Paper Citation Record · LEDGER

Data-free neural PDE solvers based on Graph Neural Networks and weak forms

As of 6 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 0 inbound Pith citation observations for arXiv:2607.27901.

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pith.paper-citation-record.v1
2607.27901 v1

Coverage vector

measured 44 of 44 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-07-31T23:24:58.871783Z

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Reference resolution

44 of 44 outbound references displayed

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Outbound references

Observation 02d567ed-cbbf-4c8a-978a-e388797d0e47 · outbound

This paper cites Machine learning in computer aided engineering.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Machine learning in computer aided engineering

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:54.761542Z

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Observation 31a9d41c-fa7f-4333-9749-14f53e999936 · outbound

This paper cites Raissi, P.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Raissi, P

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:54.822029Z

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Observation a4c1c5ee-027b-455b-ab46-cc515f1975bc · outbound

This paper cites Meshgraphnet-transformer: Scalable mesh-based learned simulation for solid mechanics.arXiv preprint arXiv:2601.23177, 2026.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Meshgraphnet-transformer: Scalable mesh-based learned simulation for solid mechanics.arXiv preprint arXiv:2601.23177, 2026

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:54.911948Z

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Observation 6b591f25-e505-4c73-b18b-5d5944c9ce29 · outbound

This paper cites Learn- ing to simulate complex physics with graph networks.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Learn- ing to simulate complex physics with graph networks

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:55.004283Z

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Observation 952a204c-4a67-4679-aa8b-0ff2283bcdab · outbound

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

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Fourier Neural Operator for Parametric Partial Differential Equations

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:55.103950Z

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Observation e56a9f10-9434-41a5-b072-c7c9f45fa571 · outbound

This paper cites Learning nonlinear op- erators via deeponet based on the universal approximation theorem of operators.Nature Machine Intelligence, 3(3):218–229, 2021.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Learning nonlinear op- erators via deeponet based on the universal approximation theorem of operators.Nature Machine Intelligence, 3(3):218–229, 2021

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:55.182203Z

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Observation 4ea14d88-ff46-42f7-be0c-c078ec97616e · outbound

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

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Gnot: A general neural operator transformer for operator learning

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:55.260543Z

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Observation 498ebd18-ebf1-4212-ad00-322e3287456b · outbound

This paper cites Latent Mamba Operator for Partial Differential Equations.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Latent Mamba Operator for Partial Differential Equations

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:55.345347Z

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Observation 091e09f0-9638-4c02-a0ef-f3c39bf3b044 · outbound

This paper cites Learning the solution operator of parametric partial differential equations with physics-informed deeponets, 2021.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Learning the solution operator of parametric partial differential equations with physics-informed deeponets, 2021

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:55.440150Z

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Observation 1bf7e7d7-ad96-45f0-88df-595526e98660 · outbound

This paper cites Relational inductive biases, deep learning, and graph networks.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Relational inductive biases, deep learning, and graph networks

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:55.589506Z

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Observation a11b7b9e-aa67-490c-b81f-636dc236b134 · outbound

This paper cites Physics-informed and graph neural networks for enhanced inverse analysis.Engineering Computations, 42(7):2427–2455, 2025.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Physics-informed and graph neural networks for enhanced inverse analysis.Engineering Computations, 42(7):2427–2455, 2025

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:55.663162Z

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Observation fe82186e-7e84-436b-bc6c-debf3c1e1240 · outbound

This paper cites Learning Mesh-Based Simulation with Graph Networks.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Learning Mesh-Based Simulation with Graph Networks

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:55.690053Z

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Observation cdbd2b75-9ad9-420b-bc0f-f6d4ec2a5f0b · outbound

This paper cites On the under-reaching phenomenon in message passing neural pde solvers: Revisiting the cfl condition.Computer Methods in Applied Mechanics and Engineering, 449:118476, 2026.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms On the under-reaching phenomenon in message passing neural pde solvers: Revisiting the cfl condition.Computer Methods in Applied Mechanics and Engineering, 449:118476, 2026

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:55.765849Z

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Observation a0515cdc-4989-4194-9bce-9ae4c0fc2388 · outbound

This paper cites Recurrent u-net-based graph neural network (rugnn) for accurate deformation predictions in sheet material forming.Advanced Engineering Informatics, 69:104021, 2026.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Recurrent u-net-based graph neural network (rugnn) for accurate deformation predictions in sheet material forming.Advanced Engineering Informatics, 69:104021, 2026

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:55.860839Z

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Observation cb0fd642-5bdf-4ec9-ba89-1b597ee7e7f7 · outbound

This paper cites M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:55.938007Z

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Observation 1d7826d6-9978-4d55-990e-64736b8d49b5 · outbound

This paper cites Efficient Learning of Mesh-Based Physical Simulation with BSMS-GNN.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Efficient Learning of Mesh-Based Physical Simulation with BSMS-GNN

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:56.042393Z

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Observation ab4d23c6-1838-4739-b2b8-a7e85b43bd53 · outbound

This paper cites Predicting Physics in Mesh-reduced Space with Temporal Attention.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Predicting Physics in Mesh-reduced Space with Temporal Attention

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:56.148867Z

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Observation 490ac179-ecb6-4e27-a732-567b8c74dab9 · outbound

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Data-free neural PDE solvers based on Graph Neural Networks and weak forms Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:56.309604Z

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Observation 860faae1-be74-4ad5-b0b6-3ee4dec7a39c · outbound

This paper cites Transolver: A fast transformer solver for pdes on general geometries.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Transolver: A fast transformer solver for pdes on general geometries

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:56.398647Z

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Observation aee16058-e4c5-4ecf-ac2a-a05043d3f956 · outbound

This paper cites Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries

Reference 20

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:56.512172Z

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Observation 596d5a4a-e16d-4912-a478-8067c875b86b · outbound

This paper cites GeoTransolver: Learning Physics on Irregular Domains Using Multi-scale Geometry Aware Physics Attention Transformer.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms GeoTransolver: Learning Physics on Irregular Domains Using Multi-scale Geometry Aware Physics Attention Transformer

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:56.685257Z

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Observation bc9bf57c-63cb-4efa-be9f-e90e272e318e · outbound

This paper cites Ab-upt: Scaling neural cfd surrogates for high-fidelity automotive aerodynamics simulations via anchored-branched universal physics transformers, 2025.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Ab-upt: Scaling neural cfd surrogates for high-fidelity automotive aerodynamics simulations via anchored-branched universal physics transformers, 2025

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:56.793443Z

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Observation 1739c93e-915b-4a02-8cf6-4fed62d9bc6b · outbound

This paper cites A mechanistic analysis of transformers for dynamical systems.arXiv preprint arXiv:2512.21113, 2025.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms A mechanistic analysis of transformers for dynamical systems.arXiv preprint arXiv:2512.21113, 2025

Reference 23

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:56.944232Z

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Observation 5f90aebf-3f95-4fdb-9097-5c1603b910ba · outbound

This paper cites Hamiltonian neural networks.Advances in neural information processing systems, 32, 2019.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Hamiltonian neural networks.Advances in neural information processing systems, 32, 2019

Reference 24

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:57.124235Z

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Observation 770d980f-c382-49c2-8ab2-7742c173b427 · outbound

This paper cites Lagrangian Neural Networks.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Lagrangian Neural Networks

Reference 25

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:57.257098Z

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Observation 73214c1f-d7e2-409e-9042-00fb7cce190b · outbound

This paper cites Structure-preserving neural networks.Journal of Computational Physics, 426:109950, 2021.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Structure-preserving neural networks.Journal of Computational Physics, 426:109950, 2021

Reference 26

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:57.455043Z

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Observation 7b862e72-3d0b-49f1-8780-13823bd15a4a · outbound

This paper cites Thermodynamics of learning physical phenomena.Archives of Computa- tional Methods in Engineering, 30(8):4653–4666, 2023.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Thermodynamics of learning physical phenomena.Archives of Computa- tional Methods in Engineering, 30(8):4653–4666, 2023

Reference 27

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:57.588326Z

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Observation fe3bfbdb-cdc6-4849-8b84-519a4552279a · outbound

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Data-free neural PDE solvers based on Graph Neural Networks and weak forms Unresolved cited work

Reference 28

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:57.658402Z

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Observation c08f9b63-f6d0-45a4-98ca-0663684c8786 · outbound

This paper cites Elsayed, Abedulgader Baktheer, and Fadi Aldakheel.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Elsayed, Abedulgader Baktheer, and Fadi Aldakheel

Reference 29

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:57.746238Z

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Observation 407bc6cf-e254-4f39-aa9b-eb08fb7b44ce · outbound

This paper cites Structure-preserving model order reduction of Hamiltonian systems.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Structure-preserving model order reduction of Hamiltonian systems

Reference 30

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:57.836143Z

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Observation fac216f8-c002-4425-9d55-ba4869cf984c · outbound

This paper cites Symplectic learning for hamiltonian neural networks.Journal of Computa- tional Physics, 494:112495, December 2023.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Symplectic learning for hamiltonian neural networks.Journal of Computa- tional Physics, 494:112495, December 2023

Reference 31

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:57.927545Z

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Observation 83fa4ac4-267c-44b1-93af-0684b2cbc1af · outbound

This paper cites Physics-informed neural networks for modeling rate- and temperature-dependent plasticity.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Physics-informed neural networks for modeling rate- and temperature-dependent plasticity

Reference 32

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:57.988183Z

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Observation affa2f7a-fe79-4577-96e6-43811f96d77c · outbound

This paper cites Challenges in training pinns: A loss landscape perspective, 2024.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Challenges in training pinns: A loss landscape perspective, 2024

Reference 33

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:58.036337Z

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Observation 384682ba-d974-4d79-a02d-14c3b2fde057 · outbound

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Data-free neural PDE solvers based on Graph Neural Networks and weak forms Unresolved cited work

Reference 34

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Observation ea2c4a85-bf4d-4526-be50-36d49ebf2686 · outbound

This paper cites The deep ritz method: A deep learning-based numerical algorithm for solving variational problems, 2017.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms The deep ritz method: A deep learning-based numerical algorithm for solving variational problems, 2017

Reference 35

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:58.189836Z

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Observation a7c28736-0624-4905-8a00-3e45a560c416 · outbound

This paper cites A deep energy method for finite deformation hyperelasticity.European Journal of Mechanics-A/Solids, 80:103874, 2020.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms A deep energy method for finite deformation hyperelasticity.European Journal of Mechanics-A/Solids, 80:103874, 2020

Reference 36

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:58.243906Z

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This paper cites Hamel, Kyle Johnson, Reese Jones, and Nikolaos Bouklas.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Hamel, Kyle Johnson, Reese Jones, and Nikolaos Bouklas

Reference 37

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:58.294915Z

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Observation 9455a995-b220-473d-a675-26ecb0d13734 · outbound

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Data-free neural PDE solvers based on Graph Neural Networks and weak forms Unresolved cited work

Reference 38

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:58.352194Z

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Observation 812f3564-e1d9-42ed-b26a-6619bac82a44 · outbound

This paper cites Learning, solving and optimizing pdes with tensorgalerkin: an efficient high-performance galerkin assembly algorithm, 2026.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Learning, solving and optimizing pdes with tensorgalerkin: an efficient high-performance galerkin assembly algorithm, 2026

Reference 39

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:58.414474Z

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Observation 30cc3e7f-0429-4373-93f6-e097ab1d0070 · outbound

This paper cites WINO: A Weak-Form Physics Informed Neural Operator for Hyperelasticity on Variable Domains.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms WINO: A Weak-Form Physics Informed Neural Operator for Hyperelasticity on Variable Domains

Reference 40

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:58.594046Z

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Observation 6d72488a-0e05-4b68-9244-a7aad4998328 · outbound

This paper cites Elsevier, 2005.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Elsevier, 2005

Reference 41

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Observation 6898f6fc-ae12-4aea-b27e-6d72d5e808ea · outbound

This paper cites John wiley & sons, 2014.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms John wiley & sons, 2014

Reference 42

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Observation decf4c26-7f36-4efe-919a-f9beb63002f9 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Adam: A Method for Stochastic Optimization

Reference 43

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:58.814171Z

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Observation 129bba24-3218-46c3-8182-5a86502ad4c4 · outbound

This paper cites SGDR: Stochastic Gradient Descent with Warm Restarts.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms SGDR: Stochastic Gradient Descent with Warm Restarts

Reference 44

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:58.871783Z

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