Paper Citation Record · LEDGER

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs

As of 9 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 1 inbound Pith citation observation for arXiv:2506.04613.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2506.04613 v3

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T10:43:44.584609Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T11:58:22.535134Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-05T11:58:22.721218Z

Reference resolution

31 of 31 outbound references displayed

verified exact1
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External citation measurements

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Outbound references

Observation 84251d7b-9cc3-4529-8e6c-09737fd0a87b · outbound

This paper cites Random matrices and complexity of spin glasses.Communications on Pure and Applied Mathematics, 66(2):165–201, 2013.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs Random matrices and complexity of spin glasses.Communications on Pure and Applied Mathematics, 66(2):165–201, 2013

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:43:48.189941Z

Source-reported events for the cited work

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

Observation 3d42f094-9d84-490e-83bd-ea04d6bfda23 · outbound

This paper cites SIAM, 2018.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs SIAM, 2018

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:43:47.980951Z

Source-reported events for the cited work

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

Observation 14fd8863-1802-4660-a54b-c8f2a0a8b2c2 · outbound

This paper cites Statistics of critical points of gaussian fields on large- dimensional spaces.Physical review letters, 98(15):150201, 2007.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs Statistics of critical points of gaussian fields on large- dimensional spaces.Physical review letters, 98(15):150201, 2007

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:43:47.713880Z

Source-reported events for the cited work

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

Observation c6416c62-7365-4714-95cd-b24d6cc7d2b4 · outbound

This paper cites Optimization of random feature method in the high-precision regime.Communications on Applied Mathematics and Computation, 6(2):1490–1517, 2024.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs Optimization of random feature method in the high-precision regime.Communications on Applied Mathematics and Computation, 6(2):1490–1517, 2024

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:43:47.551724Z

Source-reported events for the cited work

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

Observation 91cb40ab-6fcc-4634-b08f-2400b899ee2a · outbound

This paper cites The loss surfaces of multilayer networks.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs The loss surfaces of multilayer networks

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:43:47.375925Z

Source-reported events for the cited work

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

Observation 32e74a73-2348-4b21-9f5a-a1601ef0bdf0 · outbound

This paper cites Approximation by superpositions of a sigmoidal function.Mathematics of control, signals and systems, 2(4):303–314, 1989.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs Approximation by superpositions of a sigmoidal function.Mathematics of control, signals and systems, 2(4):303–314, 1989

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-07T10:43:42.409142Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6174133e-9097-4fcc-ace8-4c50b8850b61 · outbound

This paper cites Hierarchical extreme learning machine for solving partial differential equations.Available at SSRN 4775113.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs Hierarchical extreme learning machine for solving partial differential equations.Available at SSRN 4775113

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:43:47.223090Z

Source-reported events for the cited work

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

Observation e5bd4c34-698f-46f8-930b-bdbe1acc97f3 · outbound

This paper cites High-re solutions for incompressible flow using the navier- stokes equations and a multigrid method.Journal of Computational Physics, 48(3):387–411, 1982.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs High-re solutions for incompressible flow using the navier- stokes equations and a multigrid method.Journal of Computational Physics, 48(3):387–411, 1982

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:43:47.031988Z

Source-reported events for the cited work

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

Observation 20bc2e9c-b00d-4fa7-8c93-f0ce5e73a44f · outbound

This paper cites Multilayer feedforward networks are universal approximators.Neural networks, 2(5):359–366, 1989.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs Multilayer feedforward networks are universal approximators.Neural networks, 2(5):359–366, 1989

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-07T10:43:42.669065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e42e6063-084d-4601-9fe5-dd15c765269f · outbound

This paper cites Trends in extreme learning machines: A review.Neural Networks, 61:32–48, 2015.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs Trends in extreme learning machines: A review.Neural Networks, 61:32–48, 2015

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:43:46.917220Z

Source-reported events for the cited work

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

Observation 5ba130f9-067b-4eab-be29-5fd36ff4cfc9 · outbound

This paper cites Extreme learning machine: theory and applications.Neurocomputing, 70(1-3):489–501, 2006.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs Extreme learning machine: theory and applications.Neurocomputing, 70(1-3):489–501, 2006

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-07T10:43:42.833078Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0252974b-26ae-4944-9a6b-9cbcb081aeb7 · outbound

This paper cites an unresolved cited work.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-07T10:43:46.751412Z

Source-reported events for the cited work

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

Observation 0f60429a-1deb-48a3-a85d-7ceff4d94494 · outbound

This paper cites Adaptive activation functions accelerate convergence in deep and physics-informed neural networks.Journal of Computational Physics, 404:109136, 2020.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs Adaptive activation functions accelerate convergence in deep and physics-informed neural networks.Journal of Computational Physics, 404:109136, 2020

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:43:46.565849Z

Source-reported events for the cited work

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

Observation a20df0c9-2b36-42da-9604-b06b57c0bf17 · outbound

This paper cites Nature Reviews Physics, 2021.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs Nature Reviews Physics, 2021

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:43:46.394119Z

Source-reported events for the cited work

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

Observation 27aa1a2d-d28a-4815-ba5d-cc5e2ed6930c · outbound

This paper cites Deeplearningwithoutpoorlocalminima.Advances in neural information processing systems, 29, 2016.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs Deeplearningwithoutpoorlocalminima.Advances in neural information processing systems, 29, 2016

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:43:46.225117Z

Source-reported events for the cited work

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

Observation a52999e7-c1f0-4b43-802b-9ae91d180c65 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs Adam: A Method for Stochastic Optimization

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-07T10:43:43.253567Z

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Observation e91782ee-6139-4b25-90d1-208b65a87914 · outbound

This paper cites A GPS spoofing detection and classification correlator-based technique using the LASSO.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs A GPS spoofing detection and classification correlator-based technique using the LASSO

Reference 17

Resolution: metadata mismatch; local_arxiv, observed 2026-08-07T10:43:45.011912Z

Source-reported events for the cited work

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

Observation 17208d51-23c7-40e8-90a2-4ed93b9b8b88 · outbound

This paper cites KAN: Kolmogorov-Arnold Networks.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs KAN: Kolmogorov-Arnold Networks

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-07T10:43:43.455350Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6c70ff80-4549-45c1-9cef-51cbb77e1db2 · outbound

This paper cites Discontinuity computing using physics-informed neural networks.Journal of Scientific Computing, 98(1):22, 2024.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs Discontinuity computing using physics-informed neural networks.Journal of Scientific Computing, 98(1):22, 2024

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:43:46.064175Z

Source-reported events for the cited work

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

Observation 270bd21a-f532-4d51-be45-eaf5cd425a9e · outbound

This paper cites Lower bounds for approximation by mlp neural networks.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs Lower bounds for approximation by mlp neural networks

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:43:45.906762Z

Source-reported events for the cited work

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

Observation 9ede1a7c-3b4f-45c3-8f1b-cbbbac99096f · outbound

This paper cites Cambridge University Press, 1999.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs Cambridge University Press, 1999

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:43:45.722549Z

Source-reported events for the cited work

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

Observation 50f8224c-8e52-48d6-99de-5211365458c5 · outbound

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DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs Unresolved cited work

Reference 22

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Observation 0e135145-2f51-43f6-b92a-8820db20323f · outbound

This paper cites an unresolved cited work.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-07T10:43:43.915205Z

Source-reported events for the cited work

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Observation 09673eaf-1bd1-4f24-9fed-59568c47a922 · outbound

This paper cites Optimization for deep learning: theory and algorithms.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs Optimization for deep learning: theory and algorithms

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-08-07T10:43:44.851511Z

Source-reported events for the cited work

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

Observation 04b5e113-3e16-447a-9727-aa9828d05b70 · outbound

This paper cites Fourierfeatures let networks learn high frequency functions in low dimensional domains.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs Fourierfeatures let networks learn high frequency functions in low dimensional domains

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:43:45.502388Z

Source-reported events for the cited work

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

Observation 639e814d-2e77-42fd-bf2d-79767030f476 · outbound

This paper cites Gradient align- ment in physics-informed neural networks: A second-order optimization perspective.arXiv preprint arXiv:2502.00604, 2025.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs Gradient align- ment in physics-informed neural networks: A second-order optimization perspective.arXiv preprint arXiv:2502.00604, 2025

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-07T10:43:44.171203Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9cf33ed0-8648-4779-84a7-864164592e39 · outbound

This paper cites Understanding and mitigating gradient flow pathologies in physics-informed neural networks.SIAM Journal on Scientific Computing, 43(5):A3055–A3081, 2021.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs Understanding and mitigating gradient flow pathologies in physics-informed neural networks.SIAM Journal on Scientific Computing, 43(5):A3055–A3081, 2021

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-07T10:43:44.249136Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 42f1073d-781d-4210-9141-1637498389bc · outbound

This paper cites When and why PINNs fail to train: A neural tangent kernel perspective.Journal of Computational Physics, 449:110768, 2022.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs When and why PINNs fail to train: A neural tangent kernel perspective.Journal of Computational Physics, 449:110768, 2022

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-07T10:43:44.317591Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 005c9abf-6f93-4a65-9484-fc7df0d899a4 · outbound

This paper cites Multi-stage neural networks: Function approximator of machine precision.Journal of Computational Physics, 504:112865, 2024.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs Multi-stage neural networks: Function approximator of machine precision.Journal of Computational Physics, 504:112865, 2024

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-07T10:43:44.406747Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 843b2ec3-f76b-4789-a682-e8ff9a38bf62 · outbound

This paper cites Eigenvector bases for neural networks.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs Eigenvector bases for neural networks

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:43:45.286607Z

Source-reported events for the cited work

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

Observation ec372415-c614-484a-a068-d9cae0a33099 · outbound

This paper cites Towards understand- ing the condensation of neural networks at initial training.Advances in Neural Information Processing Systems, 35:2184–2196, 2022.

DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs Towards understand- ing the condensation of neural networks at initial training.Advances in Neural Information Processing Systems, 35:2184–2196, 2022

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:43:45.132334Z

Source-reported events for the cited work

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

Pith citing papers

Observation 060d6f1e-8ad7-47b8-a167-3071d528dd1a · inbound

CLINN: Conservation Law Informed Neural Network for Approximating Discontinuous Solutions cites this paper.

CLINN: Conservation Law Informed Neural Network for Approximating Discontinuous Solutions DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-08-05T11:58:22.726298Z

Source-reported events for the cited work

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