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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 8 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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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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Source-reported events for the cited work

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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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Source-reported events for the cited work

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

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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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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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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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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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source=pdf_text observed=2026-08-06T23:21:43.394824Z digest=sha256:f501492461fcbb7f52857c1fd79832e72ca86c0ebbb2c897913ab388c0653078

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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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+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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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 2026-08-08T06:32:00.761636+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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Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T23:21:43.919377Z digest=sha256:5139aa26aca83ae126780d5489ffe6f51e5641de92541b8894b16493de79408c

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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+00:00.

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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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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T23:21:44.293897Z digest=sha256:cd019c9766825dd3cafce68ceca6530b63a2ede1d8f6d7bb1ab8fbbfa9dd5f85

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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Source-reported events for the cited work

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

source=pdf_text observed=2026-08-06T23:21:44.483793Z digest=sha256:f2d65e9d3f998570350a025b0ed3ca29ceefa12653df97c3c479e4e6e52e654e

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T23:21:44.586222Z digest=sha256:1c03f7ff836dbcb08570710e9f42861fbd1a54ab5b277457b87fcea0865f211a

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T23:21:44.694931Z digest=sha256:2a05a9b319c31ccf09acb448522402aaab0733fe10c533bf76b9881425a109f7

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T23:21:44.834939Z digest=sha256:708434e9ba8c80e5f5be15e1c23c7881724119ea87f25a6c417ef65c84e2ec6b

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T23:21:44.917676Z digest=sha256:9e9cd88a688fa5307e83e02ba301944fd8c789bcff3fdaa584c09e55a3e085b2

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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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T23:21:44.987909Z digest=sha256:92e8e5bb985ef16a812a13334f99053918676dd211f7ba75c620e39a4dc51074

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
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Source-reported events for the cited work

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

source=pdf_text observed=2026-08-06T23:21:45.124955Z digest=sha256:30387db4117b2e38fde8dfb2363c07bf298bdb35c250b12f4ede3177a741f2e6

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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Resolution
unresolved
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Source-reported events for the cited work

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

source=pdf_text observed=2026-08-06T23:21:45.252557Z digest=sha256:7424604f1359c8f6426112148aabd0b48ea82f5c87f8df63314dd0bc6530657c

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

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T23:21:45.384824Z digest=sha256:32287bfee0d26a2c2a17ae3f8fc8bb875a35dfda3943fa5adde189f328645129

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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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:a82af17873497e440c87ac7d635070778e6569609440eb33b5df4cdaae1dbffe

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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Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T23:21:45.664814Z digest=sha256:f9b0a953db8df24becca63bdd40f1a866bdc83aa5a61b877f38390110b0ab7bc

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T23:21:45.754907Z digest=sha256:8cef2a5dce2abb5501397d585daff5c28c7308c7df1a099347c03805937ef63d

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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Resolution
verified fuzzy
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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T23:21:45.894828Z digest=sha256:21f4c0e68a67c81a7e419a3b910c6afdc97dd921774fbccbfd50cd609d0dab3e

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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Source-reported events for the cited work

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

source=pdf_text observed=2026-08-06T23:21:46.014833Z digest=sha256:ab7ba6ddc3f31a8fa8b08b93e20712c86b45ec720aa1dcc9cd2e64026c0ea57f

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T23:21:46.097147Z digest=sha256:86ae8c7c9577bf40075b8bf358b419e03ad75e5d199b0c6715efaf027946ec88

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-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T23:21:46.235004Z digest=sha256:e134d8142cc1f15f22332e6a1168ec76b6a8de33ed5278a2ea30c9505cab7a80

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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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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T23:21:46.384752Z digest=sha256:39b107798c9f73122eeafb10b4189b8835ab3c2ca6e67bfc8960f05ae658f617

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T23:21:46.541981Z digest=sha256:665ef5282f01030a062a8c19cd3d6c9a5eb7d6450a39211ef1410a3267e170b4

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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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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T23:21:46.704823Z digest=sha256:afb287e2de96e51d3d08e3fb000d38ad063510da594f185fd1ed2ba2e414c5df

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T23:21:46.844109Z digest=sha256:afb12fcb5a30f2022ef70252e38dcfcb7f784d4be0e5f4b7513f61047cfc578a

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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unresolved
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:cac7d5bb0610bb7203b56ef71764502b0442859ab93ab3a8e5648780ac244530

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T23:21:47.445011Z digest=sha256:c3755e4eb48e9b3c0577025b3fe46a3ebb4e495ee1bd434705ab0c69bfdb115e

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:a96642269854fe83b43fa6b684e00d4637b4b437178968741b29e3188c27ae31

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T23:21:47.816027Z digest=sha256:4d1ba50c89836076f5c97a26eb68bc8ae731bfa00c44119854971696c16e9ad4

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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verified exact
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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T23:21:47.984862Z digest=sha256:162b152b2fee53f30e2dcff4d3c1013a68ca74d215d9090f9fdfd4eac4dbba77

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:bff44579adb7129c15617984e1b3232277a9df96463e3879cecc1116cf6463df

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T23:21:48.277439Z digest=sha256:06610e6dcdfa70d502fa011fb1c8802d345487cabbc4bf7ba08914c045150da0

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
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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unresolved
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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+00:00.

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