Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains | Paper Citation Record

Observation 709ef5e3-baa4-4074-855b-cf9a657b5f2c · outbound

This paper cites A unified deep artificial neural network approach to partial differential equations in complex geometries.Neurocomputing, 317:28–41, 2018.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains A unified deep artificial neural network approach to partial differential equations in complex geometries.Neurocomputing, 317:28–41, 2018

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.081098Z

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Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Unresolved cited work

Reference 2

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This paper cites Two-grid finite volume element method for the time-dependent Schr¨ odinger equation.Computers & Mathematics with Applications, 108:185–195, 2022.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Two-grid finite volume element method for the time-dependent Schr¨ odinger equation.Computers & Mathematics with Applications, 108:185–195, 2022

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.073304Z

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This paper cites Bridging traditional and machine learning-based algorithms for solving PDEs: the random feature method.Journal of Machine Learning, 1(3):268–298, 2022.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Bridging traditional and machine learning-based algorithms for solving PDEs: the random feature method.Journal of Machine Learning, 1(3):268–298, 2022

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.067093Z

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Observation 10242854-d6aa-4239-b5e0-82609d5a4a71 · outbound

This paper cites Analysis of absorbing boundary conditions for the anomalous diffusion in comb model on unbounded domain by finite volume method.Applied Mathematics Letters, 144:108712, 2023.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Analysis of absorbing boundary conditions for the anomalous diffusion in comb model on unbounded domain by finite volume method.Applied Mathematics Letters, 144:108712, 2023

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.075384Z

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This paper cites Local randomized neural networks with hybridized discontinuous Petrov– Galerkin methods for Stokes–Darcy flows.Physics of Fluids, 36(8):087138, 2024.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Local randomized neural networks with hybridized discontinuous Petrov– Galerkin methods for Stokes–Darcy flows.Physics of Fluids, 36(8):087138, 2024

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.070971Z

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Observation e5307a5e-78f4-4060-ad21-0b7e8482d048 · outbound

This paper cites Adaptive growing randomized neural networks for solving partial differential equations.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Adaptive growing randomized neural networks for solving partial differential equations

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-07-01T11:05:41.684674Z

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Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Unresolved cited work

Reference 8

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Reference 9

Resolution: unresolved; raw_fallback, observed 2026-07-06T23:23:03.032942Z

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Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-07-06T23:23:03.034543Z

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This paper cites The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems.Communications in Mathematics and Statistics, 6(1):1–12.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems.Communications in Mathematics and Statistics, 6(1):1–12

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.083005Z

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Observation bf96b598-d4b6-4142-932f-0c35b1a2bcd6 · outbound

This paper cites Two FEM-BEM methods for the numerical solution of 2D transient elastodynamics problems in unbounded domains.Computers & Mathematics with Applications, 114:132–150, 2022.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Two FEM-BEM methods for the numerical solution of 2D transient elastodynamics problems in unbounded domains.Computers & Mathematics with Applications, 114:132–150, 2022

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.088725Z

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Observation cb180e89-5256-4ab0-8bbc-5fdc25c7ecea · outbound

This paper cites A new absorbing layer approach for solving the nonlinear Schr¨ odinger equation.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains A new absorbing layer approach for solving the nonlinear Schr¨ odinger equation

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.092912Z

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Observation edc5663f-76a6-4bda-b00a-a061127dc921 · outbound

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Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-07-06T23:23:03.059623Z

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Observation 90cf6af3-150b-44b7-8e0c-118786eaecac · outbound

This paper cites Dissipation-preserving rational spectral-Galerkin method for strongly damped nonlinear wave system involving mixed fractional Laplacians in unbounded domains.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Dissipation-preserving rational spectral-Galerkin method for strongly damped nonlinear wave system involving mixed fractional Laplacians in unbounded domains

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.061627Z

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Observation bf2e24b0-7347-44d4-8411-900b95d28384 · outbound

This paper cites Explicit time-domain analysis of wave propagation in unbounded domains using the scaled boundary finite element method.Engineering Analysis with Boundary Elements, 168:105891, 2024.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Explicit time-domain analysis of wave propagation in unbounded domains using the scaled boundary finite element method.Engineering Analysis with Boundary Elements, 168:105891, 2024

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.069097Z

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Observation ac1a6501-3dd0-4e36-9aad-d9ba533b922a · outbound

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Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-07-06T23:23:03.100260Z

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Observation 7d516682-7b09-4b3c-b9c9-f765997cbc59 · outbound

This paper cites Numerical solution of the regularized logarithmic Schr¨ odinger equation on unbounded domains.Applied Numerical Mathematics, 140:91–103, 2019.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Numerical solution of the regularized logarithmic Schr¨ odinger equation on unbounded domains.Applied Numerical Mathematics, 140:91–103, 2019

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.104286Z

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Observation ba06dd94-a845-4e8a-b056-78b17927a3db · outbound

This paper cites Local randomized neural networks with finite difference methods for interface problems.Journal of Computational Physics, 529:113847, 2025.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Local randomized neural networks with finite difference methods for interface problems.Journal of Computational Physics, 529:113847, 2025

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.050400Z

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This paper cites A finite element method for elliptic optimal control problem in the unbounded domain.Journal of Applied Mathematics and Computing, 71(3):4375–4396, 2025.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains A finite element method for elliptic optimal control problem in the unbounded domain.Journal of Applied Mathematics and Computing, 71(3):4375–4396, 2025

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.052435Z

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This paper cites Analysis and Hermite spectral approximation of diffusive-viscous wave equations in unbounded domains arising in geophysics.Journal of Scientific Computing, 95:51, 2023.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Analysis and Hermite spectral approximation of diffusive-viscous wave equations in unbounded domains arising in geophysics.Journal of Scientific Computing, 95:51, 2023

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.046771Z

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This paper cites Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks

Reference 22

Resolution: verified exact; arxiv_id, observed 2026-07-01T11:05:41.681859Z

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Observation 7aba94fc-92e4-4c3b-8c58-10f45158bba2 · outbound

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Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-07-06T23:23:03.048519Z

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Observation b60e5907-d627-4259-ac09-f707d7df3baf · outbound

This paper cites Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-07-01T11:05:41.678945Z

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Observation 7a030753-6a62-4959-9608-fceb83b3c04d · outbound

This paper cites Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-07-01T11:05:41.676115Z

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Observation 3381db7e-fba9-4e99-a9f9-da11bf6f1c93 · outbound

This paper cites Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.055645Z

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Observation f113ee2e-c191-45f8-9783-48df9346863d · outbound

This paper cites Overlapping Schwarz preconditioners for randomized neural networks with domain decomposition.Computer Methods in Applied Mechanics and Engineering, 442:118011, 2025.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Overlapping Schwarz preconditioners for randomized neural networks with domain decomposition.Computer Methods in Applied Mechanics and Engineering, 442:118011, 2025

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.057825Z

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Observation 435607a6-a55f-4350-ac86-268464630a0e · outbound

This paper cites Randomized neural networks with Petrov–Galerkin methods for solving linear elasticity and Navier–Stokes equations.Journal of Engineering Mechanics, 150(4):04024010.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Randomized neural networks with Petrov–Galerkin methods for solving linear elasticity and Navier–Stokes equations.Journal of Engineering Mechanics, 150(4):04024010

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.063625Z

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Observation 872f668a-272b-4f59-b409-102e0c6a93a7 · outbound

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Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-07-06T23:23:03.084695Z

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Observation fe583b1e-432f-488f-bb34-c0aef0e4b6f2 · outbound

This paper cites Some recent advances on spectral methods for unbounded domains.Communications in Computational Physics, 5(2-4):195–241, 2009.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Some recent advances on spectral methods for unbounded domains.Communications in Computational Physics, 5(2-4):195–241, 2009

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.038586Z

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Observation f4f4a5d5-9ce8-47d3-b55f-f191b1f22b3e · outbound

This paper cites Greedy training algorithms for neural networks and applications to PDEs.Journal of Computational Physics, 484:112084, 2023.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Greedy training algorithms for neural networks and applications to PDEs.Journal of Computational Physics, 484:112084, 2023

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.031250Z

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Observation 90c1785d-bd96-459e-809d-9716d95994c3 · outbound

This paper cites Rate of convergence of two moments consistent finite volume scheme for non-classical divergence coagulation equation.Applied Numerical Mathematics, 187:120–137, 2023.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Rate of convergence of two moments consistent finite volume scheme for non-classical divergence coagulation equation.Applied Numerical Mathematics, 187:120–137, 2023

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.086535Z

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Observation 3e49af8d-da07-4719-ba14-35a5a6be2b36 · outbound

This paper cites Dgm: A deep learning algorithm for solving partial differential equations.Journal of Computational Physics, 375:1339–1364.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Dgm: A deep learning algorithm for solving partial differential equations.Journal of Computational Physics, 375:1339–1364

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.036696Z

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Observation a63152f6-28c0-4877-ba41-c31223e351a4 · outbound

This paper cites Local randomized neural networks with discontinuous Galerkin methods for partial differential equations.Journal of Computational and Applied Mathematics, 445:115830.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Local randomized neural networks with discontinuous Galerkin methods for partial differential equations.Journal of Computational and Applied Mathematics, 445:115830

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.042801Z

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Observation 733fe8a0-9dbe-4afb-b057-93503c7c465a · outbound

This paper cites Randomized neural networks for partial differential equation on static and evolving surfaces.arXiv preprint arXiv:2603.01689, 2026.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Randomized neural networks for partial differential equation on static and evolving surfaces.arXiv preprint arXiv:2603.01689, 2026

Reference 35

Resolution: verified exact; arxiv_id, observed 2026-07-01T11:05:41.670731Z

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Observation ea805c94-6a60-4465-b6f2-dbc2294de937 · outbound

This paper cites Numerical solution of coupled nonlinear Klein-Gordon equations on unbounded domains.Physical Review E, 106(2):025317, 2022.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Numerical solution of coupled nonlinear Klein-Gordon equations on unbounded domains.Physical Review E, 106(2):025317, 2022

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.044752Z

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Observation 9e1d007f-51aa-497a-870f-e39515ed304e · outbound

This paper cites Physics-informed neural networks combined with polynomial interpolation to solve nonlinear partial differential equations.Computers & Mathematics with Applications, 132:48–62, 2023.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Physics-informed neural networks combined with polynomial interpolation to solve nonlinear partial differential equations.Computers & Mathematics with Applications, 132:48–62, 2023

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.079114Z

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Observation e427f734-dc6a-4195-a4e0-ef91bd7b57d3 · outbound

This paper cites Efficient spectral element method for the Euler equations on unbounded domains.Applied Mathematics and Computation, 487:129080, 2025.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Efficient spectral element method for the Euler equations on unbounded domains.Applied Mathematics and Computation, 487:129080, 2025

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.094809Z

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Observation 9b9fb85d-749b-4881-ba6e-75832ea8c375 · outbound

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Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-07-06T23:23:03.098522Z

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Observation cc5af2de-2d25-49ca-85f2-3288ae462159 · outbound

This paper cites Adaptive-Distribution Randomized Neural Networks for PDEs: A Low-Dimensional Distribution-Learning Framework.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Adaptive-Distribution Randomized Neural Networks for PDEs: A Low-Dimensional Distribution-Learning Framework

Reference 40

Resolution: verified exact; local_arxiv, observed 2026-07-01T11:05:41.673531Z

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Observation 6ced299c-d350-4c29-8fac-cc2bc2d812e2 · outbound

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Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Unresolved cited work

Reference 41

Resolution: unresolved; raw_fallback, observed 2026-07-06T23:23:03.096487Z

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Observation 91f647ae-3ec3-48b0-b089-ebb80aa36988 · outbound

This paper cites Transferable neural networks for partial differential equations.Journal of Scientific Computing, 99(1):2.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Transferable neural networks for partial differential equations.Journal of Scientific Computing, 99(1):2

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.106234Z

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Observation c48931cd-8388-4bcc-af2e-16d535bbac15 · outbound

This paper cites A highly efficient numerical method for the time-fractional diffusion equation on unbounded domains.Journal of Scientific Computing, 99(2):47, 2024.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains A highly efficient numerical method for the time-fractional diffusion equation on unbounded domains.Journal of Scientific Computing, 99(2):47, 2024

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T23:23:03.091049Z

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