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Paper Citation Record · LEDGER

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts

As of 18 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 0 inbound Pith citation observations for arXiv:2412.06842.

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

pith.paper-citation-record.v1
2412.06842 v1

Coverage vector

measured 40 of 40 reference resolution

Typed states for the displayed outbound observations.

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measured 40 of 40 standing notices

One-hop event checks from named stored sources.

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measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

40 of 40 outbound references displayed

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External citation measurements

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Outbound references

Observation 5b8f3d55-ac4b-4de7-bc1f-3ebb626704aa · outbound

This paper cites Physics-Informed Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems 22 Involving Nonlinear Partial Differential Equations,.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Physics-Informed Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems 22 Involving Nonlinear Partial Differential Equations,

Reference 1

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Observation 6535b806-649d-4da6-a8b1-a1c919859f63 · outbound

This paper cites Physics-Informed Machine Learning,.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Physics-Informed Machine Learning,

Reference 2

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Observation f6776554-4dee-49f7-8b36-f2b712945d97 · outbound

This paper cites Parallel Physics-Informed Neural Networks via Domain Decomposition,.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Parallel Physics-Informed Neural Networks via Domain Decomposition,

Reference 3

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Observation 75936631-f5d4-4bed-a23b-3d344cea1835 · outbound

This paper cites Physics- Informed Neural Networks (PINNs) for Fluid Mechanics: A Review,.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Physics- Informed Neural Networks (PINNs) for Fluid Mechanics: A Review,

Reference 4

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Observation 9d34d12b-71c5-49b8-a361-55da35d0bfba · outbound

This paper cites Respecting causality is all you need for training physics-informed neural networks.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Respecting causality is all you need for training physics-informed neural networks

Reference 5

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Observation 4cba3410-a991-4c2d-890e-b56e74965eba · outbound

This paper cites Partition of Unity Networks: Deep Hp-Approximation,.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Partition of Unity Networks: Deep Hp-Approximation,

Reference 6

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Observation 0b3844e5-3426-4f51-b0c3-25520b828a7d · outbound

This paper cites The Partition of Unity Finite Element Method: Basic Theory and Applications,.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts The Partition of Unity Finite Element Method: Basic Theory and Applications,

Reference 7

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Observation a4f9d7d8-4bd9-4747-8c81-b0aa973f9cbc · outbound

This paper cites Probabilistic partition of unity networks: clustering based deep approximation.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Probabilistic partition of unity networks: clustering based deep approximation

Reference 8

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Observation 90794584-3a7b-40d6-b04f-d98813d81359 · outbound

This paper cites Probabilistic Partition of Unity Networks for High-dimensional Regression Problems,.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Probabilistic Partition of Unity Networks for High-dimensional Regression Problems,

Reference 9

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Observation 103989d7-875e-41a2-9636-24416c776a93 · outbound

This paper cites Modeling of One-Dimensional Ablation with Porous Flow Using Finite Control Volume Procedure.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Modeling of One-Dimensional Ablation with Porous Flow Using Finite Control Volume Procedure

Reference 10

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Observation 0d89fcff-7aab-43c7-b31e-605201b8af4e · outbound

This paper cites Mesh Deformation Boundary Conditions for Three-Dimensional Ablation Solvers,.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Mesh Deformation Boundary Conditions for Three-Dimensional Ablation Solvers,

Reference 11

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Observation 1f5fdb15-d18e-4ada-b005-b24fdd45197c · outbound

This paper cites High-Temperature Liquid Metal Infusion Considering Surface Tension- Viscosity Dissipation,.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts High-Temperature Liquid Metal Infusion Considering Surface Tension- Viscosity Dissipation,

Reference 12

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Observation 3ba408d1-e071-429e-8f95-5877cdb0b378 · outbound

This paper cites Sensitivity of Viscosity on Molten Ti Infusion into a B4C- Packed Bed at the Microscale,.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Sensitivity of Viscosity on Molten Ti Infusion into a B4C- Packed Bed at the Microscale,

Reference 13

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Observation b1e9054c-6466-444f-be49-4880cc01bb06 · outbound

This paper cites A., 2010, Three Dimensional Finite Element Ablative Thermal Response Anal- ysis Applied to Heatshield Penetration Design, Georgia Institute of Technology.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts A., 2010, Three Dimensional Finite Element Ablative Thermal Response Anal- ysis Applied to Heatshield Penetration Design, Georgia Institute of Technology

Reference 14

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Observation 27a37488-51c7-4961-85c0-cc77ae320ea1 · outbound

This paper cites Flow Mechanics in Ablative Thermal Protection Systems,.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Flow Mechanics in Ablative Thermal Protection Systems,

Reference 15

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Observation ee108b18-4da8-460c-8411-959238b90a00 · outbound

This paper cites On the Stability of Combustion and Laser-Produced Ablation Fronts,.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts On the Stability of Combustion and Laser-Produced Ablation Fronts,

Reference 16

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Observation 92cb1e1f-878b-4e79-bfda-01685d2bd4b2 · outbound

This paper cites Rayleigh–Taylor and Richtmyer–Meshkov Instabilities: A Journey through Scales,.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Rayleigh–Taylor and Richtmyer–Meshkov Instabilities: A Journey through Scales,

Reference 17

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This paper cites Nonintrusive Manufactured Solutions for Ablation,.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Nonintrusive Manufactured Solutions for Ablation,

Reference 18

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This paper cites Code Verification by the Method of Manufactured Solutions,.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Code Verification by the Method of Manufactured Solutions,

Reference 19

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Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Unresolved cited work

Reference 20

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This paper cites Albany: Us- ing Component-Based Design to Develop a Flexible, Generic Multiphysics Analysis Code,.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Albany: Us- ing Component-Based Design to Develop a Flexible, Generic Multiphysics Analysis Code,

Reference 21

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Observation cae360f6-b34b-4cd2-a153-110835f0b9a2 · outbound

This paper cites Albany/FELIX: A Parallel, Scalable and Robust, Finite Element, First-Order Stokes Approximation Ice Sheet Solver Built for Advanced Analysis,.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Albany/FELIX: A Parallel, Scalable and Robust, Finite Element, First-Order Stokes Approximation Ice Sheet Solver Built for Advanced Analysis,

Reference 22

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Observation c275b422-f177-4c71-b8ab-6b8c4d736722 · outbound

This paper cites MPAS-Albany Land Ice (MALI): A Variable-Resolution Ice Sheet Model for Earth System Modeling Using Voronoi Grids,.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts MPAS-Albany Land Ice (MALI): A Variable-Resolution Ice Sheet Model for Earth System Modeling Using Voronoi Grids,

Reference 23

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Observation fa09ba86-7325-4486-acc7-c538ede98711 · outbound

This paper cites Verification and Validation in Com- putational Fluid Dynamics,.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Verification and Validation in Com- putational Fluid Dynamics,

Reference 24

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This paper cites L., and Roy, C.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts L., and Roy, C

Reference 25

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This paper cites L., and Kutz, J.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts L., and Kutz, J

Reference 26

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Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts M., Ebeida, M

Reference 27

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This paper cites M., Bohnhoff, W.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts M., Bohnhoff, W

Reference 28

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Observation 4fb272aa-6b4f-42c7-b5ec-fa62e6eef520 · outbound

This paper cites Parameter Sensitivity and Statistical Cor- relation Found in Atmospheric Turbulence Studies,.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Parameter Sensitivity and Statistical Cor- relation Found in Atmospheric Turbulence Studies,

Reference 29

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Observation c89a9be4-dba3-44aa-8703-ae8992d61b26 · outbound

This paper cites Mesh Adaptability Technique for Canonical Turbulent Jet Flows via Reinforcement Learning,.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Mesh Adaptability Technique for Canonical Turbulent Jet Flows via Reinforcement Learning,

Reference 30

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Observation 689c23e6-1495-4d8f-9ea2-86c8058cbf89 · outbound

This paper cites an unresolved cited work.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Unresolved cited work

Reference 31

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Observation f37394b4-0f00-42f2-9c4a-7487d50584d0 · outbound

This paper cites Forward and Inverse Modeling of Ice Sheet Flow Using Physics-informed Neural Networks: Application to Helheim Glacier, Greenland,.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Forward and Inverse Modeling of Ice Sheet Flow Using Physics-informed Neural Networks: Application to Helheim Glacier, Greenland,

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T20:30:38.569907Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-11T20:30:38.031986Z digest=sha256:cc914ea579798b5c50715b1571e6a6fdc54a9d90224faf4e2aa155786402edde

Observation eb8f1a63-fd53-4574-8969-e24f0b0335d3 · outbound

This paper cites Discovering the Rheology of Antarc- tic Ice Shelves via Physics-Informed Deep Learning.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Discovering the Rheology of Antarc- tic Ice Shelves via Physics-Informed Deep Learning

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T20:30:38.554757Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-11T20:30:38.036459Z digest=sha256:09153cc4aa59bae54a9bd6357d7f8091eb60aa17ac11ec25bae65162d3878b16

Observation a4300ea8-d356-4974-8ca9-3293f6a2eeee · outbound

This paper cites One-Dimensional Ice Shelf Hardness Inversion: Clus- tering Behavior and Collocation Resampling in Physics-Informed Neural Networks,.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts One-Dimensional Ice Shelf Hardness Inversion: Clus- tering Behavior and Collocation Resampling in Physics-Informed Neural Networks,

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T20:30:38.538941Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-11T20:30:38.040904Z digest=sha256:1352d8ba6d613eeb472c55c9678b12aa468692c499fb0ba8035d5c85d04910f9

Reference 35

Resolution
unresolved
no resolver link, observed 2026-08-11T20:30:38.045490Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T20:30:38.045490Z digest=sha256:ccf393e5800f6c1392982c2a5e77424852bd2ff34623c681111eb996b7955569

Observation b14a9e35-1415-4917-960d-de8f4917fe3f · outbound

This paper cites Activation Functions: Comparison of trends in Practice and Research for Deep Learning.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Activation Functions: Comparison of trends in Practice and Research for Deep Learning

Reference 36

Resolution
unresolved
no resolver link, observed 2026-08-11T20:30:38.050674Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T20:30:38.050674Z digest=sha256:4cd789d51bfee52e0e074797e53f734c8c32469c37cc424d7992e194c29feba9

Reference 37

Resolution
unresolved
no resolver link, observed 2026-08-11T20:30:38.055773Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T20:30:38.055773Z digest=sha256:c793d5593cd931510aefd70abf6b46226a9e7a801429053e64f5777a08a2f547

Reference 38

Resolution
unresolved
no resolver link, observed 2026-08-11T20:30:38.060800Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T20:30:38.060800Z digest=sha256:fa708036ee99e3cebc0837f58f0c812746721ffb17bbe70aab1108216b53eaac

Observation 2fa8503a-3b0f-4b90-8015-d1ef96003f8c · outbound

This paper cites L2 Regularization versus Batch and Weight Normalization.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts L2 Regularization versus Batch and Weight Normalization

Reference 39

Resolution
unresolved
no resolver link, observed 2026-08-11T20:30:38.065681Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T20:30:38.065681Z digest=sha256:6924292ad5ebfe1a7fad1aa044b38ff27e1acc0b3341338ecfb9df1be4a1411a

Observation 7b227cb9-7c82-4bd9-947f-ab674b30bcfd · outbound

This paper cites Understanding the Difficulty of Training Deep Feed- forward Neural Networks,.

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts Understanding the Difficulty of Training Deep Feed- forward Neural Networks,

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T20:30:38.522513Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-11T20:30:38.070485Z digest=sha256:400903a95e851fa30e9f285b8909b8118a5add2e52262be83dd275c33cab51a6

Pith citing papers

No inbound Pith citation observations are available.