Paper Citation Record · LEDGER

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries

As of 19 August 2026, this Paper Citation Record lists 48 of 48 outbound references and 0 inbound Pith citation observations for arXiv:2510.25731.

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

pith.paper-citation-record.v1
2510.25731 v2

Coverage vector

measured 48 of 48 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T07:32:30.722586Z

measured 48 of 48 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 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

48 of 48 outbound references displayed

verified exact2
verified fuzzy0
unresolved43
parse uncertain0
malformed identifier3
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 71614209-226b-4355-8875-2285c5a8fa1a · outbound

This paper cites Lie Point Symmetry and Physics Informed Networks.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Lie Point Symmetry and Physics Informed Networks

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.350623Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c87031c6-7afd-414f-be4e-f63ca3e68f1b · outbound

This paper cites an unresolved cited work.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.361750Z

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Observation 1b91d51f-0dda-44ec-aa07-a3612a747b79 · outbound

This paper cites an unresolved cited work.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.369576Z

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Observation 02bd3464-ddfe-4537-ae26-16fade4da92a · outbound

This paper cites an unresolved cited work.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.378119Z

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Observation cf7f8b69-3e52-4b85-bc31-3e418856d6ad · outbound

This paper cites Lie Point Symmetry Data Augmentation for Neural PDE Solvers.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Lie Point Symmetry Data Augmentation for Neural PDE Solvers

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.387993Z

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Observation fd54b118-0406-4d82-9415-c5963a4e42d8 · outbound

This paper cites A comparative study of some computer algebra packages which determine the Lie point symmetries of differential equations.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries A comparative study of some computer algebra packages which determine the Lie point symmetries of differential equations

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.395357Z

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Unavailable: canonical work link unavailable.

Observation 28954195-68b9-4398-8514-22d655c08c9c · outbound

This paper cites The computer calculation of Lie point symmetries of large systems of differential equations.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries The computer calculation of Lie point symmetries of large systems of differential equations

Reference 7

Resolution: verified exact; doi, observed 2026-08-04T07:34:12.725434Z

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 0b0b2a84-8c7e-4536-804c-ebc183b35533 · outbound

This paper cites Group equivariant convolutional networks.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Group equivariant convolutional networks

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.418293Z

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Observation 8b740931-4c56-4275-a538-c6e91e28597d · outbound

This paper cites Lagrangian neural networks.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Lagrangian neural networks

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.424575Z

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Observation 23c79049-e10d-4c18-ab6a-127708114b36 · outbound

This paper cites an unresolved cited work.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.430019Z

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Observation 39ab142c-f146-4770-9cac-103d0a48abb8 · outbound

This paper cites an unresolved cited work.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.436544Z

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Observation 7640a806-414f-48bc-9e12-856472531645 · outbound

This paper cites The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate

Reference 12

Resolution: malformed identifier; no resolver link, observed 2026-08-04T07:32:30.443942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a08a45ca-7fb0-43a9-b7b5-381403b726c3 · outbound

This paper cites Hamiltonian neural networks.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Hamiltonian neural networks

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.449929Z

Source-reported events for the cited work

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Observation 8080db46-e4fc-4957-9235-a14e0af826e4 · outbound

This paper cites Symbolic Software for Lie Symmetry Analysis.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Symbolic Software for Lie Symmetry Analysis

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.455009Z

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Observation a20d57f1-e2c7-4818-8538-981dacc9ab86 · outbound

This paper cites Extended physics-informed neural networks (XPINNs): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Extended physics-informed neural networks (XPINNs): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.460274Z

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Observation cd16b344-08e5-406b-bd0e-26286d2c7348 · outbound

This paper cites an unresolved cited work.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.465035Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e0a03643-dad6-4253-813a-39c90446534d · outbound

This paper cites Physics- informed machine learning.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Physics- informed machine learning

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.470288Z

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Observation 840fd397-46ca-4d0d-b938-b5cef226346e · outbound

This paper cites Characterizing possible failure modes in physics-informed neural networks.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Characterizing possible failure modes in physics-informed neural networks

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.476380Z

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Observation 0968042d-e724-4cc0-ae8f-9fdb929b64db · outbound

This paper cites Artificial Neural Networks for Solving Ordinary and Partial Differential Equations.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Artificial Neural Networks for Solving Ordinary and Partial Differential Equations

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.486756Z

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Unavailable: canonical work link unavailable.

Observation 4f96d490-2977-450e-94ff-c9792e7e9e8b · outbound

This paper cites PINNACLE: PINN Adaptive ColLocation and Experimental Points Selection.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries PINNACLE: PINN Adaptive ColLocation and Experimental Points Selection

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.493525Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c6ecedfd-4ac6-46b4-a163-fa8111b2972d · outbound

This paper cites an unresolved cited work.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.503365Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f30e6d12-7e76-45f1-a83f-56f6cf19d635 · outbound

This paper cites Physics-informed neural networks with hard constraints for inverse design.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Physics-informed neural networks with hard constraints for inverse design

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.510584Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 086fcb70-3e2d-4f92-a4ab-7b240c068751 · outbound

This paper cites PPINNs: Physics-informed neural networks with prior.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries PPINNs: Physics-informed neural networks with prior

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.517931Z

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Unavailable: canonical work link unavailable.

Observation eebcaaa9-a8a8-49e5-94d2-a7de6b58c24b · outbound

This paper cites Self-Supervised Learning with Lie Symmetries for Partial Differential Equations.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Self-Supervised Learning with Lie Symmetries for Partial Differential Equations

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.523488Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0ca61101-f1cf-4d6c-b275-10956f183707 · outbound

This paper cites an unresolved cited work.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.529999Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 09fc6ee8-768e-4634-961a-a5c7302c3f50 · outbound

This paper cites Variable projection for nonlinear least squares problems.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Variable projection for nonlinear least squares problems

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.537036Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3cedc9a4-e0f5-4a87-b636-a2a41fab15e5 · outbound

This paper cites Lie Symmetries of Differential Equations: Classical Results and Recent Contri- butions.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Lie Symmetries of Differential Equations: Classical Results and Recent Contri- butions

Reference 27

Resolution: verified exact; doi, observed 2026-08-04T07:34:12.561422Z

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 845d7a31-5e19-4439-b5ce-3f0d6c1b76f9 · outbound

This paper cites ReLie: a Reduce program for Lie group analysis of differential equations.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries ReLie: a Reduce program for Lie group analysis of differential equations

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.552598Z

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Unavailable: canonical work link unavailable.

Observation 4fe470c8-9600-4be9-84dd-a76094f30d0e · outbound

This paper cites an unresolved cited work.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Unresolved cited work

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.561228Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e74ef88d-16be-489c-a6cb-0919a67ac672 · outbound

This paper cites Symmetry and explicit solutions of partial differential equations.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Symmetry and explicit solutions of partial differential equations

Reference 30

Resolution: malformed identifier; no resolver link, observed 2026-08-04T07:32:30.574689Z

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Observation deab01f0-41cf-46c5-a5c4-c27c16c57283 · outbound

This paper cites an unresolved cited work.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Unresolved cited work

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.582749Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d61fcbef-15d6-4f16-ab5e-b64d121e9365 · outbound

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

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial dif- ferential equations

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.589043Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1aa65342-a797-47e5-9f63-81dc41cd8e64 · outbound

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

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Challenges in Training PINNs: A Loss Landscape Perspective

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.599998Z

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Observation 952b260a-c04a-4c9a-83e6-e691d2a8ab9b · outbound

This paper cites an unresolved cited work.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Unresolved cited work

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.608461Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0638c4e1-cb13-465c-90e8-575fdf97c1b3 · outbound

This paper cites DGM: A deep learning algorithm for solving partial differential equations.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries DGM: A deep learning algorithm for solving partial differential equations

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.619525Z

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Unavailable: canonical work link unavailable.

Observation c139d7d5-2271-41d5-b2a6-0fee18d06f25 · outbound

This paper cites Practical Guide to the Symbolic Computation of Symmetries of Differential Equations.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Practical Guide to the Symbolic Computation of Symmetries of Differential Equations

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.629362Z

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Unavailable: canonical work link unavailable.

Observation b6748a8c-a81b-46a4-bcae-a8c66d8218db · outbound

This paper cites Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.636863Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8b5fba76-9a4b-4e30-bb1a-bd4ebeaf1fc5 · outbound

This paper cites Solving Differential Equations with Genetic Programming.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Solving Differential Equations with Genetic Programming

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.644623Z

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Observation 724d0a6a-9144-4f6a-9146-e2ad521e8029 · outbound

This paper cites Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspective.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspective

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.652382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8a877869-91ed-4362-8ba5-6438aa6b0235 · outbound

This paper cites An Expert's Guide to Training Physics-informed Neural Networks.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries An Expert's Guide to Training Physics-informed Neural Networks

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.658305Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 59853b10-f777-4e0b-95ff-f6dcc4208899 · outbound

This paper cites Understanding and Mitigating Gradient Flow Patholo- gies in Physics-Informed Neural Networks.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Understanding and Mitigating Gradient Flow Patholo- gies in Physics-Informed Neural Networks

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.666328Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e4c82f8c-4d11-4607-9d5e-6195ff49192b · outbound

This paper cites When and why PINNs fail to train: A neural tangent kernel perspective.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries When and why PINNs fail to train: A neural tangent kernel perspective

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.673538Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 52164e0b-f8bf-49c5-a9d4-5b87ad7bf93d · outbound

This paper cites an unresolved cited work.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Unresolved cited work

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.683089Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4eec0d56-6a4a-411f-a5fe-fa52c1f0ed5b · outbound

This paper cites A Comprehensive Study of Non-Adaptive and Residual-Based Adaptive Sampling for Physics-Informed Neural Networks.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries A Comprehensive Study of Non-Adaptive and Residual-Based Adaptive Sampling for Physics-Informed Neural Networks

Reference 44

Resolution: malformed identifier; no resolver link, observed 2026-08-04T07:32:30.692841Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e0ac995d-7365-4fe8-8685-3c9882200523 · outbound

This paper cites Latent Space Symmetry Discovery.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Latent Space Symmetry Discovery

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.702433Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 36b6e1ba-8146-4a53-b5f3-413dc43152dc · outbound

This paper cites Symmetry-Informed Governing Equa- tion Discovery.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Symmetry-Informed Governing Equa- tion Discovery

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.709327Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f9d82f1c-49de-465f-bbf1-2155dba210ab · outbound

This paper cites A Symmetry Group Based Supervised Learning Method for Solving Partial Differential Equations.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries A Symmetry Group Based Supervised Learning Method for Solving Partial Differential Equations

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.716933Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 01c64f81-0d87-427a-9505-8f5f507fee0f · outbound

This paper cites Enforcing continuous symmetries in physics-informed neural network for solving forward and inverse problems of partial differential equations.

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries Enforcing continuous symmetries in physics-informed neural network for solving forward and inverse problems of partial differential equations

Reference 48

Resolution: unresolved; no resolver link, observed 2026-08-04T07:32:30.722586Z

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Unavailable: canonical work link unavailable.

Pith citing papers

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