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Paper Citation Record · LEDGER

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks

As of 23 August 2026, this Paper Citation Record lists 61 of 61 outbound references and 0 inbound Pith citation observations for arXiv:2412.08229.

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pith.paper-citation-record.v1
2412.08229 v1

Coverage vector

measured 61 of 61 reference resolution

Typed states for the displayed outbound observations.

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measured 61 of 61 standing notices

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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

61 of 61 outbound references displayed

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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 32f15b66-cd77-4281-bc9a-d1352732e68c · outbound

This paper cites Kovasznay.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Kovasznay

Reference 1

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Observation ae92db72-065c-46d1-99d0-7a1f05ab1365 · outbound

This paper cites an unresolved cited work.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Unresolved cited work

Reference 2

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Observation 13b786e6-dfe4-49e0-8483-d4e43496ea38 · outbound

This paper cites For clarity, it is defined as ∇(n) = ∇(n) α1...αn = ∂ ∂xa1.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks For clarity, it is defined as ∇(n) = ∇(n) α1...αn = ∂ ∂xa1

Reference 3

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Observation 8dd7293d-9ae6-41ed-a372-f78e5e7b43ce · outbound

This paper cites Turbulent flows.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Turbulent flows

Reference 4

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Observation 758a4c41-60e2-4836-a554-71664c40628c · outbound

This paper cites an unresolved cited work.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Unresolved cited work

Reference 5

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Observation 5b390485-cbe8-4192-a9e9-e8f0ab9db21e · outbound

This paper cites Extreme flow simulations reveal skeletal adaptations of deep-sea sponges.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Extreme flow simulations reveal skeletal adaptations of deep-sea sponges

Reference 6

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Observation b611196a-0302-4483-9a14-8b16869a1cc3 · outbound

This paper cites Department of Energy.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Department of Energy

Reference 7

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Source-reported events for the cited work

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Observation b81024b1-b2f2-45ed-83d4-93cdfefd767b · outbound

This paper cites The lattice boltzmann equation: A new tool for computa- tional fluid-dynamics.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks The lattice boltzmann equation: A new tool for computa- tional fluid-dynamics

Reference 8

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Observation e7e3838c-383e-404c-9ed2-f05fefa1aa6d · outbound

This paper cites Machine learning for fluid mechanics.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Machine learning for fluid mechanics

Reference 9

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Observation 17915044-0fa5-4097-a0c9-c4d94a3daac9 · outbound

This paper cites Physics- informed machine learning approach for reconstructing reynolds stress modeling discrepancies based on dns data.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Physics- informed machine learning approach for reconstructing reynolds stress modeling discrepancies based on dns data

Reference 10

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Source-reported events for the cited work

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Observation 75438fda-d2c1-4e1d-8487-cf918bf2ff9b · outbound

This paper cites A primer on di- rect numerical simulation of turbulence – methods, pro- cedures and guidelines.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks A primer on di- rect numerical simulation of turbulence – methods, pro- cedures and guidelines

Reference 11

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Observation 8c8f205b-b01e-47bc-a755-2fb181509048 · outbound

This paper cites Deep fluids: A generative network for parameterized fluid simulations.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Deep fluids: A generative network for parameterized fluid simulations

Reference 12

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation 62acb3da-2bfb-40cf-bfd8-6b4bfe983bf0 · outbound

This paper cites Lattice boltzmann method for fluid flows.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Lattice boltzmann method for fluid flows

Reference 13

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Observation 723d040b-6573-4598-b370-07df6a3f453f · outbound

This paper cites The lattice boltzmann method.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks The lattice boltzmann method

Reference 14

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation c9ebdca3-ec3d-45d0-ab03-516e3d16ab19 · outbound

This paper cites Subgrid modelling for two-dimensional turbu- lence using neural networks.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Subgrid modelling for two-dimensional turbu- lence using neural networks

Reference 15

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation 83290e48-6f31-446e-b394-7f1c20f43928 · outbound

This paper cites Lattice Boltzmann simulations on irregular grids: Introduction of the NATriuM library.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Lattice Boltzmann simulations on irregular grids: Introduction of the NATriuM library

Reference 16

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Source-reported events for the cited work

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Observation 500cf7a8-f141-4143-a836-3a15406c0ab8 · outbound

This paper cites High-order semi-lagrangian kinetic scheme for compressible turbulence.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks High-order semi-lagrangian kinetic scheme for compressible turbulence

Reference 17

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verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation faadcae9-1e02-4c10-baa1-a492518c0e30 · outbound

This paper cites Progress of discrete unified gas- kinetic scheme for multiscale flows.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Progress of discrete unified gas- kinetic scheme for multiscale flows

Reference 18

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation a5365413-aae1-452b-925f-e6d40f17fb61 · outbound

This paper cites Semi-lagrangian off-lattice boltzmann method for weakly compressible flows.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Semi-lagrangian off-lattice boltzmann method for weakly compressible flows

Reference 19

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation 81e44e6f-f912-40eb-b451-c59bf4e5f395 · outbound

This paper cites Ricot, S.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Ricot, S

Reference 20

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Source-reported events for the cited work

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Observation e308edcf-1e52-4eec-a0b2-8c92b13aa5bd · outbound

This paper cites Gibbs’ principle for the lattice-kinetic theory of fluid dy- namics.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Gibbs’ principle for the lattice-kinetic theory of fluid dy- namics

Reference 21

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Observation d76328ca-817f-42ed-a021-d3e588d2eece · outbound

This paper cites The cumulant lattice boltzmann equation in three dimensions: Theory and validation.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks The cumulant lattice boltzmann equation in three dimensions: Theory and validation

Reference 22

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No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation e804082f-d7f4-4a96-b2fc-8fdbc9d0d65c · outbound

This paper cites Interface-capturing lattice boltzmann equation model for two-phase flows.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Interface-capturing lattice boltzmann equation model for two-phase flows

Reference 23

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No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation c1a3e7ce-ccc0-4066-add5-9748726070ce · outbound

This paper cites Hosseini, M.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Hosseini, M

Reference 24

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation fa3fb1d6-e0f2-4a4f-86d4-34462942532d · outbound

This paper cites Lettuce: Pytorch-based lattice boltzmann framework.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Lettuce: Pytorch-based lattice boltzmann framework

Reference 25

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verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation cfb8c3ce-06ab-40d9-b13b-217591f9fecb · outbound

This paper cites Toward learning lattice boltzmann collision operators.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Toward learning lattice boltzmann collision operators

Reference 26

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation 012461f4-bb39-4df4-8a80-789ebe09cdc8 · outbound

This paper cites Pseudoentropic derivation of the regularized lattice boltzmann method.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Pseudoentropic derivation of the regularized lattice boltzmann method

Reference 27

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation 812447f3-57f6-4629-88c9-a371ff744f7d · outbound

This paper cites Enhancing lattice kinetic schemes for fluid dynamics with Lattice-Equivariant Neural Networks.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Enhancing lattice kinetic schemes for fluid dynamics with Lattice-Equivariant Neural Networks

Reference 28

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation d731bbbd-067f-45f4-84e2-0e5224892da4 · outbound

This paper cites Kinetic data-driven approach to turbulence subgrid modeling.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Kinetic data-driven approach to turbulence subgrid modeling

Reference 29

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verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation 2f6d8a2f-0fac-40db-b2e5-03fe06741b41 · outbound

This paper cites Xlb: A differentiable massively parallel lattice boltzmann li- brary in python.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Xlb: A differentiable massively parallel lattice boltzmann li- brary in python

Reference 30

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raw_fallback, observed 2026-08-11T18:09:49.578378Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation a1576d94-51f7-4202-ab59-d52cf1a828b7 · outbound

This paper cites Lattice boltzmann method with ar- tificial bulk viscosity using a neural collision operator.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Lattice boltzmann method with ar- tificial bulk viscosity using a neural collision operator

Reference 31

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verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation 94cf1b5e-b690-4814-9a24-6987429cc716 · outbound

This paper cites Theory of the lattice boltzmann method: Dispersion, dissipation, isotropy, galilean invariance, and stability.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Theory of the lattice boltzmann method: Dispersion, dissipation, isotropy, galilean invariance, and stability

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.558469Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.058060Z digest=sha256:f413c772e716434332dde727dd4645ba046637ce4d0dedb11ebb094db9d14630

Observation dc04bf84-727e-4d8e-9649-ea8df339040b · outbound

This paper cites Incompressible limits of lattice boltzmann equations using multiple relaxation times.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Incompressible limits of lattice boltzmann equations using multiple relaxation times

Reference 33

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verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.550332Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation 390f6e2f-822e-4df6-aead-618ea1aea81c · outbound

This paper cites However, these sets are chosen as constant values through the simulation and do not adapt to dynamic changes including laminar- turbulent transition.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks However, these sets are chosen as constant values through the simulation and do not adapt to dynamic changes including laminar- turbulent transition

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.884637Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:48.938072Z digest=sha256:831d70e86bc8a2b1584115e99153dfc50fc312c6fb2029005dea5d58789b516f

Observation e3839b14-8425-477b-bb83-a88b04f396c5 · outbound

This paper cites Investigation of a con- tinuous adjoint-based optimization procedure for aeroa- coustic control of plane jets.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Investigation of a con- tinuous adjoint-based optimization procedure for aeroa- coustic control of plane jets

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.568765Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.054178Z digest=sha256:3ebd7145d2127a2e095327622ddee275349b7409ba31270796969b465bcb3cb7

Observation 8729ee96-261f-4b1b-8189-5d3c0ef67113 · outbound

This paper cites Group equivariant con- volutional networks.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Group equivariant con- volutional networks

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.523037Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.071610Z digest=sha256:02c7a44bf3bc9bf69a609b101925d6a88b2b11efc02bb14d7a5a0c1415b979ee

Observation ba63bd90-17d3-4a30-ab97-2263b9bdd4a3 · outbound

This paper cites Equivariant convolutional networks.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Equivariant convolutional networks

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.513646Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.074718Z digest=sha256:af94d1402ee9b1c55b701b413701f717832c32d0324eedb6f3c1f39a180f91bd

Observation 0678a111-e072-4b4a-b0c3-7acf8805215c · outbound

This paper cites Linear and brute force stability of orthogonal moment multiple-relaxation- time lattice boltzmann methods applied to homogeneous isotropic turbulence.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Linear and brute force stability of orthogonal moment multiple-relaxation- time lattice boltzmann methods applied to homogeneous isotropic turbulence

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.542085Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.065026Z digest=sha256:5c420232aa16c802a27ffbc767d6e4f83b33658a36706f7c8710786231e7ea4e

Observation 497a9f70-7a29-487f-ac4f-e9e8e0958b59 · outbound

This paper cites This method in- volves a force function ˆFα (k, t) in a Fourier space that distributes the force across a range of small wave num- bers facilitated by randomly generated phases.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks This method in- volves a force function ˆFα (k, t) in a Fourier space that distributes the force across a range of small wave num- bers facilitated by randomly generated phases

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.864023Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:48.945922Z digest=sha256:4e713754801df5421c09706431cb2cd2993015692751253ebfa2f5605e954976

Observation d0a40c7e-4c06-4b38-af53-0ca4706f9ea8 · outbound

This paper cites On equations of state in a lat- tice boltzmann method.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks On equations of state in a lat- tice boltzmann method

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.533424Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.068230Z digest=sha256:0f1e13f709e8ba16298d669ee416f85a1f30100d5facebaada6d40e93dd75ca6

Observation 1ed4dd52-b640-493e-bba0-5726ef0fb9f5 · outbound

This paper cites Fiorina and S.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Fiorina and S

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.473592Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.088857Z digest=sha256:39fbf88a13622964baf9f9d8cdf9493a62221b437c550c8baeab14541354e5f2

Observation 613fcb6d-d322-4171-93a5-cbb2a775bf42 · outbound

This paper cites Comments on the Kolmogorov hypothe- sis of local isotropy in the smallscales.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Comments on the Kolmogorov hypothe- sis of local isotropy in the smallscales

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.503287Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.077993Z digest=sha256:5505bd6ac5adeeb582813fd3964eb9d853c80cd288caa143b3e5c85a35270238

Observation 837a975a-dcb8-48e2-9c95-50fe22082220 · outbound

This paper cites Random forcing of three-dimensional homogeneous turbulence.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Random forcing of three-dimensional homogeneous turbulence

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.493159Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.081172Z digest=sha256:6d84adb21955bff2a8939541a7859b93a05d65dbbcac67f8f322ce4ef581744d

Observation 980e4e25-fdb1-4f60-a2e4-0513400f15c6 · outbound

This paper cites Mathew, H.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Mathew, H

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.483365Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.085567Z digest=sha256:603066af80a24e40090be0b3370ba53182bc1a27c375ac42c6eac31d330ffea2

Observation 285630d4-8bc6-4cee-9dbe-7f4c92d8d6df · outbound

This paper cites an unresolved cited work.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Unresolved cited work

Reference 45

Resolution
unresolved
raw_fallback, observed 2026-08-11T18:09:49.435155Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.101927Z digest=sha256:9b3d4ddc48b3e8ce5abf2cf3c2d6e62b1637b25bfc6493a7d900f34de9527f2f

Observation 57c0bfec-435c-4e51-b77b-d0c3c7c333c5 · outbound

This paper cites Lattice Boltzmann method with regularized pre-collision distribution func- tions.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Lattice Boltzmann method with regularized pre-collision distribution func- tions

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.464120Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.092051Z digest=sha256:e56adb26f9c085b04f7c5a0c7d886105d939fd1f9292a178b8291e75e07b288b

Observation 55f42735-634f-4f5f-8b75-893be1ce246d · outbound

This paper cites Stolz and N.A.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Stolz and N.A

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.454182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.094969Z digest=sha256:779d31ca41fc406508a69e9b9fbdf533aa1cb9cbcff1db00c80f1f41a4eb20a1

Observation cd0ad254-1d4f-452b-947c-6a3efc7a948b · outbound

This paper cites Mathew, R.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Mathew, R

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.443869Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.098608Z digest=sha256:9915844baeeff2d33350b3f63b5e18c8cd8add5ffb3fab443979aead45a9dbb5

Observation 07f5474c-6886-4e1f-b9b4-6f105a97152f · outbound

This paper cites High-order cfd methods: current status and perspective.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks High-order cfd methods: current status and perspective

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.395596Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.117272Z digest=sha256:1e730215fd72650e5b968ef842bd4e13364f241751763ee4c2a386eed146bf39

Observation 86fbdc79-e2dd-45ba-9e1a-37b17c256aff · outbound

This paper cites The fundamental bgk operator calculates the predicted profiles with con- siderable accuracy but lacks stability when the flow field becomes turbulent.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks The fundamental bgk operator calculates the predicted profiles with con- siderable accuracy but lacks stability when the flow field becomes turbulent

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.855383Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:48.950002Z digest=sha256:59eee8424ae5bb3de2a636199f6a6d5bf20412fb6038e33035fff4e4b98449b8

Observation 314bc63f-4fda-4876-8535-4c40cfc19fa3 · outbound

This paper cites A comparison of second- and sixth-order methods for large-eddy simulations.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks A comparison of second- and sixth-order methods for large-eddy simulations

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.425777Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.105919Z digest=sha256:9faf536075370504280d0b4836f63fe063553f2a172094d302c380c2775f1b21

Observation 6a74e748-8a85-4e43-bafd-39891f21d146 · outbound

This paper cites Cambridge University Press, 2007.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Cambridge University Press, 2007

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.415458Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.109713Z digest=sha256:74adced1a9602d9fda36ae05c6f75d6992071e00c428b1fede21c9d5837b9077

Observation 46d6b88a-2e4c-494c-868b-d63a29fd3e7a · outbound

This paper cites Implicit Large-Eddy Simulation: Theory and Application , pages 743–750.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Implicit Large-Eddy Simulation: Theory and Application , pages 743–750

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.405753Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.113852Z digest=sha256:3ccdfbe2c5f0a332e42cb6a7eddfdd0e1884409e08ae6fe4ef098e26d8b67b07

Observation ae23abbe-9c5e-45bc-99bd-361f87513457 · outbound

This paper cites Small-scale structure of the taylor–green vortex.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Small-scale structure of the taylor–green vortex

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.384914Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.120741Z digest=sha256:ff303889ae155d736b192277f61d90370925685f52acf6fabe746b1da2e2ed50

Observation 29b883f3-7600-4e81-aa7f-abcea9f0feb9 · outbound

This paper cites An immersed boundary method for complex incompressible flows.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks An immersed boundary method for complex incompressible flows

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.374797Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.123394Z digest=sha256:a02644a28bbd323f393641722fa325dce4347f4ddaa0266952983a8c5d5738de

Observation a71283a4-b210-438d-b2f4-99a19700af2c · outbound

This paper cites Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.365101Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.125996Z digest=sha256:321e7efed5e15e5ac357d04768ee3387b20b4060d2aed4e16627f444b9869a99

Observation a42e035c-1baf-4aea-9fb1-26f866263f11 · outbound

This paper cites A cartesian grid method for modeling multiple moving objects in 2d incompress- ible viscous flow.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks A cartesian grid method for modeling multiple moving objects in 2d incompress- ible viscous flow

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.353403Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.128532Z digest=sha256:f143e6949e5140ddab9782aebfb79b130f49b64db63cfb0ab916b435f266dfcb

Observation de6f5a14-7a39-40ad-963e-c31d472cea63 · outbound

This paper cites A novel immersed boundary velocity correction–lattice boltz- mann method and its application to simulate flow past a circular cylinder.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks A novel immersed boundary velocity correction–lattice boltz- mann method and its application to simulate flow past a circular cylinder

Reference 58

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.219514Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.131152Z digest=sha256:fe0e6f433fe6fc93c5dd95def6acab0942a6b1cb137a16a5c1e9b17769ecb31e

Observation 768e7ec7-61d8-4aeb-8eb0-582c8dfa2d0e · outbound

This paper cites Preconditioned multigrid methods for unsteady incompressible flows.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Preconditioned multigrid methods for unsteady incompressible flows

Reference 59

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.209187Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.133893Z digest=sha256:036b2e7f22f5fda964afcf682b1b787a3fba6a74cf074c0a529e19a94d4013cb

Observation a613cc5b-84f8-46d1-8ab1-d64c153b6c17 · outbound

This paper cites An edge-based method for the incompressible navier–stokes equations on polygonal meshes.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks An edge-based method for the incompressible navier–stokes equations on polygonal meshes

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.197605Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.136889Z digest=sha256:85e570298ce63d1e35d1cbc8621f2ea520a0a5c1e1eb12dd5409855f21c2195d

Observation 814ec784-c9d9-43c9-9d9d-ebae84d82c91 · outbound

This paper cites Characteristics of the plane turbulent near wake of a circular cylinder.

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Characteristics of the plane turbulent near wake of a circular cylinder

Reference 61

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:09:49.185945Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T18:09:49.139663Z digest=sha256:7d596da287396d728d7a28c5bc2a477a35cb4c53f5604eb1954ebb14cad29198

Pith citing papers

No inbound Pith citation observations are available.