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Paper Citation Record · LEDGER

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators

As of 21 August 2026, this Paper Citation Record lists 67 of 67 outbound references and 1 inbound Pith citation observation for arXiv:2506.18427.

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

pith.paper-citation-record.v1
2506.18427 v1

Coverage vector

measured 67 of 67 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T23:21:48.755569Z

measured 68 of 68 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T12:50:00.467557Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-05T12:50:05.293783Z

Reference resolution

67 of 67 outbound references displayed

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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f9970113-e57c-4fc7-a2e2-3ffbd5a9addc · outbound

This paper cites Finite volume methods.Handbook of numerical analysis, 7:713–1018, 2000.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Finite volume methods.Handbook of numerical analysis, 7:713–1018, 2000

Reference 1

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation b2a09162-11a7-4107-84cc-32dfec06bf50 · outbound

This paper cites Klaus-Jurgen Bathe, 2006.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Klaus-Jurgen Bathe, 2006

Reference 2

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation fdeaa68f-9144-4a0b-b991-1dfe492b4e64 · outbound

This paper cites SIAM, 2007.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators SIAM, 2007

Reference 3

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Source-reported events for the cited work

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Observation 5c79021a-5068-4589-9dad-c323b1d0a933 · outbound

This paper cites Smoothed particle hydrodynamics and its diverse applications.Annual Review of Fluid Mechanics, 44(1):323–346, 2012.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Smoothed particle hydrodynamics and its diverse applications.Annual Review of Fluid Mechanics, 44(1):323–346, 2012

Reference 4

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 2e597795-e36c-4d0c-82a1-22c622597a00 · outbound

This paper cites A quasi-linear reproducing kernel particle method.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators A quasi-linear reproducing kernel particle method

Reference 5

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 31d6198a-f066-4b51-853d-a3e2222b1cb3 · outbound

This paper cites Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems.Jour- nal of Computational Physics, 397:108850, 2019.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems.Jour- nal of Computational Physics, 397:108850, 2019

Reference 6

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 34e33ed0-3be2-41ca-b4dd-979911ef5169 · outbound

This paper cites fpinns: Fractional physics-informed neural networks.SIAM Journal on Scientific Computing, 41(4):A2603–A2626, 2019.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators fpinns: Fractional physics-informed neural networks.SIAM Journal on Scientific Computing, 41(4):A2603–A2626, 2019

Reference 7

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 60fd96bd-58b9-478f-a219-b3e0b74c7f3f · outbound

This paper cites Deepxde: A deep learning library for solving differential equations.SIAM review, 63(1):208–228, 2021.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Deepxde: A deep learning library for solving differential equations.SIAM review, 63(1):208–228, 2021

Reference 8

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Observation 256ea121-417f-4a43-824e-e99d91f51105 · outbound

This paper cites Gradient-enhanced physics- informed neural networks for forward and inverse pde problems.Computer Methods in Applied Mechanics and Engineering, 393:114823, 2022.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Gradient-enhanced physics- informed neural networks for forward and inverse pde problems.Computer Methods in Applied Mechanics and Engineering, 393:114823, 2022

Reference 9

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Observation 23a1e5fb-b62a-47f1-b4ea-a0465e01c53d · outbound

This paper cites Physics-informed machine learning.Nature Reviews Physics, 3(6):422–440, 2021.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Physics-informed machine learning.Nature Reviews Physics, 3(6):422–440, 2021

Reference 10

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Observation ae442ce2-b7ed-4fe4-9438-eda985aca511 · outbound

This paper cites A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks

Reference 11

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Observation 3fcc64b9-53bd-4727-85d3-94cf965ec9e9 · outbound

This paper cites an unresolved cited work.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Unresolved cited work

Reference 12

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 27c40ae4-53e3-4cc6-a25d-1340c6ea97e1 · outbound

This paper cites An improved 2d finite element model for bolt load distribution analysis of composite multi-bolt single-lap joints.Composite Structures, 253:112770, 2020.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators An improved 2d finite element model for bolt load distribution analysis of composite multi-bolt single-lap joints.Composite Structures, 253:112770, 2020

Reference 13

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation c3c552a7-e5a7-4c58-9ce2-f7fddc385746 · outbound

This paper cites Modeling strategies of finite element simulation of reinforced concrete beams strengthened with frp: A review.Journal of Compos- ites Science, 5(1):19, 2021.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Modeling strategies of finite element simulation of reinforced concrete beams strengthened with frp: A review.Journal of Compos- ites Science, 5(1):19, 2021

Reference 14

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation ce79d44b-c41d-46d0-98c2-e36049203cd7 · outbound

This paper cites Finite element analysis of slope stability using a nonlinear failure criterion.Computers and Geotechnics, 34(3):127–136, 2007.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Finite element analysis of slope stability using a nonlinear failure criterion.Computers and Geotechnics, 34(3):127–136, 2007

Reference 15

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation a20544cc-4d09-4924-97bf-b42253638589 · outbound

This paper cites On the convergence of overlapping elements and overlapping meshes.Computers & Structures, 244:106429, 2021.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators On the convergence of overlapping elements and overlapping meshes.Computers & Structures, 244:106429, 2021

Reference 16

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation d171b7b5-8020-468e-8847-b17b83db97ba · outbound

This paper cites Reduced-order modeling: new approaches for computational physics.Progress in aerospace sciences, 40(1-2):51–117, 2004.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Reduced-order modeling: new approaches for computational physics.Progress in aerospace sciences, 40(1-2):51–117, 2004

Reference 17

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-06T23:21:41.764838Z digest=sha256:3e5b1daa8fe86e93fdb4befbbf0de49b269c939afcc4e0b0de9bbcd50eb49148

Observation 3382f04b-bcbb-4a40-b4f4-1e4efc4dd099 · outbound

This paper cites Reduced-order methods for dynamic problems in topology optimization: A comparative study.Computer Methods in Applied Mechanics and Engineering, 387:114149, 2021.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Reduced-order methods for dynamic problems in topology optimization: A comparative study.Computer Methods in Applied Mechanics and Engineering, 387:114149, 2021

Reference 18

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 5593d035-eac3-4261-af14-3e93a61270f8 · outbound

This paper cites John Wiley & Sons, 2009.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators John Wiley & Sons, 2009

Reference 19

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 0c8bf09a-aadc-45bc-a3f2-f50ac71e2a3b · outbound

This paper cites A review: Applications of the spectral finite element method.Archives of Computational Methods in Engineering, 30(5):3453–3465, 2023.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators A review: Applications of the spectral finite element method.Archives of Computational Methods in Engineering, 30(5):3453–3465, 2023

Reference 20

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 6b06a8eb-e220-4b2b-99bf-8e9631f38560 · outbound

This paper cites an unresolved cited work.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Unresolved cited work

Reference 21

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 82d31c71-8bfc-491e-8a0b-8b038c7d0653 · outbound

This paper cites Plastic hinge integration methods for force-based beam–column elements.Journal of Structural Engineering, 132(2):244–252, 2006.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Plastic hinge integration methods for force-based beam–column elements.Journal of Structural Engineering, 132(2):244–252, 2006

Reference 22

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation e5951791-7ef1-4f40-ab23-06c6b59003a7 · outbound

This paper cites A new mitc4+ shell element.Com- puters & Structures, 182:404–418, 2017.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators A new mitc4+ shell element.Com- puters & Structures, 182:404–418, 2017

Reference 23

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 85c42995-17b2-44e2-97d6-24620c9a6d26 · outbound

This paper cites Galerkin formulations of isogeo- metric shell analysis: Alleviating locking with greville quadratures and higher-order elements.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Galerkin formulations of isogeo- metric shell analysis: Alleviating locking with greville quadratures and higher-order elements

Reference 24

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raw_fallback, observed 2026-08-06T23:21:59.283362Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 9ef8d05d-88c8-4470-bc37-4776f38354d4 · outbound

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

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Mionet: Learning multiple-input operators via tensor product.SIAM Journal on Scientific Computing, 44(6):A3490–A3514, 2022

Reference 25

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Observation 35cdb47c-bb92-427f-aff0-8b170bccd3ae · outbound

This paper cites Learning nonlinear operators via deeponet based on the universal approximation theorem of operators.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Learning nonlinear operators via deeponet based on the universal approximation theorem of operators

Reference 26

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Observation f4aa238d-8bae-488f-9743-d2776062f61a · outbound

This paper cites an unresolved cited work.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Unresolved cited work

Reference 27

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Observation daed2437-53ba-49d7-b10c-d08dab62f7ef · outbound

This paper cites One-shot learning for solution operators of partial differential equations.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators One-shot learning for solution operators of partial differential equations

Reference 28

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Observation 9aab277f-daa2-4ea7-b503-5929871fe969 · outbound

This paper cites Coast: Intelligent time-adaptive neural operators.arXiv preprint arXiv:2502.08574, 2025.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Coast: Intelligent time-adaptive neural operators.arXiv preprint arXiv:2502.08574, 2025

Reference 29

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Observation d06c506c-2489-403d-8aef-0ec13c58585a · outbound

This paper cites Fundiff: Diffusion models over function spaces for physics-informed generative modeling.arXiv preprint arXiv:2506.07902, 2025.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Fundiff: Diffusion models over function spaces for physics-informed generative modeling.arXiv preprint arXiv:2506.07902, 2025

Reference 30

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Observation 1195ea73-5465-4a2c-bc74-550601e39959 · outbound

This paper cites an unresolved cited work.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Unresolved cited work

Reference 31

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 474e5fb8-5a8f-4e62-9078-ee1d09b6d983 · outbound

This paper cites A physics-informed variational deeponet for predicting crack path in quasi-brittle materials.Computer Methods in Applied Mechanics and Engineering, 391:114587, 2022.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators A physics-informed variational deeponet for predicting crack path in quasi-brittle materials.Computer Methods in Applied Mechanics and Engineering, 391:114587, 2022

Reference 32

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Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T23:21:43.734833Z digest=sha256:cd3a324445ed64727e829fc94179b513855455cc303b75077224191333dfb186

Observation 5d290fd0-8c1e-416f-b0d1-cf874a8f9369 · outbound

This paper cites Neural operators for accelerating scientific simulations and design.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Neural operators for accelerating scientific simulations and design

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 73638d26-b00a-4e46-9700-96ec2b01281c · outbound

This paper cites an unresolved cited work.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Unresolved cited work

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source=pdf_text observed=2026-08-06T23:21:43.919377Z digest=sha256:912e9b5dcb2d430078bb67ed9d91a380d71615b9fcd56d2824b2911d2b7a33d2

Observation beda81ce-2d4f-4594-9371-2b64f68cb377 · outbound

This paper cites Learning nonlinear operators in latent spaces for real-time predictions of complex dynamics in physical systems.Nature Communications, 15(1):5101, 2024.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Learning nonlinear operators in latent spaces for real-time predictions of complex dynamics in physical systems.Nature Communications, 15(1):5101, 2024

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 562861f8-8ba2-4715-8ada-03a1c49e3ba3 · outbound

This paper cites On the training and generalization of deep operator net- works.SIAM Journal on Scientific Computing, 46(4):C273–C296, 2024.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators On the training and generalization of deep operator net- works.SIAM Journal on Scientific Computing, 46(4):C273–C296, 2024

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-06T23:21:44.180249Z digest=sha256:40309b15193fedfce5afef01ef4ac4c9f3152a99e4fb45bad017fd2870e35047

Observation 9ae37879-701a-4cb2-8b15-62201a26b80f · outbound

This paper cites an unresolved cited work.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Unresolved cited work

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Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T23:21:44.293897Z digest=sha256:b31b0b788adc73564b31bcf14370344ffac2f4bf9154f20c7030b0afebb35de4

Observation 9ef0b428-94aa-4af2-99f7-4cdd2fa9f6e0 · outbound

This paper cites Efficient and generalizable nested fourier-deeponet for three-dimensional geological carbon sequestration.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Efficient and generalizable nested fourier-deeponet for three-dimensional geological carbon sequestration

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raw_fallback, observed 2026-08-06T23:21:57.495564Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-06T23:21:44.483793Z digest=sha256:3f1cfa7ad57d10de27fe855f728228ca871af56bee8120fc561e51f9cb1e4148

Observation adcc74b8-f9f2-425b-b84f-40d04e8e5f8d · outbound

This paper cites A scalable framework for learning the geometry-dependent solution operators of partial differential equations.Nature Computational Science, 4(12):928–940, 2024.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators A scalable framework for learning the geometry-dependent solution operators of partial differential equations.Nature Computational Science, 4(12):928–940, 2024

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-06T23:21:44.586222Z digest=sha256:55cb159daa5129541bbd4bd897041a0469a07fe5e8baa216ff70e5f5fdbc132e

Observation add955b2-ec87-40cc-94f8-5eeed613c964 · outbound

This paper cites Quantum deeponet: Neural operators accelerated by quantum computing.Quantum, 9:1761, 2025.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Quantum deeponet: Neural operators accelerated by quantum computing.Quantum, 9:1761, 2025

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-06T23:21:44.694931Z digest=sha256:8d893e40c53607630bdb32cadd3a94989ef03832cd0fb372589f7ea66c45f974

Observation 8448568c-73b3-47d5-aa9e-3beb3f083185 · outbound

This paper cites an unresolved cited work.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Unresolved cited work

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-06T23:21:44.834939Z digest=sha256:01b8fd717b2a555dc28bac88f531cecfe98a4b969c5a03c0f83df9083f5fae0e

Observation b0cda708-1bb8-49c8-91d1-92102576947a · outbound

This paper cites A framework based on physics-informed neural networks and extreme learning for the analysis of composite structures.Computers & Structures, 265:106761, 2022.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators A framework based on physics-informed neural networks and extreme learning for the analysis of composite structures.Computers & Structures, 265:106761, 2022

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-06T23:21:44.917676Z digest=sha256:2c7a51a7585f44ee3db2f1764ccc4f866bd11d95bb7c07b87f473ac78667288a

Observation 6fd3ae8c-b816-4688-8c45-285150b3b78c · outbound

This paper cites Efficient neural topology optimization via active learning for enhancing turbulent mass transfer in fluid channels.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Efficient neural topology optimization via active learning for enhancing turbulent mass transfer in fluid channels

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Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T23:21:44.987909Z digest=sha256:d73cb5aed5193d1a9ccfd93610e0cb6a4065033afe13b676100e4afa10e5b6eb

Observation 6bdf4171-a035-4e3f-8939-ddc5a0b939a8 · outbound

This paper cites Federated scientific machine learning for approximating functions and solving differential equations with data heterogeneity.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Federated scientific machine learning for approximating functions and solving differential equations with data heterogeneity

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verified exact
local_arxiv, observed 2026-08-06T23:21:50.469980Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-06T23:21:45.124955Z digest=sha256:18afe69d11b271e051186465b808a3298b3bccbadead106749e842bc92de1966

Observation 0f038322-f8f6-4b79-93c0-07d046d297b0 · outbound

This paper cites an unresolved cited work.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Unresolved cited work

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-06T23:21:45.252557Z digest=sha256:57808fda15fe2ede9118c69421186d3e68e25d05ac8f683feec3e929e00685cb

Observation 6c75e8ec-8719-47f2-8384-e964dc3725e0 · outbound

This paper cites Solving forward and inverse PDE problems on unknown manifolds via physics-informed neural operators.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Solving forward and inverse PDE problems on unknown manifolds via physics-informed neural operators

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Source-reported events for the cited work

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source=pdf_text observed=2026-08-06T23:21:45.384824Z digest=sha256:e428b205fb42226e5266fb41b9f3e1373b12f35080ae7e474b0d8003a3026d9d

Observation 807fc6a9-2dba-448b-890c-4c9d8e012129 · outbound

This paper cites an unresolved cited work.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Unresolved cited work

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T23:21:45.524943Z digest=sha256:3fd546eab390470ffdc549f2d33630919c9a7d148431fcb89d8affcef0f8c988

Observation cf8d1467-bc2d-4bb1-b9ba-7da3639b8d8e · outbound

This paper cites hp-vpinns: Variational physics-informed neural networks with domain decomposition.Computer Methods in Applied Mechanics and Engineering, 374:113547, 2021.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators hp-vpinns: Variational physics-informed neural networks with domain decomposition.Computer Methods in Applied Mechanics and Engineering, 374:113547, 2021

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source=pdf_text observed=2026-08-06T23:21:45.664814Z digest=sha256:15c5f7aa8b02651b6688a4996f929bf68d89d544d849493d360d09d2bc9fbea4

Observation d7ffa087-2030-4ace-985b-9e970a39cff3 · outbound

This paper cites Active Neuron Least Squares: A training method for multivariate rectified neural networks.SIAM Journal on Scientific Computing, 44(4):A2253– A2275, 2022.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Active Neuron Least Squares: A training method for multivariate rectified neural networks.SIAM Journal on Scientific Computing, 44(4):A2253– A2275, 2022

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raw_fallback, observed 2026-08-06T23:21:55.484755Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-06T23:21:45.754907Z digest=sha256:a3489bd4856477ceb39a89bebc31ad7615b0e0f6cdbcb372b4b33665861823aa

Observation 4ecf1528-b24b-4910-9af5-06d9c3dd33b5 · outbound

This paper cites Hierarchical deep learning neural network (hidenn): an artificial intelligence (ai) framework for computational science and engineering.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Hierarchical deep learning neural network (hidenn): an artificial intelligence (ai) framework for computational science and engineering

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raw_fallback, observed 2026-08-06T23:21:55.095617Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-06T23:21:45.894828Z digest=sha256:8fa9df9123abd336bcedeec566a41d11a8c8927b0f38959637ff62b9c78dd33e

Observation c029f3c9-b198-4a35-b998-107cae63527b · outbound

This paper cites Exact dirichlet boundary physics- informed neural network epinn for solid mechanics.Computer Methods in Applied Mechanics and Engineering, 414:116184, 2023.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Exact dirichlet boundary physics- informed neural network epinn for solid mechanics.Computer Methods in Applied Mechanics and Engineering, 414:116184, 2023

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raw_fallback, observed 2026-08-06T23:21:54.414875Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-06T23:21:46.014833Z digest=sha256:68b8f6fb9415c7f6e211b3ca69468a96e2c6100f4e5f20bfbac21fea017fc8d6

Observation 087cabc0-9b38-4588-b9b9-524ce6703b10 · outbound

This paper cites Finite operator learning: Bridging neural operators and numerical methods for efficient parametric solution and optimization of pdes.arXiv preprint arXiv:2407.04157, 2024.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Finite operator learning: Bridging neural operators and numerical methods for efficient parametric solution and optimization of pdes.arXiv preprint arXiv:2407.04157, 2024

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verified exact
raw_fallback, observed 2026-08-06T23:21:49.944824Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-06T23:21:46.097147Z digest=sha256:f3d745a508a285155cbfaa527dc2f6576e013c6dc390558f187ddca808a36091

Observation f58d98b2-0a89-4c50-ab20-0bbbe318a9a6 · outbound

This paper cites Weak adversarial networks for high-dimensional partial differential equations.Journal of Computational Physics, 411:109409, 2020.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Weak adversarial networks for high-dimensional partial differential equations.Journal of Computational Physics, 411:109409, 2020

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source=pdf_text observed=2026-08-06T23:21:46.235004Z digest=sha256:303fbff8c8774d5922b1856681940550dddbe75a48cd860774613fa1f8eb1b8c

Observation 6d8f441c-d8e7-499e-b92d-f81bceb93f1f · outbound

This paper cites Interfacing finite elements with deep neural operators for fast multiscale modeling of mechanics problems.Computer methods in applied mechanics and engineering, 402:115027, 2022.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Interfacing finite elements with deep neural operators for fast multiscale modeling of mechanics problems.Computer methods in applied mechanics and engineering, 402:115027, 2022

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verified fuzzy
raw_fallback, observed 2026-08-06T23:21:53.970508Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-06T23:21:46.384752Z digest=sha256:3e23b625b81eca1dfb4121df04e8f6d2c708c485076454653bc3820ab9f3711c

Observation 7e87fb8c-c09a-4dfe-bc7d-f1c7bbd9c9bc · outbound

This paper cites Train small, model big: Scalable physics simulators via reduced order modeling and domain decomposition.Computer Methods in Applied Mechanics and Engineering, 427:117041, 2024.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Train small, model big: Scalable physics simulators via reduced order modeling and domain decomposition.Computer Methods in Applied Mechanics and Engineering, 427:117041, 2024

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raw_fallback, observed 2026-08-06T23:21:53.655100Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-06T23:21:46.541981Z digest=sha256:83b9bf5d0a1035cfca7894108a86caf1bcc21f17a28c4c45cfa8a064be2ee7d0

Observation dcfff330-9d95-4d90-a1f0-b6f12ee628f0 · outbound

This paper cites Why it is difficult to solve helmholtz problems with classical iterative methods.Numerical analysis of multiscale problems, pages 325–363, 2011.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Why it is difficult to solve helmholtz problems with classical iterative methods.Numerical analysis of multiscale problems, pages 325–363, 2011

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raw_fallback, observed 2026-08-06T23:21:53.392173Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-06T23:21:46.704823Z digest=sha256:550f4951e1586d621df6aa40f4d30d8092a5be0d847e2c322043c5c7047edffc

Observation 4c320107-b075-48e4-a683-56fbbd92fa3d · outbound

This paper cites Critical success factors for modular in- tegrated construction projects: A review.Building research & information, 48(7):763–784, 2020.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Critical success factors for modular in- tegrated construction projects: A review.Building research & information, 48(7):763–784, 2020

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verified fuzzy
raw_fallback, observed 2026-08-06T23:21:53.124312Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-06T23:21:46.844109Z digest=sha256:b160a1a00b11c94a9ab4009582b8a206d64b44661cdcdcffaf0126896331cbbf

Observation 556af38e-20bf-43a9-8670-b43ea2d2de36 · outbound

This paper cites A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data.Computer Methods in Applied Mechanics and Engineering, 393:114778, 2022.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data.Computer Methods in Applied Mechanics and Engineering, 393:114778, 2022

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no resolver link, observed 2026-08-06T23:21:47.036509Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T23:21:47.036509Z digest=sha256:b59292667139a842165fa14c7a5bff79dc7267f72949e53e7677495caa50e649

Observation 8f947a5a-2e86-4a5f-a41a-8f3bc4bb2e40 · outbound

This paper cites Fully convolutional network enhanced deeponet-based surrogate of predicting the travel-time fields.IEEE Trans- actions on Geoscience and Remote Sensing, 2024.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Fully convolutional network enhanced deeponet-based surrogate of predicting the travel-time fields.IEEE Trans- actions on Geoscience and Remote Sensing, 2024

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verified fuzzy
raw_fallback, observed 2026-08-06T23:21:52.698357Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-06T23:21:47.445011Z digest=sha256:0661c09b43c1fb6fa2a53e38c31569ed9a634d112f5a70d89501fd9c2c0d3e42

Observation aa7be118-795e-4d65-beef-cde5968450e8 · outbound

This paper cites Improving physics-informed DeepONets with hard constraints.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Improving physics-informed DeepONets with hard constraints

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no resolver link, observed 2026-08-06T23:21:47.595154Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T23:21:47.595154Z digest=sha256:5d2951ca7411178d663410924be5ecf86fb09187407e303df54c299e16d053c2

Observation 94afcc7e-4a06-46f9-aaec-c25e53de474d · outbound

This paper cites Bayesian deep operator learning for homogenized to fine-scale maps for multiscale pde.Multiscale Modeling & Simulation, 22(3):956–972, 2024.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Bayesian deep operator learning for homogenized to fine-scale maps for multiscale pde.Multiscale Modeling & Simulation, 22(3):956–972, 2024

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verified fuzzy
raw_fallback, observed 2026-08-06T23:21:52.424914Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-06T23:21:47.816027Z digest=sha256:ea2db749ad92284b45cad3bae9f05975a5e8efb56991f9c6811639678d356229

Observation 64b7b74e-41eb-434c-924c-e5a57b7b4e93 · outbound

This paper cites PROSE: Predicting Operators and Symbolic Expressions using Multimodal Transformers.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators PROSE: Predicting Operators and Symbolic Expressions using Multimodal Transformers

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local_arxiv, observed 2026-08-06T23:21:49.265131Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-06T23:21:47.984862Z digest=sha256:8cacaf53592b44030e23d4dd4a2182c18730967ff4486f6bad3b68d794946219

Observation e41cf396-31f6-409e-8223-090667825d65 · outbound

This paper cites Gnot: A general neural operator transformer for operator learning.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Gnot: A general neural operator transformer for operator learning

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no resolver link, observed 2026-08-06T23:21:48.144994Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T23:21:48.144994Z digest=sha256:c942b5864aba3cc5bc76098b416ec5b65672dda771bc08d7497417d9d27daf5d

Observation 8bb5ff47-8e4e-4438-a6db-e264f1d9654f · outbound

This paper cites Pfnn: A penalty-free neural network method for solving a class of second-order boundary-value problems on complex geometries.Journal of Computational Physics, 428:110085, 2021.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Pfnn: A penalty-free neural network method for solving a class of second-order boundary-value problems on complex geometries.Journal of Computational Physics, 428:110085, 2021

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verified fuzzy
raw_fallback, observed 2026-08-06T23:21:51.954975Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-06T23:21:48.277439Z digest=sha256:4151f92b276f1b844f5182016511119d955991bea25360a75dc82a4c2251cfd6

Observation 1900dfb1-f35b-4ce3-9119-a66d3b8dfe71 · outbound

This paper cites Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks.Computer Methods in Applied Mechanics and Engineering, 389:114333, 2022.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks.Computer Methods in Applied Mechanics and Engineering, 389:114333, 2022

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no resolver link, observed 2026-08-06T23:21:48.376521Z

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Observation 0f35969d-8a4e-4096-9e0f-7b5ca0dcf483 · outbound

This paper cites Systems biology informed deep learning for inferring parameters and hidden dynamics.PLoS computational biology, 16(11):e1007575, 2020.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Systems biology informed deep learning for inferring parameters and hidden dynamics.PLoS computational biology, 16(11):e1007575, 2020

Reference 66

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no resolver link, observed 2026-08-06T23:21:48.532977Z

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Observation d700ae3f-75f1-454c-bb43-fd322aa5cc64 · outbound

This paper cites Physics-informed neural networks with hard constraints for inverse design.SIAM Journal on Scientific Computing, 43(6):B1105–B1132, 2021.

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators Physics-informed neural networks with hard constraints for inverse design.SIAM Journal on Scientific Computing, 43(6):B1105–B1132, 2021

Reference 67

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verified fuzzy
raw_fallback, observed 2026-08-06T23:21:51.414944Z

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Pith citing papers

Observation 97fc8843-16d7-4550-972d-0cd853afc5f3 · inbound

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations cites this paper.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators

Reference 11

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verified exact
local_arxiv, observed 2026-08-05T12:50:05.347523Z

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source=pdf_text observed=2026-08-05T12:50:00.467557Z digest=sha256:0fe53c9cd9af7d14e96341e61ee5bd8e15fca63ee625df776e7added19eda0b1