Paper Citation Record · LEDGER

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations

As of 8 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2507.03860.

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

pith.paper-citation-record.v1
2507.03860 v1

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T20:11:32.942477Z

measured 32 of 32 standing notices

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Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

32 of 32 outbound references displayed

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External citation measurements

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Outbound references

Observation 62d5576e-28fb-4f9c-97a8-79d4c0a18d8d · outbound

This paper cites Agarwal and Donal O'Regan.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Agarwal and Donal O'Regan

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:11:34.551070Z

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Observation 462d634d-62ce-47db-8771-6eea7e3030cc · outbound

This paper cites an unresolved cited work.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:11:34.536888Z

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Observation 3bf79934-70b9-43be-a629-fe4be01771fb · outbound

This paper cites Set propagation techniques for reachability analysis.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Set propagation techniques for reachability analysis

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:11:34.522654Z

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Observation 64ee42b3-f5cb-4c69-aac4-b14329ca67c9 · outbound

This paper cites The Multimodal Universe : Enabling Large - Scale Machine Learning with 100 TB of Astronomical Scientific Data.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations The Multimodal Universe : Enabling Large - Scale Machine Learning with 100 TB of Astronomical Scientific Data

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:11:34.508409Z

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Observation 7f43cf63-c905-4951-9764-efc3a09ee8d6 · outbound

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Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:11:34.494186Z

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Observation 5229c2dd-587a-40ea-95c4-4a7938ea5f83 · outbound

This paper cites Neural taylor approximations: Convergence and exploration in rectifier networks, 2016.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Neural taylor approximations: Convergence and exploration in rectifier networks, 2016

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:11:34.480078Z

Source-reported events for the cited work

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Observation cb5f1d8d-a7f0-477f-bee3-ad9cf761ba8a · outbound

This paper cites Analytic solutions to nonlinear odes via spectral power series.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Analytic solutions to nonlinear odes via spectral power series

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:11:34.464515Z

Source-reported events for the cited work

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Observation f5266e58-ade5-4bd3-b542-bc78a1160d9e · outbound

This paper cites The stability of solutions of linear differential equations.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations The stability of solutions of linear differential equations

Reference 8

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Observation e4539076-bf9b-4376-aa47-01f01dd775dd · outbound

This paper cites Berz and K.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Berz and K

Reference 9

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Observation 02e1f3c7-b093-43f4-97bb-c6d59c1c2135 · outbound

This paper cites Reachability analysis for cyber-physical systems: Are we there yet? (invited paper).

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Reachability analysis for cyber-physical systems: Are we there yet? (invited paper)

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:11:34.300948Z

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Observation 1ea2cda8-219e-4060-afc9-e400277f3865 · outbound

This paper cites Understanding the difficulty of training deep feedforward neural networks.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Understanding the difficulty of training deep feedforward neural networks

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:11:34.124610Z

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Observation aac8c87b-0d5e-4814-9c76-9ba6cad6320b · outbound

This paper cites Hairer, G.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Hairer, G

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:11:34.023498Z

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Observation d7667228-f466-4783-85c8-4095a0a83fdb · outbound

This paper cites Dual Cone Gradient Descent for Training Physics-Informed Neural Networks.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Dual Cone Gradient Descent for Training Physics-Informed Neural Networks

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T20:11:32.854538Z

Source-reported events for the cited work

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Observation e9c31bff-4697-4329-a2dc-ba68fc371e2e · outbound

This paper cites Causally- Informed Deep Learning to Improve Climate Models and Projections.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Causally- Informed Deep Learning to Improve Climate Models and Projections

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-06T20:11:32.861257Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eb58a7bd-ab27-47fd-9b11-30a398eec2c8 · outbound

This paper cites Kingma and Jimmy Ba.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Kingma and Jimmy Ba

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-06T20:11:32.866238Z

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Observation f37454e4-ebb5-4021-a4ca-1d6586a695fd · outbound

This paper cites Systems Biology: A Textbook.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Systems Biology: A Textbook

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:11:33.984621Z

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Observation 63287020-ac20-438a-acdb-81b8e6554d5b · outbound

This paper cites an unresolved cited work.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:11:33.956853Z

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Observation 44b0e12a-f321-46f0-ae0a-ab460ed95502 · outbound

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

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Characterizing possible failure modes in physics-informed neural networks

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:11:33.922162Z

Source-reported events for the cited work

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Observation 799241c0-5197-4df0-b62f-a972bf37161b · outbound

This paper cites Medical image analysis using deep learning algorithms.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Medical image analysis using deep learning algorithms

Reference 19

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Observation 12a0ecc0-b4e8-4fb9-a9a1-10abbaab6fca · outbound

This paper cites Makino and M.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Makino and M

Reference 20

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Observation 8814ac55-c6b4-4aaf-b455-a4b24dedcbdd · outbound

This paper cites Raissi, P.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Raissi, P

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-06T20:11:32.894959Z

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Observation b917603c-7107-4eb8-a561-c31298df477a · outbound

This paper cites Multistep neural networks for data-driven discovery of nonlinear dynamical systems, 2018.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Multistep neural networks for data-driven discovery of nonlinear dynamical systems, 2018

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:11:33.821547Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation deab5a5b-3c00-415b-b77b-25fa39820968 · outbound

This paper cites an unresolved cited work.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:11:33.773343Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 6ee68393-312e-40bc-bedf-d0a4032149da · outbound

This paper cites Physics- Informed Neural Network for Ultrasound Nondestructive Quantification of Surface Breaking Cracks.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Physics- Informed Neural Network for Ultrasound Nondestructive Quantification of Surface Breaking Cracks

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-06T20:11:32.907867Z

Source-reported events for the cited work

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Observation 179d67f6-5340-4afa-aa70-30e52e9989da · outbound

This paper cites Enhanced physics-informed neural networks with Augmented Lagrangian relaxation method ( AL - PINNs ).

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Enhanced physics-informed neural networks with Augmented Lagrangian relaxation method ( AL - PINNs )

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-06T20:11:32.913405Z

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Observation 9195594f-8b96-40bc-8323-77e311e6ecad · outbound

This paper cites Rohrhofer, and Bernhard C Geiger.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Rohrhofer, and Bernhard C Geiger

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:11:33.735458Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ce70a657-a770-4533-9473-7488d3873645 · outbound

This paper cites Is L2 Physics - Informed Loss Always Suitable for Training Physics - Informed Neural Network ? 2022.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Is L2 Physics - Informed Loss Always Suitable for Training Physics - Informed Neural Network ? 2022

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:11:33.704513Z

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Observation f5508ad0-9948-4c82-9fe2-143889510064 · outbound

This paper cites Deep learning of free boundary and Stefan problems.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Deep learning of free boundary and Stefan problems

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-06T20:11:32.925845Z

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Observation f23d12f5-83ca-40d9-9bd3-2c29059c2129 · outbound

This paper cites Physics-informed Neural Implicit Flow neural network for parametric PDEs.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Physics-informed Neural Implicit Flow neural network for parametric PDEs

Reference 29

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T20:11:33.401351Z

Source-reported events for the cited work

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Observation 5beccafd-85b2-4b29-9eae-f7ddcccc3799 · outbound

This paper cites Humphrey, and George Em Karniadakis.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Humphrey, and George Em Karniadakis

Reference 30

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T20:11:33.302130Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 062b8bcf-3b19-4f56-9326-ccda261a1f03 · outbound

This paper cites Nn-poly: Approximating common neural networks with taylor polynomials to imbue dynamical system constraints.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Nn-poly: Approximating common neural networks with taylor polynomials to imbue dynamical system constraints

Reference 31

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T20:11:33.200549Z

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Observation 5512643a-a985-4a4a-ba4c-b86cd5b2d8ab · outbound

This paper cites Taylor expansion in neural networks: How higher orders yield better predictions.

Taylor-Model Physics-Informed Neural Networks (PINNs) for Ordinary Differential Equations Taylor expansion in neural networks: How higher orders yield better predictions

Reference 32

Resolution: verified exact; doi, observed 2026-08-06T20:11:32.980454Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

No inbound Pith citation observations are available.