Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System | Paper Citation Record

Observation 85668a5c-dab6-4bce-a6ea-25263af90500 · outbound

This paper cites Cambridge University Press, 3 edition, 2007.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Cambridge University Press, 3 edition, 2007

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b70d91fe-ddfa-4f3c-8511-f1a62be6a441 · outbound

This paper cites The finite volume method.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System The finite volume method

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 622000ea-2d78-4dfb-9e3a-435ba8c7fe42 · outbound

This paper cites SIAM, 2007.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System SIAM, 2007

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation abc3a522-2ba6-4e87-b32d-3ea856baa8a8 · outbound

This paper cites Pearson Education India, 2007.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Pearson Education India, 2007

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cfdf8cad-24f3-4824-9a27-a31e7a10d02e · outbound

This paper cites Numerical methods for solving partial differential equations in applied physics.Frontiers in Applied Physics and Mathematics, 1(1):79–96, 2024.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Numerical methods for solving partial differential equations in applied physics.Frontiers in Applied Physics and Mathematics, 1(1):79–96, 2024

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a49ca60d-e397-46a9-8773-895e2e4a1e09 · outbound

This paper cites Academic press, 2014.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Academic press, 2014

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 874e40d9-faa1-4d52-b5a5-ca3a87fd8ff6 · outbound

This paper cites an unresolved cited work.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c0e95796-79c9-483a-acf1-962a4d81df39 · outbound

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

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Physics- informed machine learning.Nature Reviews Physics, 3(6):422–440, 2021

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a321a009-f8da-4e23-8567-03607b8b0e87 · outbound

This paper cites Scientific machine learning through physics–informed neural networks: Where we are and what’s next.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Scientific machine learning through physics–informed neural networks: Where we are and what’s next

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eb8432db-df97-42de-aa7c-3b2bffee6a7e · outbound

This paper cites Numerical analysis of physics-informed neural networks and related models in physics-informed machine learning.Acta Numerica, 33:633–713, 2024.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Numerical analysis of physics-informed neural networks and related models in physics-informed machine learning.Acta Numerica, 33:633–713, 2024

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dd8e36e1-4500-4c15-8e72-44445dbb1571 · outbound

This paper cites Algorithms for solving high dimensional pdes: from nonlinear monte carlo to machine learning.Nonlinearity, 35(1):278, 2021.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Algorithms for solving high dimensional pdes: from nonlinear monte carlo to machine learning.Nonlinearity, 35(1):278, 2021

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c5ee9544-94cb-4caa-bedf-0e65d680e7da · outbound

This paper cites Robust control of uncertain quantum systems based on physics-informed neural networks and sampling learning.IEEE Transactions on Artificial Intelligence, 2025.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Robust control of uncertain quantum systems based on physics-informed neural networks and sampling learning.IEEE Transactions on Artificial Intelligence, 2025

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9ee93837-a49a-4524-9e13-da241b2745a3 · outbound

This paper cites Physics-informed neural networks for modeling water flows in a river channel.IEEE Transactions on Artificial Intelligence, 5(3):1001–1015, 2022.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Physics-informed neural networks for modeling water flows in a river channel.IEEE Transactions on Artificial Intelligence, 5(3):1001–1015, 2022

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 77a38fcb-2725-4983-9863-9b0c14371638 · outbound

This paper cites Quantasio: A generalized neural framework for solving 3d navier-stokes dynamics.IEEE Transactions on Artificial Intelligence, 2025.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Quantasio: A generalized neural framework for solving 3d navier-stokes dynamics.IEEE Transactions on Artificial Intelligence, 2025

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 80060943-d6a3-4cbe-953a-a9695d2d023e · outbound

This paper cites Neural network methods based on efficient optimization algorithms for solving impulsive differential equations.IEEE Transactions on Artificial Intelligence, 5(3):1067– 1076, 2024.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Neural network methods based on efficient optimization algorithms for solving impulsive differential equations.IEEE Transactions on Artificial Intelligence, 5(3):1067– 1076, 2024

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b57160b1-7e4e-4e0f-8723-f04abc8e92d4 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Adam: A Method for Stochastic Optimization

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-07-04T03:09:29.309229Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 75749808-41c6-4519-a542-0946e9f913dc · outbound

This paper cites On the limited memory bfgs method for large scale optimization.Mathematical programming, 45(1):503–528, 1989.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System On the limited memory bfgs method for large scale optimization.Mathematical programming, 45(1):503–528, 1989

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation af4672cb-ab0e-4b28-8761-63c8dbdc0a9f · outbound

This paper cites Theory of the backpropagation neural network.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Theory of the backpropagation neural network

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation afe09012-075c-4090-a43d-2a53e8a5e409 · outbound

This paper cites The old and the new: Can physics-informed deep-learning replace traditional linear solvers? Frontiers in big Data, 4:669097, 2021.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System The old and the new: Can physics-informed deep-learning replace traditional linear solvers? Frontiers in big Data, 4:669097, 2021

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e52139fd-5da0-4d93-b20a-6fcacd3fa84c · outbound

This paper cites A survey on statistical theory of deep learning: Approximation, training dynamics, and generative models.Annual Review of Statistics and Its Application, 12, 2024.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System A survey on statistical theory of deep learning: Approximation, training dynamics, and generative models.Annual Review of Statistics and Its Application, 12, 2024

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2da92b53-b770-4b67-86f1-89240b9be2bf · outbound

This paper cites Characterizing possible failure modes in physics-informed neural networks.Advances in neural information processing systems, 34:26548–26560, 2021.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Characterizing possible failure modes in physics-informed neural networks.Advances in neural information processing systems, 34:26548–26560, 2021

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 28ce8d6c-7173-4e88-addb-d6bf4b804a4e · outbound

This paper cites Physics informed extreme learning machine (pielm)–a rapid method for the numerical solution of partial differential equations.Neurocomputing, 391:96–118, 2020.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Physics informed extreme learning machine (pielm)–a rapid method for the numerical solution of partial differential equations.Neurocomputing, 391:96–118, 2020

Reference 22

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation accf4fd4-ce3e-46d2-a03b-24433edb8bc4 · outbound

This paper cites JHU press, 2013.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System JHU press, 2013

Reference 23

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation be54aa31-f8df-4174-a680-2d1f39ce8de7 · outbound

This paper cites A review of multilayer extreme learning machine neural networks.Artificial Intelligence Review, 56(11):13691–13742, 2023.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System A review of multilayer extreme learning machine neural networks.Artificial Intelligence Review, 56(11):13691–13742, 2023

Reference 24

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 182146f9-82d7-4bf5-b844-55287005f0c3 · outbound

This paper cites an unresolved cited work.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3aeac023-283f-4477-b82a-3cc4113dcd97 · outbound

This paper cites Learning and generalization characteristics of the random vector functional-link net.Neurocomputing, 6(2):163–180, 1994.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Learning and generalization characteristics of the random vector functional-link net.Neurocomputing, 6(2):163–180, 1994

Reference 26

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e5ba6409-e1dd-4397-835c-5fb6dd121a03 · outbound

This paper cites Stochastic choice of basis functions in adaptive function approximation and the functional-link net.IEEE transactions on Neural Networks, 6(6):1320–1329, 1995.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Stochastic choice of basis functions in adaptive function approximation and the functional-link net.IEEE transactions on Neural Networks, 6(6):1320–1329, 1995

Reference 27

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bc6d6739-c445-488a-91f0-aa74e655892a · outbound

This paper cites Springer, 2003.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Springer, 2003

Reference 28

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6d91af8c-ed7a-419f-adf6-90079497b90b · outbound

This paper cites Universal approximation capability of broad learning system and its structural variations.IEEE transactions on neural networks and learning systems, 30(4):1191–1204, 2018.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Universal approximation capability of broad learning system and its structural variations.IEEE transactions on neural networks and learning systems, 30(4):1191–1204, 2018

Reference 29

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 83edc82e-1843-4387-ae65-42d8745b4a87 · outbound

This paper cites an unresolved cited work.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Unresolved cited work

Reference 30

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d31948d6-5dd2-46cd-8ec9-77196ec6c4cf · outbound

This paper cites Research review for broad learning system: Algorithms, theory, and applications.IEEE Transactions on Cybernetics, 52(9):8922–8950, 2021.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Research review for broad learning system: Algorithms, theory, and applications.IEEE Transactions on Cybernetics, 52(9):8922–8950, 2021

Reference 31

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8c6ad893-73f9-493c-8a49-bf85b49d93e3 · outbound

This paper cites Analysis and variants of broad learning system.IEEE Transactions on Systems, Man, and Cybernetics: Systems, 52(1):334–344, 2020.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Analysis and variants of broad learning system.IEEE Transactions on Systems, Man, and Cybernetics: Systems, 52(1):334–344, 2020

Reference 32

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9b8e6303-0146-4d73-afbb-0efef65e7b11 · outbound

This paper cites Philip Chen.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Philip Chen

Reference 33

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8caaa01e-8bcd-4f65-b484-20cf6c175457 · outbound

This paper cites Broad convolutional neural network based industrial process fault diagnosis with incremental learning capability.IEEE Transactions on Industrial Electronics, 67(6):5081–5091, 2020.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Broad convolutional neural network based industrial process fault diagnosis with incremental learning capability.IEEE Transactions on Industrial Electronics, 67(6):5081–5091, 2020

Reference 34

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3a885f9b-4d75-4f8b-8677-dabf6861db55 · outbound

This paper cites an unresolved cited work.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Unresolved cited work

Reference 35

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b26c0834-373c-439d-893f-4d82eae43336 · outbound

This paper cites an unresolved cited work.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Unresolved cited work

Reference 36

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a0c61ddd-8595-4182-b532-251aa2fc39b3 · outbound

This paper cites an unresolved cited work.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Unresolved cited work

Reference 37

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f605802d-ce82-4998-8656-ae535f32ef46 · outbound

This paper cites an unresolved cited work.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Unresolved cited work

Reference 38

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f5275a21-873f-4b5d-8846-860bfef4e4bb · outbound

This paper cites an unresolved cited work.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Unresolved cited work

Reference 39

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1c47b0f7-551a-4708-9392-4b06107417c8 · outbound

This paper cites PINN for Dynamical Partial Differential Equations is Not Training Deeper Networks Rather Learning Advection and Time Variance.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System PINN for Dynamical Partial Differential Equations is Not Training Deeper Networks Rather Learning Advection and Time Variance

Reference 40

Resolution: verified exact; arxiv_id, observed 2026-07-04T03:09:29.306131Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 3698b792-eb41-40f5-8416-531e063c30e5 · outbound

This paper cites On the training efficiency of shallow architectures for physics informed neural networks.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System On the training efficiency of shallow architectures for physics informed neural networks

Reference 41

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6da1e921-a593-4db7-bd48-b6f550735953 · outbound

This paper cites SIAM, 1995.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System SIAM, 1995

Reference 42

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation af44dba6-6145-44c9-b354-60c3fc8abcd6 · outbound

This paper cites An interior trust region approach for nonlinear minimization subject to bounds.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System An interior trust region approach for nonlinear minimization subject to bounds

Reference 43

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6bf5eabb-8074-4fe3-a285-e272d4a18612 · outbound

This paper cites an unresolved cited work.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Unresolved cited work

Reference 44

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 54e9ffe0-6e7b-4579-a783-ef50c29cf596 · outbound

This paper cites Elsevier, 2003.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Elsevier, 2003

Reference 45

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation af4c5f9f-ed55-4b62-b7be-5738facac502 · outbound

This paper cites Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs

Reference 46

Resolution: verified exact; arxiv_id, observed 2026-07-04T03:09:29.312582Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation dca0de81-5aa9-4ffa-83c5-36da0bd7ae3e · outbound

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

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System A unified deep artificial neural network approach to partial differential equations in complex geometries.Neurocomputing, 317:28–41, 2018

Reference 47

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7f593701-86d1-458b-91cc-d3b3ec1e5697 · outbound

This paper cites Artificial neural networks for solving ordinary and partial differential equations.IEEE transactions on neural networks, 9(5):987–1000, 1998.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Artificial neural networks for solving ordinary and partial differential equations.IEEE transactions on neural networks, 9(5):987–1000, 1998

Reference 48

Resolution: unresolved; no resolver link, observed 2026-06-26T18:26:35.277057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Coverage vector

Reference resolution

Outbound references

Pith citing papers