Paper Citation Record · LEDGER

Governing Equation Discovery from Data Based on Differential Invariants

As of 14 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 2 inbound Pith citation observations for arXiv:2505.18798.

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

pith.paper-citation-record.v1
2505.18798 v1

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T14:32:14.727012Z

measured 20 of 20 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-12T00:34:34.870020Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-13T01:42:04.769952Z

Reference resolution

18 of 18 outbound references displayed

verified exact3
verified fuzzy2
unresolved13
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c5e90589-aadd-4791-866b-f76f7e07bbb8 · outbound

This paper cites Towards Multi-spatiotemporal-scale Generalized PDE Modeling.

Governing Equation Discovery from Data Based on Differential Invariants Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-07T14:32:13.704894Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c6ba211a-8888-4799-9ceb-73d1da2588b5 · outbound

This paper cites Fourier Neural Operator for Parametric Partial Differential Equations.

Governing Equation Discovery from Data Based on Differential Invariants Fourier Neural Operator for Parametric Partial Differential Equations

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-07T14:32:14.018192Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 26997fa7-df7e-4a20-8673-09ab648a6864 · outbound

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

Governing Equation Discovery from Data Based on Differential Invariants Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groups

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-07T14:32:15.116020Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f5e28334-9eed-43db-a134-639ed33c505f · outbound

This paper cites Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree search.

Governing Equation Discovery from Data Based on Differential Invariants Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree search

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-07T14:32:14.375394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6bf53712-82da-4c25-ad48-4f02fe907256 · outbound

This paper cites Physics-based Deep Learning.

Governing Equation Discovery from Data Based on Differential Invariants Physics-based Deep Learning

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-07T14:32:14.447099Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

This paper cites Generalized Lie Symmetries in Physics-Informed Neural Operators.

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 2026-08-14T06:32:32.682623+00:00.

Observation 8e64224a-e5d6-4812-ae48-7a530b6be4db · outbound

This paper cites Latent Space Symmetry Discovery.

Governing Equation Discovery from Data Based on Differential Invariants Latent Space Symmetry Discovery

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-07T14:32:14.660286Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cac521df-110b-4a94-9cc3-e012c190e44c · outbound

This paper cites an unresolved cited work.

Governing Equation Discovery from Data Based on Differential Invariants Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:32:15.551274Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 163e9bd9-e4c4-412b-9fa5-c621f277df60 · outbound

This paper cites Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients.

Governing Equation Discovery from Data Based on Differential Invariants Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients

Reference 1993

Resolution: unresolved; no resolver link, observed 2026-08-07T14:32:14.175151Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e0de77c3-40f0-4011-a254-b89bcc0cf3b6 · outbound

This paper cites Message Passing Neural PDE Solvers.

Governing Equation Discovery from Data Based on Differential Invariants Message Passing Neural PDE Solvers

Reference 2010

Resolution: unresolved; no resolver link, observed 2026-08-07T14:32:13.382456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 82e38512-1778-40b4-a0ec-36590b5d5c49 · outbound

This paper cites Contemporary symbolic regression methods and their relative performance.

Governing Equation Discovery from Data Based on Differential Invariants Contemporary symbolic regression methods and their relative performance

Reference 2018

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:32:15.807723Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 748c06c0-172e-46ac-9c83-60ac447e2e14 · outbound

This paper cites Parameterized Physics-informed Neural Networks for Parameterized PDEs.

Governing Equation Discovery from Data Based on Differential Invariants Parameterized Physics-informed Neural Networks for Parameterized PDEs

Reference 2019

Resolution: unresolved; no resolver link, observed 2026-08-07T14:32:13.463464Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 594bf6ae-6bae-45c2-b50b-a1c358e85f69 · outbound

This paper cites Learning Symbolic Physics with Graph Networks.

Governing Equation Discovery from Data Based on Differential Invariants Learning Symbolic Physics with Graph Networks

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-07T14:32:13.600906Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 14f54c54-5ea4-4f1a-a28e-f9e0dbeb4589 · outbound

This paper cites Active Learning for Neural PDE Solvers.

Governing Equation Discovery from Data Based on Differential Invariants Active Learning for Neural PDE Solvers

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-07T14:32:14.103756Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d0ddce49-4e9a-4e8a-9904-0d82a333b2ec · outbound

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

Governing Equation Discovery from Data Based on Differential Invariants Physics-guided data augmentation for learning the solution operator of linear differential equations

Reference 2022

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:32:15.675407Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 0f70513f-e194-4e9a-9d8e-6ea04322c646 · outbound

This paper cites Learning Infinitesimal Generators of Continuous Symmetries from Data.

Governing Equation Discovery from Data Based on Differential Invariants Learning Infinitesimal Generators of Continuous Symmetries from Data

Reference 2023

Resolution: verified exact; local_arxiv, observed 2026-08-07T14:32:15.311179Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b537b96e-0771-48e9-9ee0-91a8219aa9fb · outbound

This paper cites Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl.

Governing Equation Discovery from Data Based on Differential Invariants Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-07T14:32:13.530311Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 81166c24-7b29-4a3b-bda1-32b782dd7d8d · outbound

This paper cites Incorporating Symmetry into Deep Dynamics Models for Improved Generalization.

Governing Equation Discovery from Data Based on Differential Invariants Incorporating Symmetry into Deep Dynamics Models for Improved Generalization

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-08-07T14:32:14.596498Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 624d06b1-4e7d-4b2d-8cdf-452bc71c0479 · inbound

EqOD: Symmetry-Informed Stability Selection for PDE Identification cites this paper.

EqOD: Symmetry-Informed Stability Selection for PDE Identification Governing Equation Discovery from Data Based on Differential Invariants

Reference 18

Resolution: verified exact; arxiv_id, observed 2026-05-13T01:42:04.772660Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 78506afc-f94c-48bf-8ff0-57cd131657f3 · inbound

Adaptive Symmetry Discovery for Dynamical System Identification cites this paper.

Adaptive Symmetry Discovery for Dynamical System Identification Governing Equation Discovery from Data Based on Differential Invariants

Reference 87

Resolution: unresolved; no resolver link, observed 2026-08-12T00:34:34.870020Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.