Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T18:09:49.139663Z
Paper Citation Record · LEDGER
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.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T18:09:49.139663Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
61 of 61 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 32f15b66-cd77-4281-bc9a-d1352732e68c · outbound
Reference 1
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.
Observation ae92db72-065c-46d1-99d0-7a1f05ab1365 · outbound
Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Unresolved cited work
Reference 2
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.
Observation 13b786e6-dfe4-49e0-8483-d4e43496ea38 · outbound
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
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.
Observation 8dd7293d-9ae6-41ed-a372-f78e5e7b43ce · outbound
Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Turbulent flows
Reference 4
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.
Observation 758a4c41-60e2-4836-a554-71664c40628c · outbound
Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Unresolved cited work
Reference 5
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.
Observation 5b390485-cbe8-4192-a9e9-e8f0ab9db21e · outbound
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
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.
Observation b611196a-0302-4483-9a14-8b16869a1cc3 · outbound
Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Department of Energy
Reference 7
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.
Observation b81024b1-b2f2-45ed-83d4-93cdfefd767b · outbound
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
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.
Observation e7e3838c-383e-404c-9ed2-f05fefa1aa6d · outbound
Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Machine learning for fluid mechanics
Reference 9
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.
Observation 17915044-0fa5-4097-a0c9-c4d94a3daac9 · outbound
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
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.
Observation 75438fda-d2c1-4e1d-8487-cf918bf2ff9b · outbound
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
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.
Observation 8c8f205b-b01e-47bc-a755-2fb181509048 · outbound
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
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.
Observation 62acb3da-2bfb-40cf-bfd8-6b4bfe983bf0 · outbound
Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Lattice boltzmann method for fluid flows
Reference 13
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.
Observation 723d040b-6573-4598-b370-07df6a3f453f · outbound
Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks The lattice boltzmann method
Reference 14
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.
Observation c9ebdca3-ec3d-45d0-ab03-516e3d16ab19 · outbound
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
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.
Observation 83290e48-6f31-446e-b394-7f1c20f43928 · outbound
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
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.
Observation 500cf7a8-f141-4143-a836-3a15406c0ab8 · outbound
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
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.
Observation faadcae9-1e02-4c10-baa1-a492518c0e30 · outbound
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
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.
Observation a5365413-aae1-452b-925f-e6d40f17fb61 · outbound
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
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.
Observation 81e44e6f-f912-40eb-b451-c59bf4e5f395 · outbound
Reference 20
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.
Observation e308edcf-1e52-4eec-a0b2-8c92b13aa5bd · outbound
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
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.
Observation d76328ca-817f-42ed-a021-d3e588d2eece · outbound
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
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.
Observation e804082f-d7f4-4a96-b2fc-8fdbc9d0d65c · outbound
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
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.
Observation c1a3e7ce-ccc0-4066-add5-9748726070ce · outbound
Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Hosseini, M
Reference 24
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.
Observation fa3fb1d6-e0f2-4a4f-86d4-34462942532d · outbound
Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Lettuce: Pytorch-based lattice boltzmann framework
Reference 25
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.
Observation cfb8c3ce-06ab-40d9-b13b-217591f9fecb · outbound
Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Toward learning lattice boltzmann collision operators
Reference 26
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.
Observation 012461f4-bb39-4df4-8a80-789ebe09cdc8 · outbound
Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Pseudoentropic derivation of the regularized lattice boltzmann method
Reference 27
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.
Observation 812447f3-57f6-4629-88c9-a371ff744f7d · outbound
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
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.
Observation d731bbbd-067f-45f4-84e2-0e5224892da4 · outbound
Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Kinetic data-driven approach to turbulence subgrid modeling
Reference 29
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.
Observation 2f6d8a2f-0fac-40db-b2e5-03fe06741b41 · outbound
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
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.
Observation a1576d94-51f7-4202-ab59-d52cf1a828b7 · outbound
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
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.
Observation 94cf1b5e-b690-4814-9a24-6987429cc716 · outbound
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
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.
Observation dc04bf84-727e-4d8e-9649-ea8df339040b · outbound
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
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.
Observation 390f6e2f-822e-4df6-aead-618ea1aea81c · outbound
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
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.
Observation e3839b14-8425-477b-bb83-a88b04f396c5 · outbound
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
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.
Observation 8729ee96-261f-4b1b-8189-5d3c0ef67113 · outbound
Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Group equivariant con- volutional networks
Reference 36
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.
Observation ba63bd90-17d3-4a30-ab97-2263b9bdd4a3 · outbound
Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Equivariant convolutional networks
Reference 37
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.
Observation 0678a111-e072-4b4a-b0c3-7acf8805215c · outbound
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
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.
Observation 497a9f70-7a29-487f-ac4f-e9e8e0958b59 · outbound
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
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.
Observation d0a40c7e-4c06-4b38-af53-0ca4706f9ea8 · outbound
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
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.
Observation 1ed4dd52-b640-493e-bba0-5726ef0fb9f5 · outbound
Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Fiorina and S
Reference 41
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.
Observation 613fcb6d-d322-4171-93a5-cbb2a775bf42 · outbound
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
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.
Observation 837a975a-dcb8-48e2-9c95-50fe22082220 · outbound
Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Random forcing of three-dimensional homogeneous turbulence
Reference 43
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.
Observation 980e4e25-fdb1-4f60-a2e4-0513400f15c6 · outbound
Reference 44
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.
Observation 285630d4-8bc6-4cee-9dbe-7f4c92d8d6df · outbound
Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Unresolved cited work
Reference 45
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.
Observation 57c0bfec-435c-4e51-b77b-d0c3c7c333c5 · outbound
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
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.
Observation 55f42735-634f-4f5f-8b75-893be1ce246d · outbound
Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Stolz and N.A
Reference 47
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.
Observation cd0ad254-1d4f-452b-947c-6a3efc7a948b · outbound
Reference 48
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.
Observation 07f5474c-6886-4e1f-b9b4-6f105a97152f · outbound
Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks High-order cfd methods: current status and perspective
Reference 49
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.
Observation 86fbdc79-e2dd-45ba-9e1a-37b17c256aff · outbound
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
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.
Observation 314bc63f-4fda-4876-8535-4c40cfc19fa3 · outbound
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
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.
Observation 6a74e748-8a85-4e43-bafd-39891f21d146 · outbound
Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Cambridge University Press, 2007
Reference 52
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.
Observation 46d6b88a-2e4c-494c-868b-d63a29fd3e7a · outbound
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
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.
Observation ae23abbe-9c5e-45bc-99bd-361f87513457 · outbound
Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Small-scale structure of the taylor–green vortex
Reference 54
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.
Observation 29b883f3-7600-4e81-aa7f-abcea9f0feb9 · outbound
Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks An immersed boundary method for complex incompressible flows
Reference 55
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.
Observation a71283a4-b210-438d-b2f4-99a19700af2c · outbound
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
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.
Observation a42e035c-1baf-4aea-9fb1-26f866263f11 · outbound
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
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.
Observation de6f5a14-7a39-40ad-963e-c31d472cea63 · outbound
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
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.
Observation 768e7ec7-61d8-4aeb-8eb0-582c8dfa2d0e · outbound
Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks Preconditioned multigrid methods for unsteady incompressible flows
Reference 59
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.
Observation a613cc5b-84f8-46d1-8ab1-d64c153b6c17 · outbound
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
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.
Observation 814ec784-c9d9-43c9-9d9d-ebae84d82c91 · outbound
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
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.
No inbound Pith citation observations are available.