec-4cbb-abe0-1b261f3abdca · outbound

This paper cites In-Context Learning of Linear Systems: Generalization Theory and Applications to Operator Learning.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems In-Context Learning of Linear Systems: Generalization Theory and Applications to Operator Learning

Reference 33

Resolution
unresolved
no resolver link, observed 2026-08-16T00:16:22.751732Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-16T00:16:22.751732Z digest=sha256:3ac242a91e57a68451778cb52ed87328d0da00cd117b8de2b5dc4e78e6150cc9

Observation 712d853d-949b-46ca-a55f-3fdc0df74798 · outbound

This paper cites Unsupervised solution operator learning for mean-field games via sampling- invariant parametrizations.Journal of Computational Physics, 2025.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Unsupervised solution operator learning for mean-field games via sampling- invariant parametrizations.Journal of Computational Physics, 2025

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:16:23.309063Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.756427Z digest=sha256:ea7e2468b3fb94654a17c98ddbd10da4aae588920c4904ee22351a774171a3fd

Observation f319262c-577e-4876-be51-049cc560c5a8 · outbound

This paper cites Wang, Pierre Erbacher, and Patrick Gallinari.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Wang, Pierre Erbacher, and Patrick Gallinari

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:16:23.295964Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.760907Z digest=sha256:90427b06cccdd903aaf0a5c16f9836b3ff9447a4c35510978a8127d06578fc60

Observation 003aec4f-cad1-475e-a68c-2fda7909a42c · outbound

This paper cites ENMA: tokenwise autoregression for generative neural PDE operators.Preprint at arXiv:2506.06158, 2025.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems ENMA: tokenwise autoregression for generative neural PDE operators.Preprint at arXiv:2506.06158, 2025

Reference 36

Resolution
verified exact
raw_fallback, observed 2026-08-16T00:16:23.001598Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.765098Z digest=sha256:48d8cec8ad44bd56ab17124777c752ce68a83f22ad28d886f417ebf5d8118c3a

Observation 8e8474aa-7741-4b4b-8e18-5e8179b68bf9 · outbound

This paper cites Pretrained transformers as universal computation engines.AAAI Conference on Artificial Intelligence, 2022.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Pretrained transformers as universal computation engines.AAAI Conference on Artificial Intelligence, 2022

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:16:23.283797Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.769878Z digest=sha256:bea9d805853f490ffc3d37cc0ea346d2efa891699462fa96eb45333de17c691e

Observation 8d16c6ed-ec95-4547-95a1-cf6b32026147 · outbound

This paper cites Efficient approximation of deep ReLU networks for functions on low dimensional manifolds.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Efficient approximation of deep ReLU networks for functions on low dimensional manifolds

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:16:23.270558Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.773764Z digest=sha256:9ff6ac2f509e902bea620cef94d695868fd422cda9ec2dd8e4ab853ae25763f5

Observation 6e2982a1-d1b4-4535-bbe3-bf7a5f6f9636 · outbound

This paper cites Towards a foundation model for partial differential equations: Multi-operator learning and extrapolation.Physical Review E, 111(3):035304, 2025.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Towards a foundation model for partial differential equations: Multi-operator learning and extrapolation.Physical Review E, 111(3):035304, 2025

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:16:23.257377Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.777771Z digest=sha256:b97744a1c30a55d0704f5b6042f4ec09c1c6e0bcda8e6d52d8901a161a07d8d4

Observation fbf3549c-0e9e-4b2d-981d-fc82cf369473 · outbound

This paper cites an unresolved cited work.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Unresolved cited work

Reference 40

Resolution
unresolved
raw_fallback, observed 2026-08-16T00:16:23.242312Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.782683Z digest=sha256:849c08204351f94d0005bb4ccf4a079010782acc28235f6ede0bfd899f013bf6

Observation 27e78fa4-609c-4d1f-9305-7140701129e5 · outbound

This paper cites Qwen2.5 Technical Report.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Qwen2.5 Technical Report

Reference 41

Resolution
unresolved
no resolver link, observed 2026-08-16T00:16:22.787075Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-16T00:16:22.787075Z digest=sha256:208fea279cf50e7a008a9fe52ac5ac303e5186548be3c5bfda1c9590dbd1ff0e

Observation c673813f-3d29-44bb-94d5-a3abbbe62d8a · outbound

This paper cites An efficient quasi-Newton method with tensor product imple- mentation for solving quasi-linear elliptic equations and systems.Journal of Scientific Computing, 103:89, 2025.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems An efficient quasi-Newton method with tensor product imple- mentation for solving quasi-linear elliptic equations and systems.Journal of Scientific Computing, 103:89, 2025

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:16:23.229413Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.791490Z digest=sha256:47aa74d854750f6dc9f5ddffb466d43fd2cbcc4a4476193fa37b5373cf88fbdf

Observation 99a2878c-0385-4510-a204-fa592a149e88 · outbound

This paper cites Stepien, Erica M.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Stepien, Erica M

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:16:23.216439Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.795622Z digest=sha256:e265d90e634997581a0ba4674ac9b50a5a2724a3141e136b570300362c2195db

Observation 7e23df48-dfa8-4299-b612-b83eb1403cb0 · outbound

This paper cites Aronow, and Leili Shahri- yari.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Aronow, and Leili Shahri- yari

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:16:23.204154Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.799757Z digest=sha256:6a69abfbc3c4f3880d5bda1a881d10d5c183dc657d2bd6271cdc040ef1d10f27

Observation 235b21be-aa01-49d5-ae17-6a6f0daeda46 · outbound

This paper cites Rempala, and Hye-Won Kang.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Rempala, and Hye-Won Kang

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:16:23.189259Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.804169Z digest=sha256:6f0eaedb8d0fca6f888337487fe1ef3537a2116c4bb5cfd73fb061a30a234039

Observation 6af54da7-c7bb-49a2-8ec4-7f76e63289cd · outbound

This paper cites A topology-based network tree for the prediction of protein– protein binding affinity changes following mutation.Nature Machine Intelligence, 2(2):116–123, 2020.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems A topology-based network tree for the prediction of protein– protein binding affinity changes following mutation.Nature Machine Intelligence, 2(2):116–123, 2020

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:16:23.175506Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.808781Z digest=sha256:8c11235dafa65e71bc7cf94a48498597901c2d47175bc5c6d168ed1a3b973ba1

Observation 8180b5ed-0bb3-4f81-8f0b-820e91b128a3 · outbound

This paper cites Order matters: sequence to sequence for sets.International Conference on Learning Representations (ICLR), 2016.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Order matters: sequence to sequence for sets.International Conference on Learning Representations (ICLR), 2016

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:16:23.162433Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.813098Z digest=sha256:bc9b757085a4a62ab36146a6987040eae1e2c0c09b28002ed00bdf0177b5ed5b

Observation 100d874e-aae7-4d0f-bc6b-9f5b76d3780f · outbound

This paper cites End-to-end object detection with transformers.European Conference on Computer Vision (ECCV), 2020.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems End-to-end object detection with transformers.European Conference on Computer Vision (ECCV), 2020

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:16:23.148679Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.817202Z digest=sha256:cd96378ea4bcfea1de50832352c093f30b52ff9b5be871012d8ea8fdd19b4df3

Observation cd917e7a-71a5-49bb-b9eb-3667b0674c3b · outbound

This paper cites Fleet, and Geoffrey Hinton.

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems Fleet, and Geoffrey Hinton

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:16:23.135015Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T00:16:22.821206Z digest=sha256:776897cd2e0481ecdcca52c7d230040c5a5965606d261604f498cd4e13a4e958

Pith citing papers

No inbound Pith citation observations are available.