Paper Citation Record · LEDGER

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem

As of 12 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:2607.23501.

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

pith.paper-citation-record.v1
2607.23501 v1

Coverage vector

measured 30 of 30 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-07-30T20:43:14.040115Z

measured 30 of 30 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 0 of 0 inbound itemization

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measured 0 of 1 external citation measurements

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Reference resolution

30 of 30 outbound references displayed

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Outbound references

Observation f154f405-4c04-4026-9adb-25a105181803 · outbound

This paper cites Breen, Christopher N.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem Breen, Christopher N

Reference 1

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Observation 97ff14aa-c61b-44ab-9f5d-53be9bd584e2 · outbound

This paper cites On relative periodic solutions of the planar general three-body problem.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem On relative periodic solutions of the planar general three-body problem

Reference 2

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Observation 9d44fbf6-f82b-4862-918c-a1c7b056fbd4 · outbound

This paper cites A remarkable periodic solution of the three-body problem in the case of equal masses.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem A remarkable periodic solution of the three-body problem in the case of equal masses

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-30T20:43:13.954970Z

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Observation e0684015-03db-48ab-b4d4-47b82e3f73b5 · outbound

This paper cites Scientific machine learning through physics-informed neural networks: Where we are and what's next.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem Scientific machine learning through physics-informed neural networks: Where we are and what's next

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-30T20:43:13.958217Z

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Observation 75e68650-723e-4cef-98d2-d5ec0a6f43a3 · outbound

This paper cites De motu rectilineo trium corporum se mutuo attrahentium.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem De motu rectilineo trium corporum se mutuo attrahentium

Reference 5

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Observation e0f64dfc-4d65-4ace-a00d-05b512f96dd3 · outbound

This paper cites FO-PINNs: A First-Order formulation for Physics Informed Neural Networks.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem FO-PINNs: A First-Order formulation for Physics Informed Neural Networks

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-30T20:43:13.964970Z

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Observation 258dbeec-1b1d-4ec2-9e80-abb7bebbdaff · outbound

This paper cites Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-30T20:43:13.968632Z

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Observation e46c577a-08dc-4639-a3ca-1a9ab8aa3abb · outbound

This paper cites Kingma and Jimmy Ba.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem Kingma and Jimmy Ba

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-30T20:43:13.972167Z

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Observation c055fd6a-9eb8-4b52-ac6a-3f046d063d1a · outbound

This paper cites Lagaris, Aristidis Likas, and Dimitrios I.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem Lagaris, Aristidis Likas, and Dimitrios I

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-30T20:43:13.975272Z

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Observation 397e5953-4c4a-4e49-918f-e97b5a62cfc3 · outbound

This paper cites Essai sur le probl\` e me des trois corps.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem Essai sur le probl\` e me des trois corps

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-30T20:43:13.978547Z

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Observation 8e702519-bb77-4980-8249-a8dae7a80519 · outbound

This paper cites More than six hundred new families of Newtonian periodic planar collisionless three-body orbits.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem More than six hundred new families of Newtonian periodic planar collisionless three-body orbits

Reference 11

Resolution: verified exact; doi, observed 2026-07-30T20:46:01.021248Z

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Observation cc3011b1-fb33-4ec2-96a4-2627c08cfaa1 · outbound

This paper cites One family of 13315 stable periodic orbits of non-hierarchical unequal-mass triple systems.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem One family of 13315 stable periodic orbits of non-hierarchical unequal-mass triple systems

Reference 12

Resolution: verified exact; doi, observed 2026-07-30T20:46:01.006506Z

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Observation 787dc4de-e42c-4d5a-add2-0c4206015a7f · outbound

This paper cites Three-body problem---from Newton to supercomputer plus machine learning.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem Three-body problem---from Newton to supercomputer plus machine learning

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-30T20:43:13.988253Z

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Observation 805f5447-f308-4881-9ade-c494ce9c90e1 · outbound

This paper cites Decoupled weight decay regularization.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem Decoupled weight decay regularization

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-30T20:43:13.991472Z

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Observation 4acac386-cf3c-44fb-8b7d-81b29ba22661 · outbound

This paper cites DeepXDE : A deep learning library for solving differential equations.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem DeepXDE : A deep learning library for solving differential equations

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-30T20:43:13.994556Z

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Observation 2057a20a-5a8e-46b4-be3b-ec012152f570 · outbound

This paper cites Matzakos and Christos A.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem Matzakos and Christos A

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-30T20:43:13.997401Z

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Observation 991a27e8-cec7-479b-b3da-f09c8f8e5297 · outbound

This paper cites Meyer, Glen R.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem Meyer, Glen R

Reference 17

Resolution: verified exact; doi, observed 2026-07-30T20:46:00.992603Z

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Observation c53893dd-296a-4316-842b-2d9ac459e41c · outbound

This paper cites Central configurations.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem Central configurations

Reference 18

Resolution: verified exact; doi, observed 2026-07-30T20:46:00.979545Z

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Observation 872d594a-d71a-40f7-b36f-95f753a6ed21 · outbound

This paper cites Braids in classical dynamics.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem Braids in classical dynamics

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-30T20:43:14.007274Z

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Observation c9460ad0-70bd-45b2-a632-862542e56b9d · outbound

This paper cites Advancing Solutions for the Three-Body Problem Through Physics-Informed Neural Networks.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem Advancing Solutions for the Three-Body Problem Through Physics-Informed Neural Networks

Reference 20

Resolution: unresolved; no resolver link, observed 2026-07-30T20:43:14.010318Z

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Observation b8857da4-f959-4c08-a9da-adfb894859e9 · outbound

This paper cites Les M\' e thodes nouvelles de la m\' e canique c\' e leste , volume 1.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem Les M\' e thodes nouvelles de la m\' e canique c\' e leste , volume 1

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-30T20:43:14.013708Z

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Observation bb3b242e-0119-4148-916e-0d3cce379dd0 · outbound

This paper cites On the spectral bias of neural networks.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem On the spectral bias of neural networks

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-30T20:43:14.016654Z

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Observation 2ba88ede-6cef-401c-836c-7f997763cee5 · outbound

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

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Reference 23

Resolution: unresolved; no resolver link, observed 2026-07-30T20:43:14.019422Z

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Observation 7c906a76-cd27-4b52-8b36-b05e8df098f6 · outbound

This paper cites an unresolved cited work.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem Unresolved cited work

Reference 24

Resolution: unresolved; no resolver link, observed 2026-07-30T20:43:14.022293Z

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Observation 43da8652-d21a-4c01-946b-a90e96404e18 · outbound

This paper cites Physics-informed neural networks without loss balancing: A direct term scaling approach for nonlinear 1D problems.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem Physics-informed neural networks without loss balancing: A direct term scaling approach for nonlinear 1D problems

Reference 25

Resolution: verified exact; doi, observed 2026-07-30T20:46:00.966189Z

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Observation e4664b57-204c-4752-9dfb-411de40182de · outbound

This paper cites Dmitra s inovi\' c.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem Dmitra s inovi\' c

Reference 26

Resolution: unresolved; no resolver link, observed 2026-07-30T20:43:14.028318Z

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Observation 6421e74b-db3c-4877-82f4-598c1baa8c02 · outbound

This paper cites Understanding and mitigating gradient flow pathologies in physics-informed neural networks.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem Understanding and mitigating gradient flow pathologies in physics-informed neural networks

Reference 27

Resolution: unresolved; no resolver link, observed 2026-07-30T20:43:14.031426Z

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Observation d3ee7a1f-6010-40a4-aa74-e6cc4212a66e · outbound

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

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks

Reference 28

Resolution: unresolved; no resolver link, observed 2026-07-30T20:43:14.034298Z

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Observation 8dc96966-8639-45ae-9e3e-14f86f62ae07 · outbound

This paper cites A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks

Reference 29

Resolution: unresolved; no resolver link, observed 2026-07-30T20:43:14.037245Z

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Observation 157dd3e9-630b-44cd-85c9-9c3c886f4ca9 · outbound

This paper cites Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemble.

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemble

Reference 30

Resolution: unresolved; no resolver link, observed 2026-07-30T20:43:14.040115Z

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Pith citing papers

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