Paper Citation Record · LEDGER

Learn Singularly Perturbed Solutions via Homotopy Dynamics

As of 18 August 2026, this Paper Citation Record lists 64 of 64 outbound references and 1 inbound Pith citation observation for arXiv:2502.00488.

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

pith.paper-citation-record.v1
2502.00488 v3

Coverage vector

measured 64 of 64 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-09T18:57:13.680130Z

measured 65 of 65 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T17:55:54.489942Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T17:55:57.740488Z

Reference resolution

64 of 64 outbound references displayed

verified exact4
verified fuzzy37
unresolved21
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 875a5fb0-f671-4101-b123-e73413d5d4bb · outbound

This paper cites write newline.

Learn Singularly Perturbed Solutions via Homotopy Dynamics write newline

Reference 1

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Observation d280d7f2-f1c0-499f-b502-6ca7fd0f073c · outbound

This paper cites an unresolved cited work.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Unresolved cited work

Reference 2

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Observation b597ddda-75d5-4016-8513-c5ffbbdf9658 · outbound

This paper cites A convergence theory for deep learning via over-parameterization.

Learn Singularly Perturbed Solutions via Homotopy Dynamics A convergence theory for deep learning via over-parameterization

Reference 3

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Observation 3c284303-85df-497a-a123-bc3e7c74bc16 · outbound

This paper cites S., Hu, W., Li, Z., Salakhutdinov, R.

Learn Singularly Perturbed Solutions via Homotopy Dynamics S., Hu, W., Li, Z., Salakhutdinov, R

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:57:15.095942Z

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Observation 277a8f21-0494-4ca1-8a3e-be40eae4cf89 · outbound

This paper cites an unresolved cited work.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Unresolved cited work

Reference 5

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Observation 0961b715-e641-4dac-b765-cae3226c5422 · outbound

This paper cites and Greville, T.

Learn Singularly Perturbed Solutions via Homotopy Dynamics and Greville, T

Reference 6

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Observation 3431470d-0850-4e9e-a1b2-17523918c944 · outbound

This paper cites an unresolved cited work.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Unresolved cited work

Reference 7

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Observation e8d30f63-87a2-468c-aef3-8b092cedb1b2 · outbound

This paper cites and Gu, Q.

Learn Singularly Perturbed Solutions via Homotopy Dynamics and Gu, Q

Reference 8

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Observation 345c5c56-6a28-41b0-a6be-2881ae8526ef · outbound

This paper cites Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations

Reference 9

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Observation 6727ef35-05fd-49ce-8220-d500938e6fb1 · outbound

This paper cites Quantifying Training Difficulty and Accelerating Convergence in Neural Network-Based PDE Solvers.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Quantifying Training Difficulty and Accelerating Convergence in Neural Network-Based PDE Solvers

Reference 10

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Source-reported events for the cited work

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Observation 8f090883-4935-45ca-8ec3-5941596ab1d5 · outbound

This paper cites Bridging traditional and machine learning-based algorithms for solving PDEs : the random feature method.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Bridging traditional and machine learning-based algorithms for solving PDEs : the random feature method

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:57:15.019659Z

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Observation 2a954e92-a30a-46cb-8452-30752669502e · outbound

This paper cites and Hao, W.

Learn Singularly Perturbed Solutions via Homotopy Dynamics and Hao, W

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:57:15.003487Z

Source-reported events for the cited work

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Observation fd3a38ae-0e3a-4273-9ca0-ac5548851c77 · outbound

This paper cites S., Giampaolo, F., Rozza, G., Raissi, M., and Piccialli, F.

Learn Singularly Perturbed Solutions via Homotopy Dynamics S., Giampaolo, F., Rozza, G., Raissi, M., and Piccialli, F

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:57:14.989733Z

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Observation 2c05629a-0e61-4569-83c8-35a85be577f2 · outbound

This paper cites and Wang, Y.

Learn Singularly Perturbed Solutions via Homotopy Dynamics and Wang, Y

Reference 14

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Observation 4fe0543d-ae5c-4864-9e8c-0f6af95a75e6 · outbound

This paper cites Gradient descent finds global minima of deep neural networks.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Gradient descent finds global minima of deep neural networks

Reference 15

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Observation eb921b1f-1d5f-4035-ae00-4e3f19427c59 · outbound

This paper cites and Yu, B.

Learn Singularly Perturbed Solutions via Homotopy Dynamics and Yu, B

Reference 16

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Observation 4eaf18f1-4b39-44ef-aa2b-3af2eb96b81f · outbound

This paper cites an unresolved cited work.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Unresolved cited work

Reference 17

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Observation 89f2d4f6-433c-4e15-845b-9eede5ed7983 · outbound

This paper cites Gradient descent finds the global optima of two-layer physics-informed neural networks.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Gradient descent finds the global optima of two-layer physics-informed neural networks

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:57:14.920839Z

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Observation 84d8eb4c-3baa-49d1-9519-a02f3b0cc4c3 · outbound

This paper cites Failure-informed adaptive sampling for pinns, part ii: combining with re-sampling and subset simulation.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Failure-informed adaptive sampling for pinns, part ii: combining with re-sampling and subset simulation

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:57:14.906364Z

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Observation 40565d0e-b493-4249-a331-fa478fe16229 · outbound

This paper cites A deep learning method for the dynamics of classic and conservative Allen-Cahn equations based on fully-discrete operators.

Learn Singularly Perturbed Solutions via Homotopy Dynamics A deep learning method for the dynamics of classic and conservative Allen-Cahn equations based on fully-discrete operators

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:57:14.891288Z

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Observation b3aff821-0e25-47da-a41f-96ef7ea4b19e · outbound

This paper cites and Bengio, Y.

Learn Singularly Perturbed Solutions via Homotopy Dynamics and Bengio, Y

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:57:14.876249Z

Source-reported events for the cited work

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Observation 6a51db29-8256-4975-94c5-70c57f543f7a · outbound

This paper cites Elliptic problems in nonsmooth domains.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Elliptic problems in nonsmooth domains

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:57:14.861600Z

Source-reported events for the cited work

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Observation 56ea858b-b0c1-4308-9d93-818a984b1f81 · outbound

This paper cites Solving high-dimensional partial differential equations using deep learning.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Solving high-dimensional partial differential equations using deep learning

Reference 23

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This paper cites and Yang, Y.

Learn Singularly Perturbed Solutions via Homotopy Dynamics and Yang, Y

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:57:14.830299Z

Source-reported events for the cited work

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Observation 73974e8f-cab9-4177-b8d0-691e3e22c1de · outbound

This paper cites P., Xi, Y., Xu, T., and Yang, Y.

Learn Singularly Perturbed Solutions via Homotopy Dynamics P., Xi, Y., Xu, T., and Yang, Y

Reference 25

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Observation 9cc5ce3d-513c-4946-bb54-c455d46e51c9 · outbound

This paper cites Newton informed neural operator for solving nonlinear partial differential equations.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Newton informed neural operator for solving nonlinear partial differential equations

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:57:14.815317Z

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Observation bc7a3d72-662f-49ca-9a7c-0cdefdb013eb · outbound

This paper cites Mgno: Efficient parameterization of linear operators via multigrid.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Mgno: Efficient parameterization of linear operators via multigrid

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:57:14.800385Z

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Observation aec82fca-f980-4da9-a3d3-eec8f840d256 · outbound

This paper cites Methods of mathematical physics.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Methods of mathematical physics

Reference 28

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Observation a4a22fbe-567e-4a06-be11-851735337cf3 · outbound

This paper cites Frequency-adaptive multi-scale deep neural networks.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Frequency-adaptive multi-scale deep neural networks

Reference 29

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Observation 97672360-61ec-4fb1-a795-a4c3750ede69 · outbound

This paper cites E., Kevrekidis, I.

Learn Singularly Perturbed Solutions via Homotopy Dynamics E., Kevrekidis, I

Reference 30

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Learn Singularly Perturbed Solutions via Homotopy Dynamics and Kreiss, H.-O

Reference 31

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Learn Singularly Perturbed Solutions via Homotopy Dynamics Unresolved cited work

Reference 32

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Observation 08271289-5640-4738-98a2-092d4bb4176e · outbound

This paper cites Dosnet as a non-black-box pde solver: When deep learning meets operator splitting.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Dosnet as a non-black-box pde solver: When deep learning meets operator splitting

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:57:14.734503Z

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Learn Singularly Perturbed Solutions via Homotopy Dynamics Unresolved cited work

Reference 34

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Learn Singularly Perturbed Solutions via Homotopy Dynamics and Mathias, R

Reference 35

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Observation 09d9e906-ed9c-4990-8ede-f97c5a11a14c · outbound

This paper cites Z., and Zhu, J.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Z., and Zhu, J

Reference 36

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Observation 01b6f495-ba47-4138-9854-47ef32987e52 · outbound

This paper cites Towards an Understanding of Residual Networks Using Neural Tangent Hierarchy (NTH).

Learn Singularly Perturbed Solutions via Homotopy Dynamics Towards an Understanding of Residual Networks Using Neural Tangent Hierarchy (NTH)

Reference 37

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This paper cites B., Azizzadenesheli, K., liu, B., Bhattacharya, K., Stuart, A., and Anandkumar, A.

Learn Singularly Perturbed Solutions via Homotopy Dynamics B., Azizzadenesheli, K., liu, B., Bhattacharya, K., Stuart, A., and Anandkumar, A

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:57:14.679017Z

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Observation 69fcbd39-2bee-45fd-98aa-2445fedd97e0 · outbound

This paper cites Deep nonparametric estimation of operators between infinite dimensional spaces.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Deep nonparametric estimation of operators between infinite dimensional spaces

Reference 39

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Observation fda43ff9-9eea-4d67-b322-c1132d2180ee · outbound

This paper cites Mitigating spectral bias for the multiscale operator learning.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Mitigating spectral bias for the multiscale operator learning

Reference 40

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Observation 4775917d-a4d0-489e-b183-2548f20eb2d1 · outbound

This paper cites Multi-scale deep neural network (mscalednn) for solving poisson-boltzmann equation in complex domains.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Multi-scale deep neural network (mscalednn) for solving poisson-boltzmann equation in complex domains

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:57:14.651386Z

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Observation 08f1c082-af11-4197-873f-c622f3d6d82c · outbound

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Learn Singularly Perturbed Solutions via Homotopy Dynamics Unresolved cited work

Reference 42

Resolution: unresolved; raw_fallback, observed 2026-08-09T18:57:14.636942Z

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Observation bf0c5374-bf0d-4a65-9d19-8da4c13917b7 · outbound

This paper cites A priori generalization analysis of the deep Ritz method for solving high dimensional elliptic partial differential equations.

Learn Singularly Perturbed Solutions via Homotopy Dynamics A priori generalization analysis of the deep Ritz method for solving high dimensional elliptic partial differential equations

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:57:14.621947Z

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Observation 0806837c-fb6e-4d3b-b2a1-0fd3c9787acd · outbound

This paper cites Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-09T18:57:13.596940Z

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Learn Singularly Perturbed Solutions via Homotopy Dynamics and Ghosh, S

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:57:14.606153Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 3fedcb79-3cbc-411a-805d-b23353e198a1 · outbound

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Learn Singularly Perturbed Solutions via Homotopy Dynamics Unresolved cited work

Reference 46

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Observation f6115a5e-3d37-4d9a-8cee-4113e3af62ba · outbound

This paper cites PyTorch: An Imperative Style, High-Performance Deep Learning Library.

Learn Singularly Perturbed Solutions via Homotopy Dynamics PyTorch: An Imperative Style, High-Performance Deep Learning Library

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-09T18:57:13.609572Z

Source-reported events for the cited work

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Observation c4cfe89e-61be-4650-8d06-6d4bf0089db7 · outbound

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

Learn Singularly Perturbed Solutions via Homotopy Dynamics Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:57:14.576019Z

Source-reported events for the cited work

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Observation 00a4751b-dae3-48bd-81ae-3b9580ed4f00 · outbound

This paper cites Challenges in Training PINNs: A Loss Landscape Perspective.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Challenges in Training PINNs: A Loss Landscape Perspective

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-09T18:57:13.618083Z

Source-reported events for the cited work

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Observation c4f5dc3e-5995-4809-b841-e8e32177336f · outbound

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Learn Singularly Perturbed Solutions via Homotopy Dynamics Unresolved cited work

Reference 50

Resolution: unresolved; raw_fallback, observed 2026-08-09T18:57:14.560919Z

Source-reported events for the cited work

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Observation 1bf3a8b8-fa24-4787-9a8a-93a81c323457 · outbound

This paper cites Local randomized neural networks with discontinuous Galerkin methods for partial differential equations.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Local randomized neural networks with discontinuous Galerkin methods for partial differential equations

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:57:14.544318Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 0f53b19d-2ac6-4bd9-bbc9-822477799b46 · outbound

This paper cites High-dimensional probability: An introduction with applications in data science, volume 47.

Learn Singularly Perturbed Solutions via Homotopy Dynamics High-dimensional probability: An introduction with applications in data science, volume 47

Reference 52

Resolution: unresolved; no resolver link, observed 2026-08-09T18:57:13.631299Z

Source-reported events for the cited work

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Observation aaafb182-b07f-4bd9-854c-fddb94d8398c · outbound

This paper cites Multi-scale deep neural network (mscalednn) methods for oscillatory stokes flows in complex domains.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Multi-scale deep neural network (mscalednn) methods for oscillatory stokes flows in complex domains

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:57:14.519739Z

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Observation ba40c153-223b-4ee6-9249-b9b2e68b90e6 · outbound

This paper cites On the eigenvector bias of fourier feature networks: From regression to solving multi-scale pdes with physics-informed neural networks.

Learn Singularly Perturbed Solutions via Homotopy Dynamics On the eigenvector bias of fourier feature networks: From regression to solving multi-scale pdes with physics-informed neural networks

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:57:14.504187Z

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Observation 805769a0-0232-4d7c-8f58-ca965a945ecc · outbound

This paper cites Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks

Reference 55

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Observation 2b117afc-5bb4-41d5-96b6-91363b1d6c1a · outbound

This paper cites A variational analysis for the moving finite element method for gradient flows.

Learn Singularly Perturbed Solutions via Homotopy Dynamics A variational analysis for the moving finite element method for gradient flows

Reference 56

Resolution: verified exact; local_arxiv, observed 2026-08-09T18:57:14.050134Z

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Observation 3b917c31-3a7f-4e7f-a5c8-b1c3629ec778 · outbound

This paper cites J., Zhang, Y., and Luo, T.

Learn Singularly Perturbed Solutions via Homotopy Dynamics J., Zhang, Y., and Luo, T

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:57:14.489762Z

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Observation 88adccf6-44e3-427c-a214-08914efd8b74 · outbound

This paper cites DeepONet for solving PDEs : Generalization analysis in Sobolev training.

Learn Singularly Perturbed Solutions via Homotopy Dynamics DeepONet for solving PDEs : Generalization analysis in Sobolev training

Reference 58

Resolution: verified exact; raw_fallback, observed 2026-08-09T18:57:14.026126Z

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Observation 1fe6c38c-c806-48a4-b60d-e23b32da9696 · outbound

This paper cites and He, J.

Learn Singularly Perturbed Solutions via Homotopy Dynamics and He, J

Reference 59

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:57:14.474944Z

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Observation 358a853e-ac78-428d-a981-93db40f6f3b6 · outbound

This paper cites and Xiang, Y.

Learn Singularly Perturbed Solutions via Homotopy Dynamics and Xiang, Y

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:57:14.460087Z

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Observation 9a23f61b-9dd4-44a7-bbf4-0af64e9d28d6 · outbound

This paper cites Nearly Optimal Approximation Rates for Deep Super ReLU Networks on Sobolev Spaces.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Nearly Optimal Approximation Rates for Deep Super ReLU Networks on Sobolev Spaces

Reference 61

Resolution: unresolved; no resolver link, observed 2026-08-09T18:57:13.668386Z

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Observation ec7df417-81e5-4ac8-a2a3-98763116f937 · outbound

This paper cites Homotopy relaxation training algorithms for infinite-width two-layer relu neural networks.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Homotopy relaxation training algorithms for infinite-width two-layer relu neural networks

Reference 62

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:57:14.444744Z

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Observation 1137b230-4c98-4bee-a3ba-ebaab0a25610 · outbound

This paper cites Energy-dissipative evolutionary deep operator neural networks.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Energy-dissipative evolutionary deep operator neural networks

Reference 63

Resolution: unresolved; no resolver link, observed 2026-08-09T18:57:13.676231Z

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This paper cites Annealed adaptive importance sampling method in pinns for solving high dimensional partial differential equations.

Learn Singularly Perturbed Solutions via Homotopy Dynamics Annealed adaptive importance sampling method in pinns for solving high dimensional partial differential equations

Reference 64

Resolution: metadata mismatch; raw_fallback, observed 2026-08-09T18:57:13.836202Z

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Pith citing papers

Observation be1bdf78-76af-44fb-bbc4-1f8343866699 · inbound

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems cites this paper.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Learn Singularly Perturbed Solutions via Homotopy Dynamics

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-06T17:55:57.881339Z

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