Paper Citation Record · LEDGER

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks

As of 5 August 2026, this Paper Citation Record lists 42 of 42 outbound references and 1 inbound Pith citation observation for arXiv:2605.29211.

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pith.paper-citation-record.v1
2605.29211 v1

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Reference resolution

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External citation measurements

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Outbound references

Observation 7bfff1d0-788c-4986-aa23-6d5d86258856 · outbound

This paper cites MacArt, and Justin Sirignano.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks MacArt, and Justin Sirignano

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-06-29T06:03:07.786603Z

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Observation ecf33618-b252-4cd7-b753-dd7b935d4dff · outbound

This paper cites A model for collision processes in gases. i. small amplitude processes in charged and neutral one-component systems.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks A model for collision processes in gases. i. small amplitude processes in charged and neutral one-component systems

Reference 2

Resolution: verified exact; doi, observed 2026-06-29T06:03:07.796924Z

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Observation b9e606f9-162d-4b88-b64f-05667f5114d8 · outbound

This paper cites an unresolved cited work.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Unresolved cited work

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-06-29T06:03:08.424115Z

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Observation aea0ca42-ee5a-4e19-9b35-6acb466e30f8 · outbound

This paper cites Flow over an espresso cup: inferring three-dimensional velocity and pressure fields from tomographic background oriented schlieren via physics-informed neural networks.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Flow over an espresso cup: inferring three-dimensional velocity and pressure fields from tomographic background oriented schlieren via physics-informed neural networks

Reference 4

Resolution: verified exact; doi, observed 2026-06-29T06:03:07.748259Z

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Observation 575600f3-4672-423f-a71c-b176b65b3fb3 · outbound

This paper cites Cercignani.The Boltzmann equation and its applications, volume 67 ofApplied Mathematical Sciences.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Cercignani.The Boltzmann equation and its applications, volume 67 ofApplied Mathematical Sciences

Reference 5

Resolution: verified exact; doi, observed 2026-06-29T06:03:07.801745Z

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Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Unresolved cited work

Reference 6

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Observation 63de18e1-110f-4abe-95dc-af7b9d1fd012 · outbound

This paper cites Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations

Reference 7

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Observation fa622efe-8f61-4814-ac7b-6c42d6df1bbc · outbound

This paper cites and Pareschi, L.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks and Pareschi, L

Reference 8

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Observation a7fcb249-9936-4749-a96e-b038c8acb859 · outbound

This paper cites Physics of Fluids34(7), 075117 (2022) https://doi.org/10.1063/5.0095270.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Physics of Fluids34(7), 075117 (2022) https://doi.org/10.1063/5.0095270

Reference 9

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Observation 97369803-6f7e-4bda-bb80-2b9b977ec18e · outbound

This paper cites Physics-informed deep-learning applications to experimental fluid mechanics.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Physics-informed deep-learning applications to experimental fluid mechanics

Reference 10

Resolution: verified exact; doi, observed 2026-06-29T06:03:07.749260Z

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Observation fe9e17f0-44d1-4c81-8ab8-a8a02bb0f89f · outbound

This paper cites A benchmark study of kinetic models for shock waves.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks A benchmark study of kinetic models for shock waves

Reference 11

Resolution: verified exact; doi, observed 2026-06-29T06:03:07.803998Z

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This paper cites 2010 , issn =.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks 2010 , issn =

Reference 12

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Observation dfbe965d-6f45-419e-a649-75e99c0b9fb2 · outbound

This paper cites Observable-augmented manifold learning for multi-source turbulent flow data.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Observable-augmented manifold learning for multi-source turbulent flow data

Reference 13

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Observation 9280acee-717b-4578-9a82-40651fa4d30f · outbound

This paper cites Grad, On the kinetic theory of rarefied gases, Comm.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Grad, On the kinetic theory of rarefied gases, Comm

Reference 14

Resolution: verified exact; doi, observed 2026-06-29T06:03:07.811691Z

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Observation 53db6746-b9d8-4c9e-bf89-0a9cbdbbed91 · outbound

This paper cites Gu and D.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Gu and D

Reference 15

Resolution: verified exact; doi, observed 2026-06-29T06:03:07.783539Z

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Observation 85d5effe-9396-4cb3-b247-d62adbc9e95f · outbound

This paper cites Hirschfelder, Charles F.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Hirschfelder, Charles F

Reference 16

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Observation 59bd7586-04b6-4e17-aaab-22e195f4e9dc · outbound

This paper cites Efficient asymptotic-preserving schemes for some multiscale kinetic equations.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Efficient asymptotic-preserving schemes for some multiscale kinetic equations

Reference 17

Resolution: verified exact; doi, observed 2026-06-29T06:03:07.758532Z

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Observation 798e1ab9-28e1-4cf8-a36b-5c60c7201ecf · outbound

This paper cites Asymptotic-Preserving Neural Networks for Multiscale Time-Dependent Linear Transport Equations.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Asymptotic-Preserving Neural Networks for Multiscale Time-Dependent Linear Transport Equations

Reference 18

Resolution: verified exact; arxiv_id, observed 2026-06-29T06:03:07.804167Z

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Observation fe17b9c5-7375-48a6-8e4c-b2d812cda893 · outbound

This paper cites Asymptotic-Preserving Neural Networks for Multiscale Kinetic Equations.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Asymptotic-Preserving Neural Networks for Multiscale Kinetic Equations

Reference 19

Resolution: verified exact; arxiv_id, observed 2026-06-29T06:03:07.791441Z

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Observation 77854733-b520-43dc-bcea-edcec54c859b · outbound

This paper cites Karniadakis and Ali Beskok.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Karniadakis and Ali Beskok

Reference 20

Resolution: verified exact; doi, observed 2026-06-29T06:03:07.741132Z

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Observation fabe8fad-3624-45d4-bcd8-5445c531b5b6 · outbound

This paper cites A Theory-guided Weighted $L^2$ Loss for solving the BGK model via Physics-informed neural networks.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks A Theory-guided Weighted $L^2$ Loss for solving the BGK model via Physics-informed neural networks

Reference 21

Resolution: verified exact; local_arxiv, observed 2026-06-29T06:03:07.760804Z

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Observation 32a2aa4a-ae84-4b1b-93d1-0843e2b3b3dc · outbound

This paper cites David Levermore.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks David Levermore

Reference 22

Resolution: verified exact; doi, observed 2026-06-29T06:03:07.768662Z

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Observation fc515cb5-a66a-4886-a70a-0e4df0878f5b · outbound

This paper cites A bi-fidelity based asymptotic-preserving neural network for the semiconductor boltzmann equation and its inverse problem.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks A bi-fidelity based asymptotic-preserving neural network for the semiconductor boltzmann equation and its inverse problem

Reference 23

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Observation 8c7757bc-538f-4c8d-bb0a-4bb55d3eaa1f · outbound

This paper cites Physics-informed neural networks for solving forward and inverse flow problems via the Boltzmann--BGK formulation.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Physics-informed neural networks for solving forward and inverse flow problems via the Boltzmann--BGK formulation

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-06-29T06:03:07.807013Z

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Observation a5805c84-4b20-4040-b457-46cbea254ee0 · outbound

This paper cites Probabilistic neural networks for fluid flow surrogate modeling and data recovery.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Probabilistic neural networks for fluid flow surrogate modeling and data recovery

Reference 25

Resolution: verified exact; doi, observed 2026-06-29T06:03:07.799509Z

Source-reported events for the cited work

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Observation d23a2a11-143c-4fc8-95e2-136d4afa097a · outbound

This paper cites Discrete velocity model and implicit scheme for the BGK equation of rarefied gas dynamics.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Discrete velocity model and implicit scheme for the BGK equation of rarefied gas dynamics

Reference 26

Resolution: verified exact; doi, observed 2026-06-29T06:03:07.739175Z

Source-reported events for the cited work

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Observation da6f234a-de20-4790-a998-e164732539ba · outbound

This paper cites Assessments of epistemic uncertainty using Gaussian stochastic weight averaging for fluid-flow regression.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Assessments of epistemic uncertainty using Gaussian stochastic weight averaging for fluid-flow regression

Reference 27

Resolution: verified exact; arxiv_id, observed 2026-06-29T06:03:07.765111Z

Source-reported events for the cited work

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Observation 5569a625-fc0a-43f6-a692-62ea247706e2 · outbound

This paper cites Separable physics-informed neural networks for solving the BGK model of the Boltzmann equation.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Separable physics-informed neural networks for solving the BGK model of the Boltzmann equation

Reference 28

Resolution: verified exact; doi, observed 2026-06-29T06:03:07.799301Z

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Observation 6f1e9807-c02b-409a-85d6-94d3089037db · outbound

This paper cites Stochastic numerics for the Boltzmann equation.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Stochastic numerics for the Boltzmann equation

Reference 29

Resolution: verified exact; doi, observed 2026-06-29T06:03:07.809798Z

Source-reported events for the cited work

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Observation af72fac7-dbff-4b49-aa3e-6aeeaff1629b · outbound

This paper cites Neural networks for rarefiedgasdynamics: Relaxationproblem,polyatomicshockwaves,andhypersoniccylinderflow.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Neural networks for rarefiedgasdynamics: Relaxationproblem,polyatomicshockwaves,andhypersoniccylinderflow

Reference 30

Resolution: verified exact; doi, observed 2026-06-29T06:03:07.787919Z

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Observation e61b9b0a-80e1-49ac-a450-1f1dcdb4d6e6 · outbound

This paper cites Physics constrained neural collision operators for hard sphere surrogates and ab initio angle prediction in direct simulation Monte Carlo.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Physics constrained neural collision operators for hard sphere surrogates and ab initio angle prediction in direct simulation Monte Carlo

Reference 31

Resolution: verified exact; doi, observed 2026-06-29T06:03:07.758153Z

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Observation 0902f9b5-48eb-4c6c-970e-7dedc7fe3c65 · outbound

This paper cites Homogeneous relaxation and shock wave problems: Assessment of the simplified and generalized bernoulli trial collision schemes.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Homogeneous relaxation and shock wave problems: Assessment of the simplified and generalized bernoulli trial collision schemes

Reference 32

Resolution: verified exact; doi, observed 2026-06-29T06:03:07.756623Z

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Observation ef3b3b92-e3ea-4dbc-9ab2-2c58b076739a · outbound

This paper cites Molecular Gas Dynamics: Theory, Techniques, and Applications.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Molecular Gas Dynamics: Theory, Techniques, and Applications

Reference 33

Resolution: verified exact; doi, observed 2026-06-29T06:03:07.813587Z

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Observation 75809a83-469d-489b-b05e-631281e317da · outbound

This paper cites Struchtrup, Macroscopic Transport Equations for Rarefied Gas Flows, Interaction of Me- chanics and Mathematics, Springer, Berlin, 2005, https://doi.org/10.1007/3-540-32386-4.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Struchtrup, Macroscopic Transport Equations for Rarefied Gas Flows, Interaction of Me- chanics and Mathematics, Springer, Berlin, 2005, https://doi.org/10.1007/3-540-32386-4

Reference 34

Resolution: verified exact; doi, observed 2026-06-29T06:03:07.762665Z

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Observation 9b01b5a0-f870-45c4-a127-95b9f81e3ce2 · outbound

This paper cites Regularization of Grad 's 13 moment equations: Derivation and linear analysis.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Regularization of Grad 's 13 moment equations: Derivation and linear analysis

Reference 35

Resolution: verified exact; doi, observed 2026-06-29T06:03:07.783774Z

Source-reported events for the cited work

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Observation 8024f1ad-3d6e-4ae5-91a1-41b8adc26d08 · outbound

This paper cites Physics-constrained Bayesian neural network for fluid flow reconstruction with sparse and noisy data.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Physics-constrained Bayesian neural network for fluid flow reconstruction with sparse and noisy data

Reference 36

Resolution: verified exact; doi, observed 2026-06-29T06:03:07.776804Z

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Observation e0c73fa8-a00c-4b8a-9af8-5b23ce611b23 · outbound

This paper cites an unresolved cited work.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Unresolved cited work

Reference 37

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Observation c738bfd5-7dce-40c9-9934-fa53cd8bc7bc · outbound

This paper cites Modeling nonequilibrium gas flow based on moment equations.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Modeling nonequilibrium gas flow based on moment equations

Reference 38

Resolution: verified exact; doi, observed 2026-06-29T06:03:07.773041Z

Source-reported events for the cited work

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Observation 80ec9b93-9224-4b0d-9d71-6bad191a7972 · outbound

This paper cites Regularized 13-moment equations: shock structure calculations and comparison to Burnett models.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Regularized 13-moment equations: shock structure calculations and comparison to Burnett models

Reference 39

Resolution: verified exact; doi, observed 2026-06-29T06:03:07.743506Z

Source-reported events for the cited work

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Observation 0205d043-21d8-42d8-a3ce-89540ffb02b1 · outbound

This paper cites Xu, J.-C.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Xu, J.-C

Reference 40

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Observation 32a38c1e-6a09-4ac1-883b-5f7badea4b34 · outbound

This paper cites Filtered partial differential equations: a robust surrogate constraint in physics-informed deep learning framework.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Filtered partial differential equations: a robust surrogate constraint in physics-informed deep learning framework

Reference 41

Resolution: verified exact; doi, observed 2026-06-29T06:03:07.815638Z

Source-reported events for the cited work

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Observation f8818a8b-3f54-450d-be3d-7ce340895c75 · outbound

This paper cites Kerswell, and P.

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks Kerswell, and P

Reference 42

Resolution: verified exact; doi, observed 2026-06-29T06:03:07.805774Z

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Pith citing papers

Observation da3178f3-3e2b-47e8-baf7-3f548d95ccd9 · inbound

Closure-channel identifiability and two-channel recovery in monatomic kinetic normal shocks cites this paper.

Closure-channel identifiability and two-channel recovery in monatomic kinetic normal shocks Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks

Reference 48

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