Paper Citation Record · LEDGER

Generalized Lie Symmetries in Physics-Informed Neural Operators

As of 20 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 1 inbound Pith citation observation for arXiv:2502.00373.

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

pith.paper-citation-record.v1
2502.00373 v2

Coverage vector

measured 35 of 35 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-09T19:19:49.638818Z

measured 36 of 36 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T14:32:14.507392Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-07T14:32:14.863233Z

Reference resolution

35 of 35 outbound references displayed

verified exact3
verified fuzzy27
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ff7d6f6f-88b4-44c3-94b0-53911e247067 · outbound

This paper cites Lie point symmetry and physics-informed networks.

Generalized Lie Symmetries in Physics-Informed Neural Operators Lie point symmetry and physics-informed networks

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:50.178666Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation c772b126-ffba-47f2-8508-613c12a530ed · outbound

This paper cites Invariant Physics-Informed Neural Networks for Ordinary Differential Equations.

Generalized Lie Symmetries in Physics-Informed Neural Operators Invariant Physics-Informed Neural Networks for Ordinary Differential Equations

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-08-09T19:19:49.850605Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 89da7905-2925-466a-bf60-0d18724b2173 · outbound

This paper cites MathLie a program of doing sym- metry analysis.

Generalized Lie Symmetries in Physics-Informed Neural Operators MathLie a program of doing sym- metry analysis

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:50.168314Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 563fc743-8f40-434a-8423-a6a6d45532f0 · outbound

This paper cites Lie point symmetry data augmentation for neural PDE solvers.

Generalized Lie Symmetries in Physics-Informed Neural Operators Lie point symmetry data augmentation for neural PDE solvers

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:50.156496Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 1950f560-8329-4299-83b4-197591fbe645 · outbound

This paper cites Does equivariance matter at scale?, 2024.

Generalized Lie Symmetries in Physics-Informed Neural Operators Does equivariance matter at scale?, 2024

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:50.145591Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 736debd1-92e0-4424-926f-b13c22a3e126 · outbound

This paper cites Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges.

Generalized Lie Symmetries in Physics-Informed Neural Operators Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-09T19:19:49.518066Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c9b29e42-111b-40e9-8531-41ae779275ca · outbound

This paper cites Hamiltonian Matching for Symplectic Neural Integrators.

Generalized Lie Symmetries in Physics-Informed Neural Operators Hamiltonian Matching for Symplectic Neural Integrators

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-09T19:19:49.522796Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9433bae4-f2f4-46c5-87e8-6b3d688e6aee · outbound

This paper cites Symplectic neural flows for modeling and discovery.

Generalized Lie Symmetries in Physics-Informed Neural Operators Symplectic neural flows for modeling and discovery

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-09T19:19:49.527399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ba291f39-0211-46c0-8b91-06a4f6a9d0da · outbound

This paper cites Neocognitron: A new algorithm for pattern recognition tolerant of deformations and shifts in position.

Generalized Lie Symmetries in Physics-Informed Neural Operators Neocognitron: A new algorithm for pattern recognition tolerant of deformations and shifts in position

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:50.134339Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 2f9a12c0-0555-4e89-8cb9-50192b563e36 · outbound

This paper cites Can Physics-Informed Neural Networks beat the Finite Element Method?.

Generalized Lie Symmetries in Physics-Informed Neural Operators Can Physics-Informed Neural Networks beat the Finite Element Method?

Reference 10

Resolution: verified exact; local_arxiv, observed 2026-08-09T19:19:49.711672Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation f4a45f5d-c346-4813-a09b-6dccf5fa54e2 · outbound

This paper cites Solving high-dimensional partial differential equations using 5 Generalized Lie Symmetries in PINOs deep learning.

Generalized Lie Symmetries in Physics-Informed Neural Operators Solving high-dimensional partial differential equations using 5 Generalized Lie Symmetries in PINOs deep learning

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:50.121799Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 78080ad4-935b-4e92-99f2-690c3b1853a1 · outbound

This paper cites Deep residual learning for image recog- nition.

Generalized Lie Symmetries in Physics-Informed Neural Operators Deep residual learning for image recog- nition

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:50.109716Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 9c6f14b7-9a49-4c0f-b743-0237d78ce638 · outbound

This paper cites CRC handbook of Lie group anal- ysis of differential equations, volume 3.

Generalized Lie Symmetries in Physics-Informed Neural Operators CRC handbook of Lie group anal- ysis of differential equations, volume 3

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:50.097214Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation ab51fd00-6671-4cc1-b84a-2b59f749dde8 · outbound

This paper cites Simulator-free solution of high- dimensional stochastic elliptic partial differential equations using deep neural networks.

Generalized Lie Symmetries in Physics-Informed Neural Operators Simulator-free solution of high- dimensional stochastic elliptic partial differential equations using deep neural networks

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:50.084904Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 4ba93f69-c428-483e-882c-224e54196ccf · outbound

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

Generalized Lie Symmetries in Physics-Informed Neural Operators Charac- terizing possible failure modes in physics-informed neural networks

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:50.072407Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 53c95815-0697-4150-a2ff-c494e2cc906c · outbound

This paper cites Imagenet classification with deep convolutional neural networks.

Generalized Lie Symmetries in Physics-Informed Neural Operators Imagenet classification with deep convolutional neural networks

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:50.060069Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 6ff7ca6b-83ac-44d7-9dc5-27ac9a98567c · outbound

This paper cites Equivariant neural networks and differential invariants theory for solving partial differential equations.

Generalized Lie Symmetries in Physics-Informed Neural Operators Equivariant neural networks and differential invariants theory for solving partial differential equations

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:50.048133Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 400bcfe3-c22c-429d-a60e-42ea7d042570 · outbound

This paper cites LeCun, B.

Generalized Lie Symmetries in Physics-Informed Neural Operators LeCun, B

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:50.035303Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation bb6ce32a-90f9-4680-9981-1a2e2d6ca2b4 · outbound

This paper cites Utilizing symmetry-enhanced physics-informed neural net- work to obtain the solution beyond sampling domain for partial differential equations.

Generalized Lie Symmetries in Physics-Informed Neural Operators Utilizing symmetry-enhanced physics-informed neural net- work to obtain the solution beyond sampling domain for partial differential equations

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:50.024366Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 055019e9-c259-45c3-9f63-266e7fa49f0e · outbound

This paper cites Physics-guided data augmentation for learning the solution operator of linear differential equations.

Generalized Lie Symmetries in Physics-Informed Neural Operators Physics-guided data augmentation for learning the solution operator of linear differential equations

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:50.013370Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 70ebc57d-58e4-451f-87ad-f7875dd4bd40 · outbound

This paper cites Physics-informed neural operator for learning partial differential equa- tions.

Generalized Lie Symmetries in Physics-Informed Neural Operators Physics-informed neural operator for learning partial differential equa- tions

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:50.000265Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 25740a12-3097-41d3-ab7c-0d25745b890a · outbound

This paper cites Position: Optimization in SciML should employ the function space geometry.

Generalized Lie Symmetries in Physics-Informed Neural Operators Position: Optimization in SciML should employ the function space geometry

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:49.987577Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 8aaee69e-c6d8-4eb2-994c-426adef67246 · outbound

This paper cites Applications of Lie groups to differ- ential equations, volume 107.

Generalized Lie Symmetries in Physics-Informed Neural Operators Applications of Lie groups to differ- ential equations, volume 107

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:49.975827Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation c4389902-507b-4cca-83f4-b1bd6f52bd90 · outbound

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

Generalized Lie Symmetries in Physics-Informed Neural Operators Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differ- ential equations

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:49.964103Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b3d2ba59-3aa5-431f-8d22-bf3fac8b7345 · outbound

This paper cites Applications of physics informed neural opera- tors.

Generalized Lie Symmetries in Physics-Informed Neural Operators Applications of physics informed neural opera- tors

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:49.951806Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 8e0691d8-3687-4730-aa8d-41e8b25010d6 · outbound

This paper cites Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groups.

Generalized Lie Symmetries in Physics-Informed Neural Operators Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groups

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-09T19:19:49.602401Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bb56a4b2-bcfd-4c48-9142-0b3ba2d14f04 · outbound

This paper cites DGM: A deep learning algorithm for solving par- tial differential equations.

Generalized Lie Symmetries in Physics-Informed Neural Operators DGM: A deep learning algorithm for solving par- tial differential equations

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:49.939685Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation bf0a222b-4363-4589-ada3-0ddcf72d4ed6 · outbound

This paper cites Sobolev training for physics- informed neural networks.

Generalized Lie Symmetries in Physics-Informed Neural Operators Sobolev training for physics- informed neural networks

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:49.929078Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e0753215-f93c-4e05-b7e5-3d347c73633d · outbound

This paper cites Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data.

Generalized Lie Symmetries in Physics-Informed Neural Operators Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-09T19:19:49.614401Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e7361e5f-defe-4072-864b-d932eb76eb52 · outbound

This paper cites Neural operators meet energy- based theory: Operator learning for hamiltonian and dissipative pdes, 2024.

Generalized Lie Symmetries in Physics-Informed Neural Operators Neural operators meet energy- based theory: Operator learning for hamiltonian and dissipative pdes, 2024

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:49.911373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation bd197e06-94d0-4d9b-892f-c62541a7821e · outbound

This paper cites Incorpo- rating symmetry into deep dynamics models for im- proved generalization.

Generalized Lie Symmetries in Physics-Informed Neural Operators Incorpo- rating symmetry into deep dynamics models for im- proved generalization

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:49.899454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 78f8837b-e8e0-483c-97e2-9efbd6a26b51 · outbound

This paper cites Learning the solution operator of parametric partial differential equations with physics-informed Deep- ONets.

Generalized Lie Symmetries in Physics-Informed Neural Operators Learning the solution operator of parametric partial differential equations with physics-informed Deep- ONets

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:49.887602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation cdd71a2b-f940-4a29-9f3a-bcb9232d1184 · outbound

This paper cites Biophysics Informed Pathological Regularisation for Brain Tumour Segmentation.

Generalized Lie Symmetries in Physics-Informed Neural Operators Biophysics Informed Pathological Regularisation for Brain Tumour Segmentation

Reference 33

Resolution: verified exact; local_arxiv, observed 2026-08-09T19:19:49.677407Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e5d9bceb-6b10-41b8-90a8-d1865675d95f · outbound

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

Generalized Lie Symmetries in Physics-Informed Neural Operators Enforcing continuous symmetries in physics-informed neural network for solving forward and inverse problems of partial differen- tial equations

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:49.875662Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e91e9a62-0120-46b6-98f5-be8c8518fe0a · outbound

This paper cites Physics- constrained deep learning for high-dimensional sur- rogate modeling and uncertainty quantification with- out labeled data.

Generalized Lie Symmetries in Physics-Informed Neural Operators Physics- constrained deep learning for high-dimensional sur- rogate modeling and uncertainty quantification with- out labeled data

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T19:19:49.862868Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Pith citing papers

Observation 081614c2-7b88-4b80-95a7-768d24dea17a · inbound

Governing Equation Discovery from Data Based on Differential Invariants cites this paper.

Governing Equation Discovery from Data Based on Differential Invariants Generalized Lie Symmetries in Physics-Informed Neural Operators

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-08-07T14:32:14.937401Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.