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arxiv: 2511.21352 · v3 · pith:AOZWVO6Rnew · submitted 2025-11-26 · ⚛️ physics.flu-dyn

An octree-based sampling algorithm for analyzing big simulation data

Janis Geise , Sebastian Spinner , Richard Semaan , Andre Weiner This is my paper

Pith reviewed 2026-05-25 07:40 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords sparse spatial samplingoctree gridCFD data reductionflow simulationmodal decompositiondata compressionpost-processing
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The pith

The improved Sparse Spatial Sampling algorithm reduces CFD mesh cells by 35 to 95 percent while preserving dominant flow dynamics.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents an enhanced version of the Sparse Spatial Sampling algorithm that iteratively builds a time-invariant octree grid from a user-defined metric to down-sample large time-dependent flow simulation datasets. This approach targets preservation of the chosen metric across the data while cutting the number of mesh cells substantially. The resulting smaller grid supports memory-heavy post-processing steps such as modal decomposition without requiring high-performance computing resources. Tests on three distinct flow configurations confirm the cell reductions and show that key flow features remain intact for analysis purposes. The work directly addresses the storage and processing bottlenecks that arise as simulation sizes grow.

Core claim

The enhanced S^3 algorithm iteratively generates a time-invariant octree grid based on a user-defined metric, efficiently down-sampling the data while aiming to preserve as much of the metric as possible, which reduces mesh cells by 35 to 95 percent across tested cases and enables modal decomposition and similar tasks on local workstations.

What carries the argument

The time-invariant octree grid produced by iterative refinement according to a user-defined metric, which performs the down-sampling while targeting preservation of the metric values in the flow data.

If this is right

  • Post-processing steps that previously demanded HPC resources become feasible on standard workstations for many CFD cases.
  • Memory-intensive operations such as modal decomposition of flow snapshots can be applied to longer time series or larger domains.
  • The same sampling procedure applies across different flow regimes, from transonic airfoil wakes to high-Reynolds aircraft flows.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The method could be tested on simulation types outside fluid dynamics if analogous user-defined metrics are supplied for other physical fields.
  • Combining the octree sampling with existing data compression formats might yield further reductions without additional loss of dynamics.
  • Because the grid is time-invariant, it supports consistent feature tracking across entire simulation runs where adaptive grids would vary.

Load-bearing premise

The user-defined metric used to build the octree grid is assumed to be sufficient for capturing and preserving the dominant flow dynamics required by downstream analysis tasks.

What would settle it

A side-by-side comparison of modal decomposition modes or other flow statistics computed on the original mesh versus the S^3-sampled mesh that reveals large discrepancies in the dominant structures would falsify the preservation claim.

Figures

Figures reproduced from arXiv: 2511.21352 by Andre Weiner, Janis Geise, Richard Semaan, Sebastian Spinner.

Figure 1
Figure 1. Figure 1: The three main steps of S 3 . The stopping criterion is either the maximum number of leaf cells Nℓ,max or the minimum percentage of the original metric that must be captured. The depicted test case represents a generic tandem configuration of an ONERA OAT15A airfoil (front) and a NACA64A110 airfoil (rear). 5 [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The left column shows a comparison of the original grid (2a) and the grid generated by [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Temporal mean (left) and standard deviation (right) of the absolute spatial error ∆ [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of the leading POD modes and the associated singular values for the tandem configuration. [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of the leading right-singular vectors for the tandem configuration. As for the modes, only [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The left column shows a comparison of the original grid (6a) with the grid generated by [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The left column shows a comparison of the original grid (7a) with the grid generated by [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of the first four uneven POD modes and associated singular values for the original data (left [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Comparison of the first four uneven right-singular vectors for the cylinder test case. [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Original grid in the x-z-plane at x/MAC ≈ 4.9 (10a) and in the y-z-plane at y/MAC ≈ 0.9 (10b). The airfoil geometry is proprietary to Airbus and therefore redacted in fig. (10a). 14 [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Grid generated by S 3 in the x-z-plane at x/MAC ≈ 4.9 (11a) and the y-z-plane at y/MAC ≈ 0.9 (11b). The lower row shows the interpolated metric field in the same planes. The airfoil geometry is proprietary to Airbus and therefore redacted in fig. (11a) and (11c). 15 [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Isocontours of the first two POD modes based on the Mach number field for the grid generated by [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Cell count progression with respect to the captured metric (left) and composition of the meshing times [PITH_FULL_IMAGE:figures/full_fig_p017_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Convergence behavior of the metric-based refinement for the tandem configuration and the cylinder flow [PITH_FULL_IMAGE:figures/full_fig_p020_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: The left column shows the grid generated by [PITH_FULL_IMAGE:figures/full_fig_p021_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Comparison of the first four uneven POD modes and associated singular values for the original data [PITH_FULL_IMAGE:figures/full_fig_p022_16.png] view at source ↗
read the original abstract

As computational resources continue to increase, the storage and analysis of vast amounts of data will inevitably become a bottleneck in computational fluid dynamics (CFD) and related fields. Although compression algorithms and efficient data formats can mitigate this issue, they are often insufficient when post-processing large amounts of volume data. Processing such data may require additional high-performance software and resources, or it may restrict the analysis to shorter time series or smaller regions of interest. The present work proposes an improved version of the existing \emph{Sparse Spatial Sampling} algorithm ($S^3$) to reduce the data from time-dependent flow simulations. The $S^3$ algorithm iteratively generates a time-invariant octree grid based on a user-defined metric, efficiently down-sampling the data while aiming to preserve as much of the metric as possible. Using the sampled grid allows for more efficient post-processing and enables memory-intensive tasks, such as computing the modal decomposition of flow snapshots. The enhanced version of $S^3$ is tested and evaluated on the scale-resolving simulations of the flow past a tandem configuration of airfoils in the transonic regime, the incompressible turbulent flow past a circular cylinder, and the flow around an aircraft half-model at high Reynolds and Mach numbers. $S^3$ significantly reduces the number of mesh cells by $35 \%$ to $95\%$ for all test cases while accurately preserving the dominant flow dynamics, enabling post-processing of CFD data on a local workstation rather than HPC resources for many cases.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper proposes an improved Sparse Spatial Sampling (S^3) algorithm that iteratively constructs a time-invariant octree grid from time-dependent CFD data using a user-defined metric. The method aims to down-sample the mesh while preserving the metric, thereby enabling efficient post-processing such as modal decomposition on large simulation datasets. It reports cell reductions of 35-95% on three test cases (transonic tandem airfoils, incompressible cylinder flow, and high-Re/Mach aircraft half-model) and claims accurate preservation of dominant flow dynamics, allowing analysis on local workstations rather than HPC resources.

Significance. If the preservation of dominant dynamics can be shown quantitatively, the octree-based S^3 approach would offer a practical tool for handling storage and analysis bottlenecks in large-scale CFD, extending the utility of existing sampling methods to memory-intensive tasks without requiring full-grid resources. The iterative, metric-driven construction on multiple realistic flow configurations is a positive aspect of the work.

major comments (2)
  1. [Abstract] Abstract: the central claim that S^3 'accurately preserv[es] the dominant flow dynamics' and enables unaffected modal decomposition is unsupported by any quantitative metrics (e.g., L2-norm difference between POD modes, relative modal energy error, or reconstruction error) comparing full-grid versus S^3-grid results on the three test cases. This is load-bearing because the 35-95% cell reduction is only useful if downstream tasks remain reliable.
  2. [Abstract / Methods description] The user-defined metric is presented as sufficient to capture dominant dynamics, yet no validation (such as sensitivity tests or comparison against known modal structures) is described to confirm this assumption holds for the reported test cases. Without such checks, the preservation assertion cannot be evaluated.
minor comments (1)
  1. [Abstract] The abstract refers to an 'improved version' of S^3 but does not specify the precise algorithmic changes relative to prior work; a brief comparison would clarify novelty.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments correctly identify that stronger quantitative support is needed for the preservation claims. We address each point below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that S^3 'accurately preserv[es] the dominant flow dynamics' and enables unaffected modal decomposition is unsupported by any quantitative metrics (e.g., L2-norm difference between POD modes, relative modal energy error, or reconstruction error) comparing full-grid versus S^3-grid results on the three test cases. This is load-bearing because the 35-95% cell reduction is only useful if downstream tasks remain reliable.

    Authors: We agree that the abstract claim requires quantitative backing to be fully substantiated. The manuscript presents visual comparisons of POD modes and flow structures between the full and sampled grids, but does not include explicit error norms. In the revised version we will add L2-norm differences between corresponding POD modes, relative modal energy errors, and reconstruction errors for all three test cases to provide the requested quantitative evidence. revision: yes

  2. Referee: [Abstract / Methods description] The user-defined metric is presented as sufficient to capture dominant dynamics, yet no validation (such as sensitivity tests or comparison against known modal structures) is described to confirm this assumption holds for the reported test cases. Without such checks, the preservation assertion cannot be evaluated.

    Authors: The metric is selected to target the dominant coherent structures of each flow (shock-induced pressure fluctuations for the airfoils, vorticity for the cylinder, and surface pressure for the aircraft). The three test cases provide case-specific demonstrations, yet we acknowledge the absence of dedicated sensitivity or benchmark comparisons. We will incorporate sensitivity tests on the metric threshold and, for the cylinder case, direct comparison against well-documented Strouhal-number and modal structures from the literature. revision: yes

Circularity Check

0 steps flagged

No circularity; algorithm empirically validated on independent test cases

full rationale

The paper describes an iterative octree construction driven by a user-defined metric and reports cell reductions on three distinct external CFD simulations (tandem airfoils, cylinder, aircraft half-model). No mathematical derivation, fitted parameter renamed as prediction, or self-citation chain is load-bearing for the central claim. The preservation assertion is presented as an empirical outcome rather than a definitional identity. This matches the default expectation of a non-circular algorithmic paper with external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the effectiveness of a user-chosen metric for octree construction and the assumption that the resulting downsampled field retains sufficient information for modal analysis; these elements are not derived from first principles but supplied by the user or prior simulation data.

free parameters (1)
  • user-defined metric
    The octree grid is generated iteratively from a metric supplied by the user; its specific form is not fixed by the algorithm and must be chosen for each application.
axioms (1)
  • standard math An octree data structure can be constructed to represent 3D spatial fields at multiple resolutions
    Octrees are a standard hierarchical spatial partitioning technique in computational geometry.

pith-pipeline@v0.9.0 · 5802 in / 1424 out tokens · 59285 ms · 2026-05-25T07:40:03.208349+00:00 · methodology

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Reference graph

Works this paper leans on

25 extracted references · 25 canonical work pages

  1. [1]

    Common flow problems for modal analysis implemented in OpenFOAM

    Andre Weiner and Janis Geise. Common flow problems for modal analysis implemented in OpenFOAM . url: https://github.com/AndreWeiner/flow_data. 17

    work page

  2. [2]

    Kernel Learning for Robust Dynamic Mode Decomposition: Linear and Nonlinear Disambiguation Optimization (LANDO)

    P. J. Baddoo, B. Herrmann, B. J. McKeon, and S. L. Brunton. “Kernel Learning for Robust Dynamic Mode Decomposition: Linear and Nonlinear Disambiguation Optimization (LANDO)”. In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 478.2260 (2022), p. 20210830. doi: 10.1098/ rspa.2021.0830

    work page arXiv 2022

  3. [3]

    k-Nearest Neighbour Classifiers: 2nd Edition (with Python examples)

    P. Cunningham and S. J. Delany. “k-Nearest Neighbour Classifiers: 2nd Edition (with Python examples)”. In: ACM Computing Surveys 54.6 (2022), pp. 1–25. doi: 10.1145/3459665

    work page doi:10.1145/3459665 2022

  4. [4]

    State of the Art and Future Trends in Data Reduction for High-Performance Computing

    K. Duwe, J. L¨ uttgau, G. Mania, J. Squar, A. Fuchs, M. Kuhn, E. Betke, and T. Ludwig. “State of the Art and Future Trends in Data Reduction for High-Performance Computing”. In: Supercomputing Frontiers and Innovations 7.1 (2020). Number: 1, pp. 4–36. doi: 10.14529/jsfi200101

    work page doi:10.14529/jsfi200101 2020

  5. [5]

    OpenFOAM version 2206

    ESI Group. OpenFOAM version 2206. 2206. url: https://www.openfoam.com/news/main-news/openfoam- v2206

    work page

  6. [6]

    Sparse Spatial Sampling: A mesh sampling algorithm for efficient processing of big simulation data

    D. Fernex, A. Weiner, B. Noack, and R. Semaan. “Sparse Spatial Sampling: A mesh sampling algorithm for efficient processing of big simulation data”. In: AIAA Scitech 2021 Forum . AIAA SciTech Forum. American Institute of Aeronautics and Astronautics, 2021. doi: 10.2514/6.2021-1484

    work page doi:10.2514/6.2021-1484 2021

  7. [7]

    Geise and A

    J. Geise and A. Weiner. Git repository accompanying the article. 2024. url: https://github.com/JanisGeise/ sparseSpatialSampling

    work page 2024

  8. [8]

    Goodfellow, Y

    I. Goodfellow, Y. Bengio, and A. Courville. Deep Learning. MIT Press, 2016

    work page 2016

  9. [9]

    Machine-learning based error prediction approach for coarse-grid Computational Fluid Dynamics (CG-CFD)

    B. N. Hanna, N. T. Dinh, R. W. Youngblood, and I. A. Bolotnov. “Machine-learning based error prediction approach for coarse-grid Computational Fluid Dynamics (CG-CFD)”. In: Progress in Nuclear Energy 118 (2020), p. 103140. doi: 10.1016/j.pnucene.2019.103140

    work page doi:10.1016/j.pnucene.2019.103140 2020

  10. [10]

    Electricity 2024 - Analysis and forecast to 2026

    International Energy Agency. Electricity 2024 - Analysis and forecast to 2026 . IEA. 2024

    work page 2024

  11. [11]

    Data-driven correction of coarse grid CFD simulations

    A. Kiener, S. Langer, and P. Bekemeyer. “Data-driven correction of coarse grid CFD simulations”. In: Com- puters & Fluids 264 (2023), p. 105971. doi: 10.1016/j.compfluid.2023.105971

    work page doi:10.1016/j.compfluid.2023.105971 2023

  12. [12]

    Mesh reduction with error control

    R. Klein, G. Liebich, and W. Strasser. “Mesh reduction with error control”. In: Proceedings of Seventh Annual IEEE Visualization ’96 . Proceedings of Seventh Annual IEEE Visualization ’96. 1996, pp. 311–318. doi: 10.1109/VISUAL.1996.568124

    work page doi:10.1109/visual.1996.568124 1996

  13. [13]

    Kleinert, M

    J. Kleinert, M. Ehrle, A. Waldmann, and T. Lutz. Wake Tail Plane Interactions for a Tandem Wing Config- uration in High-Speed Stall Conditions . 2023. doi: 10.1007/s13272-023-00670-1

    work page doi:10.1007/s13272-023-00670-1 2023

  14. [14]

    Numerical simulation of wake interactions on a tandem wing configuration in high-speed stall conditions

    J. Kleinert, J. Stober, and T. Lutz. “Numerical simulation of wake interactions on a tandem wing configuration in high-speed stall conditions”. In: CEAS Aeronautical Journal 14.1 (2023), pp. 171–186. doi: 10 . 1007 / s13272-022-00634-x

    work page 2023

  15. [15]

    J. Lee, K. S. Jung, Q. Gong, X. Li, S. Klasky, J. Chen, A. Rangarajan, and S. Ranka. Machine Learning Techniques for Data Reduction of CFD Applications . 2024. doi: 10.48550/arXiv.2404.18063

    work page doi:10.48550/arxiv.2404.18063 2024

  16. [16]

    Low-frequency unsteadiness in the vortex formation region of a circular cylinder

    O. Lehmkuhl, I. Rodr´ ıguez, R. Borrell, and A. Oliva. “Low-frequency unsteadiness in the vortex formation region of a circular cylinder”. In: Physics of Fluids 25.8 (2013), p. 085109. doi: 10.1063/1.4818641

    work page doi:10.1063/1.4818641 2013

  17. [17]

    Mesh deep Q network: A deep reinforcement learning framework for improving meshes in computational fluid dynamics

    C. Lorsung and A. Barati Farimani. “Mesh deep Q network: A deep reinforcement learning framework for improving meshes in computational fluid dynamics”. In: AIP Advances 13.1 (2023), p. 015026. doi: 10.1063/ 5.0138039

    work page 2023

  18. [18]

    Scikit-learn: Machine Learning in Python

    F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, E. Duchesnay, and G. Louppe. “Scikit-learn: Machine Learning in Python”. In: Journal of Machine Learning Research 12 (2012)

    work page 2012

  19. [19]

    Self-Supervised Coarsening of Unstruc- tured Grid with Automatic Differentiation

    S. Shumilin, A. Ryabov, N. Yavich, E. Burnaev, and V. Vanovskiy. “Self-Supervised Coarsening of Unstruc- tured Grid with Automatic Differentiation”. In: Forty-first International Conference on Machine Learning. 2024

    work page 2024

  20. [21]

    doi: 10.2514/1.C038119

    work page doi:10.2514/1.c038119

  21. [22]

    url: https://www.for2895.uni-stuttgart.de/

    Unsteady flow and interaction phenomena at High Speed Stall conditions, research unit FOR 2895 . url: https://www.for2895.uni-stuttgart.de/. 18

    work page

  22. [23]

    flowTorch - a Python library for analysis and reduced-order modeling of fluid flows

    A. Weiner and R. Semaan. “flowTorch - a Python library for analysis and reduced-order modeling of fluid flows”. In: Journal of Open Source Software 6.68 (2021), p. 3860. doi: 10.21105/joss.03860

    work page doi:10.21105/joss.03860 2021

  23. [24]

    Robust Dynamic Mode Decomposition Methodology for an Airfoil Undergoing Transonic Shock Buffet

    A. Weiner and R. Semaan. “Robust Dynamic Mode Decomposition Methodology for an Airfoil Undergoing Transonic Shock Buffet”. In: AIAA Journal 61.10 (2023). Publisher: American Institute of Aeronautics and Astronautics, pp. 4456–4467. doi: 10.2514/1.J062546

    work page doi:10.2514/1.j062546 2023

  24. [25]

    A Tutorial on the Proper Orthogonal Decomposition

    J. Weiss. “A Tutorial on the Proper Orthogonal Decomposition”. In: AIAA Aviation 2019 Forum . AIAA AVIATION Forum. American Institute of Aeronautics and Astronautics, 2019. doi: 10.2514/6.2019-3333

    work page doi:10.2514/6.2019-3333 2019

  25. [26]

    Note on a Method for Calculating Corrected Sums of Squares and Products

    B. P. Welford. “Note on a Method for Calculating Corrected Sums of Squares and Products”. In:Technometrics 4.3 (1962). Publisher: ASA Website, pp. 419–420. doi: 10.1080/00401706.1962.10490022. 19 A Appendix A.1 Singular value decomposition This section summarizes the fundamentals of the singular value decomposition, which is used in section 3 to compare t...

    work page doi:10.1080/00401706.1962.10490022 1962