Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields | Paper Citation Record

Observation 81f70c50-86b0-48eb-b167-dec73cc61cac · outbound

This paper cites Numerical study of slightly viscous flow.Journal of Fluid Mechanics, 57(4):785–796, 1973.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Numerical study of slightly viscous flow.Journal of Fluid Mechanics, 57(4):785–796, 1973

Reference 1

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This paper cites A stochastic Lagrangian representation of the three-dimensional incompressible Navier-Stokes equations.Communications on Pure and Applied Mathematics, 61(3):330–345, 2008.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields A stochastic Lagrangian representation of the three-dimensional incompressible Navier-Stokes equations.Communications on Pure and Applied Mathematics, 61(3):330–345, 2008

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.953996Z

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Observation ca0b8373-7c6a-4c94-ad6e-540b7b004843 · outbound

This paper cites Forward–backward stochastic differential systems associated to Navier–Stokes equations in the whole space.Stochastic Processes and their Applications, 125(7):2516–2561, 2015.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Forward–backward stochastic differential systems associated to Navier–Stokes equations in the whole space.Stochastic Processes and their Applications, 125(7):2516–2561, 2015

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.938710Z

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Observation 3f0dd673-cf40-4af9-827d-a797b55c5c65 · outbound

This paper cites An introduction to 3D stochastic fluid dynamics.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields An introduction to 3D stochastic fluid dynamics

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.921779Z

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Observation 71e4d861-c7ae-4af8-a663-8ad97be2b94f · outbound

This paper cites Butterworth-Heinemann, Oxford, second edition, 2007.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Butterworth-Heinemann, Oxford, second edition, 2007

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.906098Z

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Observation d025c66c-1298-4794-a8d6-94a317505d10 · outbound

This paper cites Pope.Turbulent Flows.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Pope.Turbulent Flows

Reference 6

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Observation 965a2d1c-0223-4c46-932a-c551e6bd2a5f · outbound

This paper cites Cambridge University Press, Cambridge, second edition, 2024.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Cambridge University Press, Cambridge, second edition, 2024

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.872880Z

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Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T14:56:05.857617Z

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Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Unresolved cited work

Reference 9

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Observation bcae14aa-60b9-4b2e-8974-d907a79a4f7e · outbound

This paper cites State observer data assimilation for RANS with time-averaged 3D-PIV data.Computers & Fluids, 218:104827, 2021.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields State observer data assimilation for RANS with time-averaged 3D-PIV data.Computers & Fluids, 218:104827, 2021

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.829454Z

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Observation 334d160e-dac2-4aec-97e1-1eaf714ecec3 · outbound

This paper cites McKeon, Denis Sipp, and Peter J.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields McKeon, Denis Sipp, and Peter J

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.814716Z

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Observation 51663d57-86fe-4898-84f5-2521375389fc · outbound

This paper cites Spectral approach for kernel-based interpolation.Annales de la Facult´ e des Sciences de Toulouse: Math´ ematiques, 21(3):439–479, 2012.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Spectral approach for kernel-based interpolation.Annales de la Facult´ e des Sciences de Toulouse: Math´ ematiques, 21(3):439–479, 2012

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.800755Z

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Observation 1540f548-7941-4a51-b493-351acaa3dc0d · outbound

This paper cites Gaussian process hydrodynamics.Applied Mathematics and Mechanics, 44(7):1175–1198, 2023.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Gaussian process hydrodynamics.Applied Mathematics and Mechanics, 44(7):1175–1198, 2023

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.784401Z

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Observation fa04ed59-f2e2-4d50-a525-17664963edf0 · outbound

This paper cites Learning “best” kernels from data in Gaussian process regression.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Learning “best” kernels from data in Gaussian process regression

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.769039Z

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Observation df0d35e7-c1e7-41df-b5ae-4a1a981d0dd0 · outbound

This paper cites Kernel Flows: From learning kernels from data into the abyss.Journal of Computational Physics, 389:22–47, 2019.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Kernel Flows: From learning kernels from data into the abyss.Journal of Computational Physics, 389:22–47, 2019

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.752202Z

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Observation d5687820-365f-45f3-9c62-6aaecdc9243f · outbound

This paper cites Learning dynamical systems from data: a simple cross-validation perspective, part I: parametric kernel flows.Physica D: Nonlinear Phenomena, 421:132817, 2021.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Learning dynamical systems from data: a simple cross-validation perspective, part I: parametric kernel flows.Physica D: Nonlinear Phenomena, 421:132817, 2021

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.735713Z

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Observation 14e0436b-84e2-43b2-9491-1a467a9bb951 · outbound

This paper cites Covariance Models for Divergence-Free and Curl-Free Random Vector Fields.Stochastic Models, 28(3):433–451, 2012.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Covariance Models for Divergence-Free and Curl-Free Random Vector Fields.Stochastic Models, 28(3):433–451, 2012

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.721092Z

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Observation 1ed70081-e68a-49ef-9064-78982214f2cc · outbound

This paper cites Boundary constrained Gaussian processes for robust physics-informed machine learning of linear partial differential equations.Journal of Machine Learning Research, 25:1–61, 2024.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Boundary constrained Gaussian processes for robust physics-informed machine learning of linear partial differential equations.Journal of Machine Learning Research, 25:1–61, 2024

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.705515Z

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Observation 665ae3d6-9292-4666-b25e-e40a11409982 · outbound

This paper cites Gaussian process regression constrained by boundary value problems.Computer Methods in Applied Mechanics and Engineering, 388:114117, 2022.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Gaussian process regression constrained by boundary value problems.Computer Methods in Applied Mechanics and Engineering, 388:114117, 2022

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.689997Z

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Observation 8546195e-d740-497f-85dc-ca688eb2d7b6 · outbound

This paper cites Know your boundaries: Constraining gaussian processes by variational harmonic features.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Know your boundaries: Constraining gaussian processes by variational harmonic features

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.674600Z

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Observation c27f1eb9-db4d-45b0-9a30-74a7b6193410 · outbound

This paper cites Brunton, Bernd R.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Brunton, Bernd R

Reference 21

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Observation 673a6caf-2377-42df-bfbc-61784fd8cb94 · outbound

This paper cites Data reconstruction for complex flows using AI: Recent progress, obstacles, and perspectives.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Data reconstruction for complex flows using AI: Recent progress, obstacles, and perspectives

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.649593Z

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Observation 62f06829-ae0e-4d68-8c0b-977107854636 · outbound

This paper cites Turbulence modeling in the age of data.Annual Review of Fluid Mechanics, 51:357–377, 2019.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Turbulence modeling in the age of data.Annual Review of Fluid Mechanics, 51:357–377, 2019

Reference 23

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Observation b9fe5762-067b-4382-aedd-63c5c233ed24 · outbound

This paper cites Bharath, and Chris D.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Bharath, and Chris D

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.624080Z

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Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-06T14:56:05.610130Z

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Observation 8be9ad67-ecf0-4a09-bfcf-e49bc13f56c3 · outbound

This paper cites The graph neural network model.IEEE Transactions on Neural Networks, 20(1):61–80, 2009.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields The graph neural network model.IEEE Transactions on Neural Networks, 20(1):61–80, 2009

Reference 26

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Observation 404a75a7-0227-4803-91c1-604a19f81da6 · outbound

This paper cites Fourier Neural Operator for Parametric Partial Differential Equations.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Fourier Neural Operator for Parametric Partial Differential Equations

Reference 27

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Observation 1258dfd6-2dd8-4eaf-b38c-f152ee96f087 · outbound

This paper cites Karniadakis.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Karniadakis

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.583728Z

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Observation 1ce2db4d-9c34-4fef-8dad-1eb69b07d8d3 · outbound

This paper cites KAN: Kolmogorov-Arnold Networks.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields KAN: Kolmogorov-Arnold Networks

Reference 29

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Observation 19a6076e-d49a-4609-a94a-f0dd6496d82f · outbound

This paper cites Poseidon: Efficient Foundation Models for PDEs.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Poseidon: Efficient Foundation Models for PDEs

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-06T14:56:04.700717Z

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Observation 2f4e63b6-2536-45ee-8019-a8c912b1d244 · outbound

This paper cites Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold Networks.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold Networks

Reference 31

Resolution: verified exact; local_arxiv, observed 2026-08-06T14:56:05.160355Z

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Observation 44c40036-39d6-4ae4-9db4-1de6c1021ede · outbound

This paper cites Prediction of turbulent channel flow using Fourier neural operator-based machine-learning strategy.Physical Review Fluids, 9(8):084604, 2024.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Prediction of turbulent channel flow using Fourier neural operator-based machine-learning strategy.Physical Review Fluids, 9(8):084604, 2024

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.568257Z

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Observation fffd2932-bd82-42e9-871c-a3f3e1adfae8 · outbound

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Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-06T14:56:05.550776Z

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Observation a8fddecb-fff2-4473-becf-baf15834d075 · outbound

This paper cites Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences

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Observation 51d83341-18fb-4125-900c-8443bbec2c0c · outbound

This paper cites Smola.Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Smola.Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.533947Z

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Observation d116c6f5-bf00-43bd-844c-797fffc026a9 · outbound

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Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-06T14:56:05.516255Z

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Observation 83729482-ec63-4e70-81a8-817d906f855b · outbound

This paper cites Solving and learning nonlinear PDEs with Gaussian processes.Journal of Computational Physics, 447:110668, 2021.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Solving and learning nonlinear PDEs with Gaussian processes.Journal of Computational Physics, 447:110668, 2021

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Observation a6b66001-06fc-4eac-895c-b2b158220abf · outbound

This paper cites Characterization of the second order random fields subject to linear distributional PDE constraints.Bernoulli, 29(4):3396–3422, 2023.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Characterization of the second order random fields subject to linear distributional PDE constraints.Bernoulli, 29(4):3396–3422, 2023

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.484313Z

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Observation 7f49bbfe-d54c-4f55-bf90-60b6ddfff854 · outbound

This paper cites On degeneracy and invariances of random fields paths with applications in Gaussian process modelling.Journal of Statistical Planning and Inference, 170:117–128, 2016.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields On degeneracy and invariances of random fields paths with applications in Gaussian process modelling.Journal of Statistical Planning and Inference, 170:117–128, 2016

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.464219Z

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Observation 212837c9-ea79-4bee-8b52-07bc0cd84375 · outbound

This paper cites Sobolev regularity of Gaussian random fields.Journal of Functional Analysis, 286(3):110241, 2024.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Sobolev regularity of Gaussian random fields.Journal of Functional Analysis, 286(3):110241, 2024

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.448218Z

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Observation a35d5075-4b24-40de-b6f2-56ad64bd2e87 · outbound

This paper cites Cambridge Monographs on Applied and Computational Mathematics.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Cambridge Monographs on Applied and Computational Mathematics

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.433250Z

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Observation c4b8c102-6a6e-4bcf-8d00-f727922b6268 · outbound

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Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Unresolved cited work

Reference 42

Resolution: unresolved; raw_fallback, observed 2026-08-06T14:56:05.417585Z

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Observation 34bc3358-14fa-41fa-86e6-89144b4a1b84 · outbound

This paper cites Kernels for multi-task learning.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Kernels for multi-task learning

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.400304Z

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Observation 16a4571c-e15d-4cb5-8a64-3a5e9582f592 · outbound

This paper cites Springer Science & Business Media, 2008.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Springer Science & Business Media, 2008

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-06T14:56:04.865903Z

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Observation 29191631-31cf-4c11-9ad9-dda401a8c7df · outbound

This paper cites Springer, Berlin, 2007.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Springer, Berlin, 2007

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.372250Z

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Observation d6ace870-b819-4927-b063-241f3a9304aa · outbound

This paper cites CRC Press, 1992.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields CRC Press, 1992

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.355179Z

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Observation 4759a70c-cbdf-4981-97b2-36757a3d3fb3 · outbound

This paper cites Cambridge University Press, 1997.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Cambridge University Press, 1997

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.335504Z

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Observation b396280c-ed3b-4857-a4a7-3e7968f68d57 · outbound

This paper cites Ladson, Jr.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Ladson, Jr

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.314933Z

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Observation dba39acb-138e-4b56-9a31-3e9a6cff0aee · outbound

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Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Unresolved cited work

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-06T14:56:04.888547Z

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Observation 5155db77-0a07-4eb2-83c5-5442de5a691f · outbound

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Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Unresolved cited work

Reference 50

Resolution: unresolved; no resolver link, observed 2026-08-06T14:56:04.893099Z

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Observation 0ec635ff-0ed5-4a5d-976a-e60779f44ac4 · outbound

This paper cites A Dynamics-Informed Gaussian Process Framework for 2D Stochastic Navier-Stokes via Quasi-Gaussianity.arXiv:2511.21281, 2025.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields A Dynamics-Informed Gaussian Process Framework for 2D Stochastic Navier-Stokes via Quasi-Gaussianity.arXiv:2511.21281, 2025

Reference 51

Resolution: verified exact; raw_fallback, observed 2026-08-06T14:56:05.119785Z

Source-reported events for the cited work

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

Observation 1d23d306-ebc2-417f-8db1-8a71dabe7730 · outbound

This paper cites Smith, Mateusz Paprocki, Ondˇ rejˇCert ´ ık, Sergey B.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Smith, Mateusz Paprocki, Ondˇ rejˇCert ´ ık, Sergey B

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.275797Z

Source-reported events for the cited work

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

Observation 2f523c0e-6a37-402e-b27c-af60fda3a9ad · outbound

This paper cites an unresolved cited work.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Unresolved cited work

Reference 53

Resolution: unresolved; raw_fallback, observed 2026-08-06T14:56:05.259410Z

Source-reported events for the cited work

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

Observation 4afa4f61-a95d-43db-a17d-56e8ff33dcc4 · outbound

This paper cites AirfRANS: High fidelity computa- tional fluid dynamics dataset for approximating Reynolds-Averaged Navier-Stokes solutions.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields AirfRANS: High fidelity computa- tional fluid dynamics dataset for approximating Reynolds-Averaged Navier-Stokes solutions

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.244208Z

Source-reported events for the cited work

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

Observation bd2c29e8-de68-4823-a62e-1d88be26424c · outbound

This paper cites Quasi-Gaussianity of the 2D stochastic Navier-Stokes equations.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Quasi-Gaussianity of the 2D stochastic Navier-Stokes equations

Reference 55

Resolution: unresolved; no resolver link, observed 2026-08-06T14:56:04.916425Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9ef7b4ce-3bd1-4f90-85b1-193b32bc59fc · outbound

This paper cites Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes.Mathematics of Computation, 94(353):1235–1280, 2025.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes.Mathematics of Computation, 94(353):1235–1280, 2025

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:56:05.227550Z

Source-reported events for the cited work

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

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