Paper Citation Record · LEDGER

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models

As of 8 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 2 inbound Pith citation observations for arXiv:2506.09830.

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pith.paper-citation-record.v1
2506.09830 v2

Coverage vector

measured 47 of 47 reference resolution

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measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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

Source: pith, observed 2026-07-03T15:58:37.903787Z

Reference resolution

47 of 47 outbound references displayed

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External citation measurements

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Outbound references

Observation 99df302e-f584-4e52-9758-afab02fee86b · outbound

This paper cites Radial basis function and related models: an overview.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Radial basis function and related models: an overview

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.929757Z

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Observation 67f02af7-793d-4b8a-aa2d-244842bc2981 · outbound

This paper cites On closures for reduced order models—a spectrum of first-principle to machine- learned avenues.Physics of Fluids, 33(9), 2021.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models On closures for reduced order models—a spectrum of first-principle to machine- learned avenues.Physics of Fluids, 33(9), 2021

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.922680Z

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Observation 716b61e9-c55b-4500-9757-82a6b6c8e883 · outbound

This paper cites Galerkin neural networks: A framework for approxi- mating variational equations with error control.SIAM Journal on Scientific Computing, 43(4):A2474–A2501, 2021.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Galerkin neural networks: A framework for approxi- mating variational equations with error control.SIAM Journal on Scientific Computing, 43(4):A2474–A2501, 2021

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.915171Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8857c1ee-6ed6-43d3-afdb-719e71107373 · outbound

This paper cites Nonlinear model order reduction via dynamic mode decomposition.SIAM Journal on Scientific Computing, 39(5):B778–B796, 2017.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Nonlinear model order reduction via dynamic mode decomposition.SIAM Journal on Scientific Computing, 39(5):B778–B796, 2017

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.908097Z

Source-reported events for the cited work

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Observation da149430-5acf-4dbf-9d8f-e0acf63d2580 · outbound

This paper cites Nonlinear model order reduc- tion based on local reduced-order bases.International Journal for Numerical Methods in Engineering, 92(10):891–916, 2012.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Nonlinear model order reduc- tion based on local reduced-order bases.International Journal for Numerical Methods in Engineering, 92(10):891–916, 2012

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.899832Z

Source-reported events for the cited work

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Observation 3223a397-b632-4bff-b52f-bc2a580b762f · outbound

This paper cites Baratta, Joseph P.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Baratta, Joseph P

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.891859Z

Source-reported events for the cited work

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Observation 149d5808-2c15-44d6-8221-6168bcf2ee44 · outbound

This paper cites an unresolved cited work.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:46:01.884066Z

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Observation df479762-d45b-4842-994d-5a4d1fc8607b · outbound

This paper cites De Gruyter, 2021.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models De Gruyter, 2021

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.876944Z

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Observation 3ece56fd-d53e-400b-8e4c-1768d5ef7f5d · outbound

This paper cites De Gruyter, 2020.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models De Gruyter, 2020

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.869893Z

Source-reported events for the cited work

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Observation 840d3e46-eb8e-44e6-9efc-84af64f66094 · outbound

This paper cites De Gruyter, 2020.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models De Gruyter, 2020

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.862828Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 85163b8b-81db-49f2-b030-6066afb51c1f · outbound

This paper cites The proper orthogonal decomposition in the analysis of turbulent flows.Annual review of fluid mechanics, 25(1):539–575, 1993.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models The proper orthogonal decomposition in the analysis of turbulent flows.Annual review of fluid mechanics, 25(1):539–575, 1993

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-07T04:45:54.704370Z

Source-reported events for the cited work

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Observation 705252bd-69cb-4632-af2e-7921af139ac3 · outbound

This paper cites Radial basis functions.Acta numerica, 9:1–38, 2000.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Radial basis functions.Acta numerica, 9:1–38, 2000

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.850456Z

Source-reported events for the cited work

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Observation 7ef23241-4737-4e47-82fa-1eaf8083fe2a · outbound

This paper cites Physics-informed ma- chine learning for reduced-order modeling of nonlinear problems.Journal of computational physics, 446:110666, 2021.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Physics-informed ma- chine learning for reduced-order modeling of nonlinear problems.Journal of computational physics, 446:110666, 2021

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.842666Z

Source-reported events for the cited work

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Observation 2c0aaa9b-f3ff-48e7-bcb7-cfe868c268ff · outbound

This paper cites Gaussian processes for ordinal regression.Journal of machine learning research, 6(7), 2005.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Gaussian processes for ordinal regression.Journal of machine learning research, 6(7), 2005

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.834718Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 30e53a94-bdea-443d-832a-b9026d858721 · outbound

This paper cites Generative adversarial reduced order modelling.Scientific Reports, 14(1):3826, 2024.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Generative adversarial reduced order modelling.Scientific Reports, 14(1):3826, 2024

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-07T04:45:55.256904Z

Source-reported events for the cited work

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Observation 27e0e890-2509-4cc3-a992-63cfaa04af3d · outbound

This paper cites A deeponet multi-fidelity approach for residual learning in reduced order modeling.Advanced Modeling and Simulation in Engineering Sciences, 10(1):12, 2023.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models A deeponet multi-fidelity approach for residual learning in reduced order modeling.Advanced Modeling and Simulation in Engineering Sciences, 10(1):12, 2023

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.821980Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 241c3f2c-75d6-4948-b27e-d0cc735afe4d · outbound

This paper cites Greedy algorithms for reduced bases in banach spaces.Constructive Approximation, 37(3):455–466, Jun 2013.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Greedy algorithms for reduced bases in banach spaces.Constructive Approximation, 37(3):455–466, Jun 2013

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.814478Z

Source-reported events for the cited work

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Observation 7aeb33ab-67ad-4645-94a7-e706c1351599 · outbound

This paper cites Operator inference for non-intrusive model reduction with quadratic manifolds.Computer Methods in Applied Mechanics and Engineering, 403:115717, 2023.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Operator inference for non-intrusive model reduction with quadratic manifolds.Computer Methods in Applied Mechanics and Engineering, 403:115717, 2023

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.807067Z

Source-reported events for the cited work

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Observation d8eb2add-aaa8-41bf-8308-bffe2822fd92 · outbound

This paper cites Singular value decomposition and least squares solutions.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Singular value decomposition and least squares solutions

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.798993Z

Source-reported events for the cited work

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Observation db58b88a-fc2d-41ed-9046-c0e4c1e1e11e · outbound

This paper cites Non-intrusive reduced order modeling of nonlinear problems using neural networks.Journal of Computational Physics, 363, 02 2018.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Non-intrusive reduced order modeling of nonlinear problems using neural networks.Journal of Computational Physics, 363, 02 2018

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.790668Z

Source-reported events for the cited work

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Observation f9e5b0c2-f81d-4acd-a992-e1db87861026 · outbound

This paper cites an unresolved cited work.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Unresolved cited work

Reference 21

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Observation b459e325-4624-46f7-ab0c-bd365479bef7 · outbound

This paper cites Hy- brid data-driven closure strategies for reduced order modeling.Applied Mathematics and Computation, 448:127920, 2023.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Hy- brid data-driven closure strategies for reduced order modeling.Applied Mathematics and Computation, 448:127920, 2023

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.774137Z

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Observation f43f683a-1209-473b-844e-146708f70e62 · outbound

This paper cites Pressure data-driven variational multiscale reduced order models.Journal of Computational Physics, 476:111904, 2023.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Pressure data-driven variational multiscale reduced order models.Journal of Computational Physics, 476:111904, 2023

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.766765Z

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Observation 9516a515-ccb8-402c-9843-b523f80e8d52 · outbound

This paper cites Rutzmoser, and Daniel J.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Rutzmoser, and Daniel J

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.758715Z

Source-reported events for the cited work

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Observation 58a2e171-2510-497d-8d0e-b78a92472366 · outbound

This paper cites Error analysis and estimation in the finite volume method with applications to fluid flows.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Error analysis and estimation in the finite volume method with applications to fluid flows

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.750860Z

Source-reported events for the cited work

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Observation 9df4c550-1d36-4880-acb1-abc0b482f50b · outbound

This paper cites Mionet: Learning multiple-input operators via tensor product.SIAM Journal on Scientific Computing, 44(6):A3490–A3514, 2022.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Mionet: Learning multiple-input operators via tensor product.SIAM Journal on Scientific Computing, 44(6):A3490–A3514, 2022

Reference 26

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Source-reported events for the cited work

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Observation 4290696b-b56f-4e65-999e-4ad05c111703 · outbound

This paper cites Nonlinear model order reduction via lifting transfor- mations and proper orthogonal decomposition.AIAA Journal, 57(6):2297–2307, 2019.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Nonlinear model order reduction via lifting transfor- mations and proper orthogonal decomposition.AIAA Journal, 57(6):2297–2307, 2019

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.737595Z

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Observation fa94e166-7b8f-4604-a065-835ae2a2cc73 · outbound

This paper cites an unresolved cited work.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:46:01.729234Z

Source-reported events for the cited work

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Observation b7bf5dd4-f08d-4864-8913-00d2c407c16a · outbound

This paper cites Model reduction of dynamical systems on nonlin- ear manifolds using deep convolutional autoencoders.Journal of Computational Physics, 404:108973, 2020.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Model reduction of dynamical systems on nonlin- ear manifolds using deep convolutional autoencoders.Journal of Computational Physics, 404:108973, 2020

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.720083Z

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Observation d2435884-af2e-4d8a-a391-8207887f8262 · outbound

This paper cites Learn- ing nonlinear operators via deeponet based on the universal approximation theorem of op- erators.Nature Machine Intelligence, 3(3):218–229, Mar 2021.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Learn- ing nonlinear operators via deeponet based on the universal approximation theorem of op- erators.Nature Machine Intelligence, 3(3):218–229, Mar 2021

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.629926Z

Source-reported events for the cited work

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Observation 9629488d-34eb-42b7-8a24-9f08ff533a34 · outbound

This paper cites Springer, 2016.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Springer, 2016

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.481845Z

Source-reported events for the cited work

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Observation 1db30b5e-1597-4c7b-ab70-f0202b1a32c0 · outbound

This paper cites A gaussian process regression approach within a data-driven pod framework for engineering problems in fluid dynamics.Mathe- matics in Engineering, 4(3):1–16, 2022.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models A gaussian process regression approach within a data-driven pod framework for engineering problems in fluid dynamics.Mathe- matics in Engineering, 4(3):1–16, 2022

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:01.134156Z

Source-reported events for the cited work

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Observation e78c475a-8d86-44e3-b000-35effe8f325f · outbound

This paper cites an unresolved cited work.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:46:00.900485Z

Source-reported events for the cited work

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Observation 47e3b59b-33c0-4f6e-a40d-19cb86d3cca8 · outbound

This paper cites Data-driven operator inference for nonintrusive projection-based model reduction.Computer Methods in Applied Mechanics and Engineer- ing, 306:196–215, July 2016.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Data-driven operator inference for nonintrusive projection-based model reduction.Computer Methods in Applied Mechanics and Engineer- ing, 306:196–215, July 2016

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:00.683319Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d24502d5-89cd-4e83-a2a0-e6caefc66a8a · outbound

This paper cites A graph convolutional autoencoder ap- proach to model order reduction for parametrized pdes.Journal of Computational Physics, 501:112762, 2024.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models A graph convolutional autoencoder ap- proach to model order reduction for parametrized pdes.Journal of Computational Physics, 501:112762, 2024

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-07T04:45:57.310003Z

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Unavailable: canonical work link unavailable.

Observation 11722311-a430-415f-b96e-398e293e5892 · outbound

This paper cites Large-eddy simulation: achievements and challenges.Progress in aerospace sciences, 35(4):335–362, 1999.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Large-eddy simulation: achievements and challenges.Progress in aerospace sciences, 35(4):335–362, 1999

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:00.479963Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b0c8462e-4553-4a04-bbf2-bf94064ebbf5 · outbound

This paper cites Pope.Turbulent Flows.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Pope.Turbulent Flows

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-07T04:45:57.446474Z

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Observation 43bfcb09-7f65-415d-9b0b-f0fcfe25b0e1 · outbound

This paper cites Springer, 2015.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Springer, 2015

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:00.264368Z

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Observation 309ba3b3-37fb-435d-9b48-5e5cd567c923 · outbound

This paper cites Springer, 2014.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Springer, 2014

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:46:00.090568Z

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Observation 2c530dc2-f631-45af-adc7-2124d3b0404d · outbound

This paper cites an unresolved cited work.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:45:59.898387Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 363ac98c-191c-45c1-a37a-87570af63c41 · outbound

This paper cites Non-linear manifold reduced- order models with convolutional autoencoders and reduced over-collocation method.Journal of Scientific Computing, 94(3):74, Feb 2023.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Non-linear manifold reduced- order models with convolutional autoencoders and reduced over-collocation method.Journal of Scientific Computing, 94(3):74, Feb 2023

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:45:59.678796Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 466b7232-34cd-4a08-a344-b72d9e49c3f4 · outbound

This paper cites SIAM, 2022.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models SIAM, 2022

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:45:59.449822Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 6451ec93-23d8-406c-95d2-9a41b8200394 · outbound

This paper cites Springer Science & Business Media, 2006.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Springer Science & Business Media, 2006

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:45:59.145364Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5153ed6f-701e-4a21-afe9-88d2aae2a350 · outbound

This paper cites Driven cavity flows by efficient numerical techniques.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Driven cavity flows by efficient numerical techniques

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:45:58.873603Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 09c5c690-0b63-438c-a566-cc1473132894 · outbound

This paper cites Greedy construction of quadratic manifolds for nonlinear dimensionality reduction and nonlinear model reduction.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Greedy construction of quadratic manifolds for nonlinear dimensionality reduction and nonlinear model reduction

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-07T04:45:58.137354Z

Source-reported events for the cited work

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Observation 3a018e61-294c-42c2-be75-24bc96a2cb27 · outbound

This paper cites Proper orthogonal decom- position closure models for turbulent flows: a numerical comparison.Computer Methods in Applied Mechanics and Engineering, 237:10–26, 2012.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Proper orthogonal decom- position closure models for turbulent flows: a numerical comparison.Computer Methods in Applied Mechanics and Engineering, 237:10–26, 2012

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:45:58.693403Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 177655eb-0e4a-4ba2-b65c-bf18f7e0cd88 · outbound

This paper cites Data-driven filtered reduced order modeling of fluid flows.SIAM Journal on Scientific Computing, 40(3):B834–B857, 2018.

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Data-driven filtered reduced order modeling of fluid flows.SIAM Journal on Scientific Computing, 40(3):B834–B857, 2018

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:45:58.514084Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

Observation f6cc134a-adb4-4cdf-9344-784735418468 · inbound

Surrogate modeling for convection-dominated parametric problems based on error learning cites this paper.

Surrogate modeling for convection-dominated parametric problems based on error learning Machine Learning-based quadratic closures for non-intrusive Reduced Order Models

Reference 13

Resolution: verified exact; local_arxiv, observed 2026-06-29T00:42:56.553885Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7eb6e727-74ec-42c9-b625-9665df1cf194 · inbound

A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems cites this paper.

A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Machine Learning-based quadratic closures for non-intrusive Reduced Order Models

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-07-03T15:58:37.905046Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.