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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 10 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 2026-08-09T06:31:02.800959+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 2026-08-09T06:31:02.800959+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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raw_fallback, observed 2026-08-06T23:22:03.905572Z

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

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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 2026-08-09T06:31:02.800959+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 2026-08-09T06:31:02.800959+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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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 2026-08-09T06:31:02.800959+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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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 2026-08-09T06:31:02.800959+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 2026-08-09T06:31:02.800959+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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raw_fallback, observed 2026-08-06T23:21:58.914875Z

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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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.

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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

Reference 33

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

Reference 34

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source=pdf_text observed=2026-08-06T23:21:43.919377Z digest=sha256:2fe774a9a1800c3b7a033fcce7a88933a13865c933f8f35eda7e1d88c776e5c3

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

Reference 35

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

Reference 36

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raw_fallback, observed 2026-08-06T23:21:57.764796Z

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.

source=pdf_text observed=2026-08-06T23:21:44.180249Z digest=sha256:4e8ea4a9176149aeb2ac9e30073f459fb2430c8c658b72fe20f7f73af7dc0b74

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

Reference 37

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T23:21:44.293897Z digest=sha256:a23812f11a7dadeb61534e65d29885fc468ec1d02dcc19265755cf254a0795d3

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

Reference 38

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verified fuzzy
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 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T23:21:44.483793Z digest=sha256:662183b47a16287e9bf409c7099cab3bcd7c89ab927718b847f426cf0748242c

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

Reference 39

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raw_fallback, observed 2026-08-06T23:21:57.154761Z

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.

source=pdf_text observed=2026-08-06T23:21:44.586222Z digest=sha256:0025774095ad959671febc97099979c8bd152af924e86eea8be7766a38937e5e

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

Reference 40

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raw_fallback, observed 2026-08-06T23:21:56.704924Z

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.

source=pdf_text observed=2026-08-06T23:21:44.694931Z digest=sha256:9ca56cb663462ef2e343af36dbfb70e200d3b3a99caac1fa8f57a5368ec9e587

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

Reference 41

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raw_fallback, observed 2026-08-06T23:21:56.357124Z

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.

source=pdf_text observed=2026-08-06T23:21:44.834939Z digest=sha256:724e40846b1ab3555094e46ab2e1a0193d37227f85c383793efcc11c6602ba28

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

Reference 42

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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.

source=pdf_text observed=2026-08-06T23:21:44.917676Z digest=sha256:c5bf3ed18997100ec6c38bd083eefda071072cc8d0fb8fef873034d1622798b3

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

Reference 43

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no resolver link, observed 2026-08-06T23:21:44.987909Z

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Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T23:21:44.987909Z digest=sha256:5e32aa2040f13f6a1e8fb3f3dcd1987b774cf58e866270d8d0886de15b84a935

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

Reference 44

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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 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T23:21:45.124955Z digest=sha256:06da1441ab028eec6a1559dae315af0b662f7df21ea6be3462f06086c34a406a

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

Reference 45

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unresolved
raw_fallback, observed 2026-08-06T23:21:55.964826Z

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.

source=pdf_text observed=2026-08-06T23:21:45.252557Z digest=sha256:06cbf9139bfa1329239ba3e7d9450a5b177417d1871fb55b32df4f54a3d5f46d

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

Reference 46

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T23:21:45.384824Z digest=sha256:73af135e4dc7921c299a4051e1e55957c63d84d4a93a8993ae72002619a8eabe

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

Reference 47

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no resolver link, observed 2026-08-06T23:21:45.524943Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T23:21:45.524943Z digest=sha256:76fdabb5930d3bb8e035776a5ed17df454f42756558a3f9aa5b07077dfa66985

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

Reference 48

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Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T23:21:45.664814Z digest=sha256:4575defcd35a63166f2b57cbd12fbaa9ba3d83b52b8f53f0540986047e74fc40

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

Reference 49

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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 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T23:21:45.754907Z digest=sha256:08d86358d7ee8f498113d6ef917d1d21327f2e84a1a7895214573a87cfdba180

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

Reference 50

Resolution
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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 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T23:21:45.894828Z digest=sha256:bc711f08b530501a1a9c2bce9cda4c10c6eee7fc51bfc9d088e3f9fb17b530ca

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

Reference 51

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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 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T23:21:46.014833Z digest=sha256:7aca71181c1c22cd4db0e7607d199d9ff62cf087c7d6d748f7d41139dde7d79f

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

Reference 52

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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 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T23:21:46.097147Z digest=sha256:79966ff563ab49a46f7526a68d186c12f1e08b5b683fc6ab360cc175aac9e8f4

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

Reference 53

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T23:21:46.235004Z digest=sha256:4e28b1113fcbe0c357bb9dd385d47e07f3c9bf13458141965738e00326c2a76f

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

Reference 54

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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 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T23:21:46.384752Z digest=sha256:df304a97814ff3320a6e6a5cbb4d94968935178274e63b8fc784a6b0c5431e77

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

Reference 55

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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 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T23:21:46.541981Z digest=sha256:2ca85a4f513dc9932bf07ae7c16c41e250a4461f703590bd5172fe49a99fc68e

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

Reference 56

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verified fuzzy
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 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T23:21:46.704823Z digest=sha256:1658a74d535e50faaccba03cceb57500fbc7be4a789a7d7f0985628e0cdec37a

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

Reference 57

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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 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T23:21:46.844109Z digest=sha256:c645128240ad67d6945a32a9fe52d787abacdd8fef00ef132957ca6c2a1f4a34

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

Reference 58

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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=sha256:2da20a48c631fbfa9849090163335a459b48d69b940d8f4b7e3defefea120e6f

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

Reference 59

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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 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T23:21:47.445011Z digest=sha256:8e1b1ee9b6bc704bcf51c8c35ecb4520a1d1f4119e6444ee0277cc4f52edb756

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

Reference 60

Resolution
unresolved
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=sha256:44b2887027ad9f2115afe3ac7b51f9cae938c25f531e73d6fd672ece332deb5e

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

Reference 61

Resolution
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 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T23:21:47.816027Z digest=sha256:137d907f40442c9840fe8cef1e426ef51fb1188795c043de51ec49fe59382d64

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

Reference 62

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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 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T23:21:47.984862Z digest=sha256:e6edf1b1ea7feb90c50e21f836c8685e9eebbda8bcc5e6942559ac655c7082b5

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

Reference 63

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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=sha256:3feeffc0bf81917ec4c930d754ff186e878b613a01f110aafd7a580eb8e72e80

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

Reference 64

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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 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T23:21:48.277439Z digest=sha256:25ca2961025f365f463a5c6927e5ff944c1f6323ea52c33873650ee950c4b2e6

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

Reference 65

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unresolved
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Unavailable: canonical work link unavailable.

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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

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

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

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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

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

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

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