Paper Citation Record · LEDGER

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation

As of 10 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2607.06091.

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

pith.paper-citation-record.v1
2607.06091 v1

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-08T16:51:40.082489Z

measured 36 of 36 standing notices

One-hop event checks from named stored sources.

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measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

36 of 36 outbound references displayed

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verified fuzzy24
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External citation measurements

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Outbound references

Observation 02997bb4-8a4b-43a6-8591-d7520d1af1db · outbound

This paper cites an unresolved cited work.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-07-08T16:55:08.457430Z

Source-reported events for the cited work

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Observation 7702c507-3d7b-477b-8552-b9ba78a9db92 · outbound

This paper cites an unresolved cited work.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-07-08T16:55:08.486961Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 15250a45-ca41-45c4-a4fe-ebcc3bad460f · outbound

This paper cites Adaptive method for the solution of 1d and 2d advec- tion–diffusion equations used in environmental engineering.Journal of Hydroinformatics, 23(6):1290–1311, 2021.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Adaptive method for the solution of 1d and 2d advec- tion–diffusion equations used in environmental engineering.Journal of Hydroinformatics, 23(6):1290–1311, 2021

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T16:55:08.449839Z

Source-reported events for the cited work

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Observation 2e59685d-1576-45aa-979c-593ed0106bf6 · outbound

This paper cites Physical Informed Neural Networks for modeling ocean pollutant.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Physical Informed Neural Networks for modeling ocean pollutant

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-07-08T16:55:08.400790Z

Source-reported events for the cited work

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Observation f3d08b22-8e1e-4d50-a1fc-15f06886749f · outbound

This paper cites Quantitative analysis of molecular transport in the extracellular space using physics-informed neural network.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Quantitative analysis of molecular transport in the extracellular space using physics-informed neural network

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T16:55:08.465146Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation ce7a65b5-3d25-4ae2-bd42-902636751e31 · outbound

This paper cites AirPhyNet: Harnessing Physics-Guided Neural Networks for Air Quality Prediction.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation AirPhyNet: Harnessing Physics-Guided Neural Networks for Air Quality Prediction

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-07-08T16:55:08.382492Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation b029d3e1-917b-484c-a3ac-5255305fe0a5 · outbound

This paper cites LeVeque.Finite Volume Methods for Hyperbolic Problems.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation LeVeque.Finite Volume Methods for Hyperbolic Problems

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T16:55:08.488659Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation bf338201-380b-4fa7-af4a-29d9851ac5d1 · outbound

This paper cites Finite volume methods.Handbook of Numerical Analysis, 7:731–1018, 2000.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Finite volume methods.Handbook of Numerical Analysis, 7:731–1018, 2000

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T16:55:08.462672Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 871a4ced-a4e0-40fa-a54c-e36937768341 · outbound

This paper cites Crank and P.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Crank and P

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T16:55:08.466814Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e7692fb9-199c-4cef-a0d3-753cad3b9d3a · outbound

This paper cites Hundsdorfer and J.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Hundsdorfer and J

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T16:55:08.473830Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f29ea9ac-ce65-48e9-84ea-3bee5d549ead · outbound

This paper cites Raissi, P.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Raissi, P

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T16:55:08.460897Z

Source-reported events for the cited work

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Observation 3fafc280-3734-4df7-b321-7fa2a5802289 · outbound

This paper cites Baydin, Barak A.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Baydin, Barak A

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T16:55:08.453588Z

Source-reported events for the cited work

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Observation 43c2c984-648b-4501-9976-dfdb0b045035 · outbound

This paper cites Karniadakis, Ioannis G.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Karniadakis, Ioannis G

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T16:55:08.478856Z

Source-reported events for the cited work

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Observation 91df78a5-3a52-45d9-8e76-2bd35db93eb4 · outbound

This paper cites di Cola, Fabio Giampaolo, Gianluigi Rozza, Maziar Raissi, and Francesco Piccialli.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation di Cola, Fabio Giampaolo, Gianluigi Rozza, Maziar Raissi, and Francesco Piccialli

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T16:55:08.455563Z

Source-reported events for the cited work

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Observation d07458cc-528e-4d9e-843c-229f5f384d1a · outbound

This paper cites Karniadakis.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Karniadakis

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T16:55:08.459193Z

Source-reported events for the cited work

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Observation 58160832-5f6b-4dbb-99ff-f611cfc328fe · outbound

This paper cites Krishnapriyan, Asghar Gholami, Shandian Zhe, Robert M.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Krishnapriyan, Asghar Gholami, Shandian Zhe, Robert M

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T16:55:08.470262Z

Source-reported events for the cited work

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Observation 1a6edb1c-d8d0-41ae-8f42-14f4dd5da336 · outbound

This paper cites an unresolved cited work.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-07-08T16:55:08.491809Z

Source-reported events for the cited work

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Observation efc7ff9a-8edc-4aef-8186-237ca9804f8d · outbound

This paper cites Understanding and mitigating gradient flow pathologies in physics-informed neural networks.SIAM Journal on Scientific Computing, 43(5):A3055–A3081.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Understanding and mitigating gradient flow pathologies in physics-informed neural networks.SIAM Journal on Scientific Computing, 43(5):A3055–A3081

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T16:55:08.468567Z

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Observation 469a63d8-57bb-4e38-8bae-5472c24f4ed0 · outbound

This paper cites When and why pinns fail to train: A neural tangent kernel perspective.Journal of Computational Physics, 449:110768.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation When and why pinns fail to train: A neural tangent kernel perspective.Journal of Computational Physics, 449:110768

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T16:55:08.472157Z

Source-reported events for the cited work

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Observation a416ed0f-135e-47f1-826d-49356d999055 · outbound

This paper cites Jagtap and George E.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Jagtap and George E

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T16:55:08.490237Z

Source-reported events for the cited work

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Observation 59581a5c-e793-4a55-88c9-5723cefe83f5 · outbound

This paper cites Jagtap, Ehsan Kharazmi, and George E.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Jagtap, Ehsan Kharazmi, and George E

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T16:55:08.485428Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 9652b9ef-3a43-438e-9b64-0a7c56489afb · outbound

This paper cites Jagtap, and George E.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Jagtap, and George E

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T16:55:08.477209Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 6e5fd124-52a5-408d-a70f-61656dcab84e · outbound

This paper cites Karniadakis.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Karniadakis

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T16:55:08.483621Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation c7567f12-921d-4931-b8c2-bf19dcffaddb · outbound

This paper cites Finite Volume Neural Network: Modeling Subsurface Contaminant Transport.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Finite Volume Neural Network: Modeling Subsurface Contaminant Transport

Reference 24

Resolution: metadata mismatch; local_arxiv, observed 2026-07-08T16:55:08.387542Z

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Observation 81545985-36d3-460f-a927-8d2e37a7cbe7 · outbound

This paper cites (U)NFV: Supervised and Unsupervised Neural Finite Volume Methods for Solving Hyperbolic PDEs.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation (U)NFV: Supervised and Unsupervised Neural Finite Volume Methods for Solving Hyperbolic PDEs

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-07-08T16:55:08.392535Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation ff69386d-99d6-40cb-b15d-062ee71505b6 · outbound

This paper cites Coupled integral pinn for conservation law.arXiv preprint arXiv:2411.11276, 2024.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Coupled integral pinn for conservation law.arXiv preprint arXiv:2411.11276, 2024

Reference 26

Resolution: verified exact; arxiv_id, observed 2026-07-08T16:55:08.398109Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation a4c4d923-4fd8-4e0f-9552-578d8471fc9a · outbound

This paper cites Patsatzis, Mario di Bernardo, Lucia Russo, and Constantinos Siettos.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Patsatzis, Mario di Bernardo, Lucia Russo, and Constantinos Siettos

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T16:55:08.447437Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 4369e7eb-5e00-4c68-b774-68b590bd8913 · outbound

This paper cites Mass-preserving spatio-temporal adaptive pinn for cahn-hilliard equations with strong nonlinearities and singularities.Preprint submitted to Elsevier, 2025.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Mass-preserving spatio-temporal adaptive pinn for cahn-hilliard equations with strong nonlinearities and singularities.Preprint submitted to Elsevier, 2025

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T16:55:08.451741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation dca11367-663e-41ae-b512-9e6ca3ac5130 · outbound

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

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation DeepXDE: A deep learning library for solving differential equations

Reference 29

Resolution: verified exact; local_arxiv, observed 2026-07-08T16:55:08.404689Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 47e47062-8ef3-4f31-91f8-ad12f3ff3b72 · outbound

This paper cites Karniadakis.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Karniadakis

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T16:55:08.443170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 88d39d17-5501-4a41-9243-fcc1636aa3dc · outbound

This paper cites Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew M.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew M

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T16:55:08.475526Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 6bb6ae84-bee6-4cd2-bebc-d547cdd07238 · outbound

This paper cites Physics-informed neural operator for learning partial differential equations.ACM / IMS Journal of Data Science, 1, 2021.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Physics-informed neural operator for learning partial differential equations.ACM / IMS Journal of Data Science, 1, 2021

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T16:55:08.482078Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation afbe1950-a664-49a8-99cc-2a2b1e6da6fd · outbound

This paper cites an unresolved cited work.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-07-08T16:55:08.480357Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 7f053237-b1a0-458f-8894-cc3a61133bf0 · outbound

This paper cites Karniadakis.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Karniadakis

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T16:55:08.445341Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 517a3f08-5170-47ff-803e-285c73fc2715 · outbound

This paper cites Composing Partial Differential Equations with Physics-Aware Neural Networks.

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation Composing Partial Differential Equations with Physics-Aware Neural Networks

Reference 35

Resolution: verified exact; local_arxiv, observed 2026-07-08T16:55:08.385047Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 91608d6a-aed3-40af-9ea2-12278810a458 · outbound

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

Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks

Reference 36

Resolution: verified exact; local_arxiv, observed 2026-07-08T16:55:08.395238Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Pith citing papers

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