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REVIEW 3 major objections 6 minor 47 references

An AI agent that cleans shear from velocity gradients can invent a better turbulence model on its own.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review · grok-4.5

2026-07-11 22:20 UTC pith:CVOENVKD

load-bearing objection Clean open TDM automation plus a simple, physically motivated SGS form; the agentic end-to-end claim is real but rests on one narrow a-posteriori test whose gains may largely be reduced dissipation. the 3 major comments →

arxiv 2607.04009 v1 pith:CVOENVKD submitted 2026-07-04 physics.flu-dyn

PhysMiner: An Agentic AI Framework for Discovering Turbulence Physics

Jiawei Chen , Han Gao , Ping He This is my paper
classification physics.flu-dyn
keywords triple decompositionvelocity gradient tensorsubgrid-scale modelingagentic AIturbulence physics discoveryperiodic hillshear contaminationvortex identification
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

PhysMiner is an automated pipeline that takes raw turbulent flow data, decomposes the velocity-gradient tensor into pure shear, rigid rotation and normal strain, and then lets language-model agents read the resulting statistics, contours and literature keywords to propose physical mechanisms and modeling fixes. Conventional gradient analysis mixes pure shear into vorticity, so vortices look fake and models over-dissipate; the triple-decomposition step removes that contamination and hands the agents clean, threshold-free vortex measures. Validated on five flows from isotropic decay to propeller wakes, the full loop is closed on the periodic-hill case: the agents recommend a simple rotation-suppression factor for the Smagorinsky eddy viscosity and the resulting model improves Reynolds-stress profiles against experiment. A growing library stores each successful case so later flows can be compared by structural similarity, letting the system accumulate inductive knowledge rather than starting from scratch every time. The practical claim is that shear-clean kinematics plus agentic review can turn CFD snapshots into usable turbulence-model upgrades without hand-tuned thresholds or expert post-processing.

Core claim

When the velocity-gradient tensor is automatically split into pure shear, rigid rotation and normal strain, language-model agents can read the resulting statistics and literature keywords, then autonomously propose and validate a rotation-suppressed Smagorinsky model whose Reynolds-stress predictions on the periodic-hill flow beat both the standard and coefficient-tuned baselines.

What carries the argument

Triple decomposition of the velocity gradient (G = G_N + G_R + G_S) together with its relative strengths gg_rr, gg_ps and gg_ns; these feed a Discover-Physics agent whose drafts are iteratively filtered by a Review agent against logical, dimensional and physical-consistency checks, while a Jaccard-tree library supplies cross-case analogies.

Load-bearing premise

The multi-agent loop plus a library of only five prior cases is assumed to be enough to generate modeling advice that is physically sound and not merely over-fitted to the single a-posteriori test flow.

What would settle it

Apply the identical end-to-end pipeline, without human intervention, to a new separated flow (for example a higher-Reynolds-number hill or a wing with ice-induced separation) and check whether the automatically generated SGS model still improves Reynolds-stress profiles relative to the same baselines.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Threshold-free vortex cores extracted from gg_rr can replace multi-threshold Q-criterion plots in routine post-processing of engineering LES.
  • Near-wall asymptotic vanishing of gg_rr, gg_ns and gg_rs supplies a natural damping mechanism that removes the need for ad-hoc van-Driest functions in algebraic SGS models.
  • Each new validated case added to the Triple Decomposition Library tightens the Jaccard-tree search, so later discoveries become increasingly informed by prior structural analogies.
  • The same dual-track (literature word-cloud + clean kinematics) workflow can be pointed at other modeling bottlenecks such as transition or multiphase interfaces once the library contains matching fingerprints.

Where Pith is reading between the lines

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

  • If the library grows to hundreds of cases, the same agent loop could systematically test whether pure-shear dominance is truly universal across Reynolds numbers and geometries, turning a five-case observation into a quantitative scaling law.
  • The rotation-suppression factor (1 − gg_rr) is simple enough that it could be inserted into existing industrial LES codes with only a one-line change, offering a low-risk path to community-wide a-posteriori checks.
  • Because the Review agent already enforces dimensional consistency, the same closed loop might later be used to co-discover both the functional form and the numerical coefficients of more elaborate triad-driven closures without separate calibration campaigns.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. PhysMiner is an agentic pipeline that couples an automated triple decomposition (TDM) of the velocity-gradient tensor with LLM-based Discover-Physics and Review agents and a self-evolving Triple Decomposition Library. The TDM module is exercised on five flows (DIT, channel, BFS, periodic hill, propeller), producing contours, domain/streamwise statistics, threshold-insensitive vortex identification via gg_rr, and vortex-core lines. On the periodic hill the full pipeline proposes two SGS strategies; Proposal 1, ν_t = C_s² Δ² |S| (1−gg_rr), is implemented a posteriori and compared with standard and retuned Smagorinsky models, showing improved Reynolds-stress profiles at x/h = 0.5, 2.0 and 6.0. The library uses Jaccard-tree distance on a 27-category fingerprint to transfer knowledge (e.g., hill vs BFS).

Significance. If the end-to-end claim holds, the work would be a concrete step beyond CFD-workflow automation toward agent-assisted mechanism discovery and model formulation in turbulence. Strengths that should be credited: (i) clean, fully automatic TDM post-processing validated across five regimes with clear elimination of shear contamination; (ii) threshold-insensitive vortex diagnostics and core-line extraction grounded in the rigid-rotation component; (iii) open-source release with a community contribution path; (iv) an SGS form motivated by observed near-wall asymptotics of gg_rr rather than by fitting the validation Reynolds stresses. These elements are valuable even if the agentic-discovery claim requires tighter evidence.

major comments (3)
  1. [§III.B.3, Table 4, Fig. 15] The central end-to-end claim (autonomous derivation of an improved SGS model) rests on a single a-posteriori LES comparison (periodic hill, Re_h = 10 595) in Fig. 15 and Table 4. Only three Smagorinsky-type variants are shown; there is no grid-convergence study, no uncertainty quantification, and no second independent geometry. Because f(gg_rr) = 1−gg_rr ≤ 1 and vanishes at walls and in vortex cores, the LLM form is a spatially varying reduction of eddy viscosity. The manuscript itself notes that a global reduction of C_s already improves the near-separation station. Without an ablation that freezes the functional form while removing or randomizing the agent-generated map, or that tests the same form on a second separated flow (e.g., BFS already in the library), it remains unclear whether the multi-agent loop contributed beyond a physically plausible damping function that follows directl
  2. [§III.B.3, Fig. 15; Abbreviations] Proposal 1 is compared only against constant-coefficient Smagorinsky (C_s = 0.10 and a retuned C_s = 0.097775). Modern baselines that already address near-wall and rotation/shear issues (dynamic Smagorinsky, WALE—listed in the Abbreviations—Vreman, σ-model, or existing Liutex/Rortex-based SGS models cited as [39–41]) are absent. Without those comparisons, “superior Reynolds-stress predictions” cannot be interpreted as an advance relative to the current LES state of the art, only relative to the classical Smagorinsky model.
  3. [§II.D, §II.E, Abstract] The reliability of the Discover-Physics + Review closed loop is asserted via four qualitative criteria (logical, dimensional, physical, literature grounding) but is not demonstrated with any quantitative audit (e.g., fraction of proposals rejected, examples of corrected hallucinations, inter-run reproducibility of the same case). Given that the library currently holds only five cases and the Jaccard-tree metric is a hand-crafted 27-category fingerprint (Table 2, Eq. 5), the claim that the pipeline produces “reliable conclusions” and progressive inductive capability needs either a multi-seed reproducibility study on the hill case or an explicit failure-mode analysis. This is load-bearing for the agentic-discovery narrative in the Abstract and §II.D.
minor comments (6)
  1. [§III.B.1, Fig. 10] Word-cloud subset (b) is labeled “Recent literature (2026)” while the arXiv stamp is 4 Jul 2026; clarify the search date window and how many papers enter each subset so the keyword analysis is reproducible.
  2. [Nomenclature; Eqs. (2)–(4); Table 4] Notation for relative contributions mixes ggss/ggww (Cauchy–Stokes) with ggrr/ggps/ggns/ggrs (TDM) and later gg_rr / gg_ps in prose and Table 4; standardize subscripts and roman vs italic throughout.
  3. [Fig. 15] Fig. 15 caption refers to “Smagorinsky LLM” without defining the exact C_s used with the (1−gg_rr) factor; state whether C_s is held at 0.10 or retuned.
  4. [Table 3; §III.A.3] The propeller case is URANS (Table 3) while the others are LES; a one-sentence caveat on interpreting TDM statistics under RANS averaging would help.
  5. [References] Several references appear as arXiv preprints or “2025/2026” conference items; ensure final bibliographic completeness and that claims attributed to them match the cited content.
  6. [§III.A.4, Eq. (6), Fig. 9] Eq. (6) for the R vector is given without stating the coordinate frame or normalization used for core-line extraction in Fig. 9; a brief algorithmic note would aid reproducibility.

Circularity Check

1 steps flagged

No load-bearing circular derivation: the SGS form is motivated by independent kinematic asymptotics and tested a posteriori against external data; only mild non-load-bearing self-citation to prior rotation-based SGS work and a self-populated library.

specific steps
  1. self citation load bearing [Sec. II.B (TDM/SGS motivation); Refs. [39]–[41], [43]; Table 4 Proposal 1]
    "The rigid rotation tensor G^R_ij is directly related to a vortex identification method R proposed by Liu et al. [8], which has also been employed to develop a subgrid-scale model [39][40][41] for large eddy simulation. … the physical interpretation of gg_rr also provides new insights for turbulence modeling [43]. … ν_t = C_s² · Δ² · |S| · f(gg_rr) where f(gg_rr)=1−gg_rr"

    Background justification that rigid-rotation / Liutex measures are suitable for SGS modeling rests partly on prior papers with author overlap (Chen/Liu group). This primes the modeling direction the Discover-Physics agent is said to rediscover. It is not load-bearing for the quantitative claim: the specific multiplicative factor (1−gg_rr) on Smagorinsky is not taken as a uniqueness result from those citations, and superiority is still checked against external experiment rather than against the cited works’ fitted values.

full rationale

The paper’s central quantitative claim is an a-posteriori LES comparison (Fig. 15) of Reynolds stresses for ν_t = C_s² Δ² |S| (1−gg_rr) against experimental periodic-hill data. That functional form is not fitted to those Reynolds-stress profiles; it is motivated by the separately observed near-wall and vortex-core asymptotics of the triple-decomposition measure gg_rr (Figs. 6, 13–14), which vanish at walls and peak in cores. Kinematic observation → model ansatz → dynamical validation against external experiment is ordinary model development, not a reduction of prediction to input by construction. The Triple Decomposition Library comparison uses geometric fingerprints and Jaccard tree distance (Eq. 5, Table 2), not the target Reynolds-stress statistics, so the closest-case match (BFS) does not force the SGS form. Mild self-reference exists: (i) the library is populated by cases previously run through the same framework, and (ii) the paper cites overlapping-author Liutex/rotation-based SGS work [39–41, 43] as background that rigid rotation is useful for SGS modeling. Neither citation is a uniqueness theorem that forbids alternatives, nor does the a-posteriori result reduce to those citations by definition. No self-definitional loop, no fitted-then-predicted quantity, and no renaming of a known empirical law as a first-principles derivation. Score 2 reflects only that minor, non-load-bearing self-citation pattern.

Axiom & Free-Parameter Ledger

1 free parameters · 3 axioms · 2 invented entities

The central claim rests on the mathematical validity of the ordered real-Schur triple decomposition, on the ability of current LLMs to perform reliable physical inference when given TDM statistics and literature keywords, and on the adequacy of a five-case library plus Jaccard-tree distance for knowledge transfer. One free coefficient (C_s) remains from classical Smagorinsky theory; the new functional form itself introduces no additional fitted constants.

free parameters (1)
  • C_s (Smagorinsky constant) = 0.10 (standard) / 0.097775 (modified)
    Retained from the baseline model; the paper compares C_s = 0.10 and a slightly reduced value 0.097775, but does not re-fit C_s for the new rotation-suppression form.
axioms (3)
  • domain assumption The ordered real Schur decomposition uniquely and objectively partitions the velocity-gradient tensor into normal-straining, pure-shearing and rigid-rotation components (Liu et al. / Arun & Colonius).
    Invoked throughout Sec. II.B and used as the sole kinematic foundation for all subsequent statistics and modeling proposals.
  • ad hoc to paper Current large-language models, when supplied with TDM statistics, spatial fields and literature keywords and when audited by a second review agent, produce physically consistent inferences free of critical hallucination.
    Core premise of the Discover-Physics / Review loop (Sec. II.C–D); no independent verification of LLM reliability is supplied beyond the single successful periodic-hill example.
  • ad hoc to paper Jaccard-tree distance on a hand-crafted 27-category flow fingerprint is a sufficient similarity metric for transferring physical insight across cases.
    Defined in Eq. (5) and Table 2; used to select the backward-facing-step case as the nearest neighbor for the periodic hill.
invented entities (2)
  • Discover-Physics Agent + Review Agent closed loop no independent evidence
    purpose: Synthesize TDM data, literature keywords and library comparisons into validated physical discoveries and modeling proposals.
    The multi-agent architecture is introduced by the paper; independent evidence of its reliability is limited to the single end-to-end demonstration.
  • Evolving Triple Decomposition Library with problem-tree fingerprints no independent evidence
    purpose: Accumulate validated TDM statistics and enable cross-case inductive reasoning via Jaccard distance.
    New knowledge-base structure; currently contains only the five cases analyzed by the authors themselves.

pith-pipeline@v1.1.0-grok45 · 21985 in / 2978 out tokens · 28874 ms · 2026-07-11T22:20:09.407938+00:00 · methodology

0 comments
read the original abstract

Uncovering the physical mechanisms of turbulent flows remains a fundamental challenge in fluid mechanics. In particular, conventional velocity-gradient analysis methods suffer from shear contamination, which hinders accurate identification of the dominant physical mechanisms. This study presents PhysMiner, an automated framework integrating the triple decomposition method of the velocity gradient tensor with large language model-driven reasoning for turbulence-physics discovery. The triple decomposition module automatically decomposes flow fields into rigid rotation, pure shearing, and normal straining components, enabling statistical analysis, contour visualization, vortex-line extraction, and threshold-insensitive vortex identification while eliminating shear contamination. These automated capabilities are validated across five benchmarks, ranging from canonical configurations to complex engineering flows. A discover-physics agent combines flow statistics, spatial structures, and literature-derived knowledge to perform pattern recognition and physical inference, while a review Agent iteratively validates physical consistency to ensure reliable conclusions. A continuously evolving Triple Decomposition Library accumulates statistical knowledge from successfully analyzed flows, enabling cross-case comparison and progressive enhancement of inductive capability. The complete PhysMiner pipeline is validated end-to-end on the periodic hill flow, where the framework autonomously generates turbulence modeling recommendations and derives an improved subgrid-scale model with superior Reynolds-stress predictions. PhysMiner is open to the public and establishes a foundation for long-term collaborative advancement in automated turbulence-physics discovery.

discussion (0)

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Reference graph

Works this paper leans on

47 extracted references · 5 linked inside Pith

  1. [1]

    SimpleEuleriantimecorrelationoffull-andnarrow-bandvelocitysignalsingrid-generated, ‘isotropic’ turbulence,

    Comte-Bellot,G.,andCorrsin,S.,“SimpleEuleriantimecorrelationoffull-andnarrow-bandvelocitysignalsingrid-generated, ‘isotropic’ turbulence,”Journal of Fluid Mechanics, Vol. 48, No. 2, 1971, pp. 273–337

    1971

  2. [2]

    Direct numerical simulation of turbulent channel flow up to,

    Lee, M., and Moser, R. D., “Direct numerical simulation of turbulent channel flow up to,”Journal of fluid mechanics, Vol. 774, 2015, pp. 395–415

    2015

  3. [3]

    Combined heat transfer and fluid dynamic measurements downstream of a backward-facing step,

    Vogel, J. C., and Eaton, J., “Combined heat transfer and fluid dynamic measurements downstream of a backward-facing step,” 1985. 29

    1985

  4. [4]

    Flow over periodic hills–numerical and experimental study in a wide range of Reynolds numbers,

    Breuer, M., Peller, N., Rapp, C., and Manhart, M., “Flow over periodic hills–numerical and experimental study in a wide range of Reynolds numbers,”Computers & Fluids, Vol. 38, No. 2, 2009, pp. 433–457

    2009

  5. [5]

    Anisotropy of turbulence at the core of the tip and hub vortices shed by a marine propeller,

    Posa, A., “Anisotropy of turbulence at the core of the tip and hub vortices shed by a marine propeller,”Journal of Fluid Mechanics, Vol. 969, 2023, p. A23

    2023

  6. [6]

    K.,An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge, UK, 2000

    Batchelor, G. K.,An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge, UK, 2000

    2000

  7. [7]

    Vortex identification: New requirements and limitations,

    Kolář, V., “Vortex identification: New requirements and limitations,”International journal of heat and fluid flow, Vol. 28, No. 4, 2007, pp. 638–652

    2007

  8. [8]

    Rortex—Anewvortexvectordefinitionandvorticitytensorandvectordecompositions,

    Liu,C.,Gao,Y.,Tian,S.,andDong,X.,“Rortex—Anewvortexvectordefinitionandvorticitytensorandvectordecompositions,” Physics of Fluids, Vol. 30, No. 3, 2018

    2018

  9. [9]

    The Schur decomposition of the velocity gradient tensor for turbulent flows,

    Keylock, C. J., “The Schur decomposition of the velocity gradient tensor for turbulent flows,”Journal of Fluid Mechanics, Vol. 848, 2018, pp. 876–905

    2018

  10. [10]

    The triple decomposition of the velocity gradient tensor as a standardized real Schur form,

    Kronborg, J., and Hoffman, J., “The triple decomposition of the velocity gradient tensor as a standardized real Schur form,” Physics of fluids, Vol. 35, No. 3, 2023

    2023

  11. [11]

    Rortex based velocity gradient tensor decomposition,

    Gao, Y., and Liu, C., “Rortex based velocity gradient tensor decomposition,”Physics of Fluids, Vol. 31, No. 1, 2019

    2019

  12. [12]

    Can vortex criteria be objectivized?

    Haller, G., “Can vortex criteria be objectivized?”Journal of Fluid Mechanics, Vol. 908, 2021, p. A25

    2021

  13. [13]

    Revisiting turbulence small-scale behavior using velocity gradient triple decomposition,

    Das, R., and Girimaji, S. S., “Revisiting turbulence small-scale behavior using velocity gradient triple decomposition,”New Journal of Physics, Vol. 22, No. 6, 2020, p. 063015

    2020

  14. [14]

    Statistical properties of shear and nonshear velocity components in isotropic turbulence and turbulent jets,

    Enoki, R., Watanabe, T., and Nagata, K., “Statistical properties of shear and nonshear velocity components in isotropic turbulence and turbulent jets,”Physical Review Fluids, Vol. 8, No. 10, 2023, p. 104602

    2023

  15. [15]

    Velocity gradient partitioning in turbulent flows,

    Arun, R., and Colonius, T., “Velocity gradient partitioning in turbulent flows,”Journal of Fluid Mechanics, Vol. 1000, 2024, p. R5

    2024

  16. [16]

    Numericalinvestigationofdiscontinuousiceeffectsonsweptwings,

    Chen,J.,Xiao,M.,Zhou,Z.,andZhang,Y.,“Numericalinvestigationofdiscontinuousiceeffectsonsweptwings,”International Journal of Heat and Fluid Flow, Vol. 120, 2026, p. 110391

    2026

  17. [17]

    OpenFOAMGPT: A retrieval-augmented large language model (LLM) agent for OpenFOAM-based computational fluid dynamics,

    Pandey, S., Xu, R., Wang, W., and Chu, X., “OpenFOAMGPT: A retrieval-augmented large language model (LLM) agent for OpenFOAM-based computational fluid dynamics,”Physics of Fluids, Vol. 37, No. 3, 2025

    2025

  18. [18]

    OpenFOAMGPT 2.0: End-to-end, trustworthy automation for computational fluid dynamics,

    Feng, J., Xu, R., and Chu, X., “OpenFOAMGPT 2.0: End-to-end, trustworthy automation for computational fluid dynamics,” arXiv preprint arXiv:2504.19338, 2025

    Pith/arXiv arXiv 2025

  19. [19]

    Foam-Agent 2.0: An End-to-End Composable Multi-Agent Framework for Automating CFD Simulation in OpenFOAM,

    Yue, L., Somasekharan, N., Zhang, T., Cao, Y., and Pan, S., “Foam-Agent 2.0: An End-to-End Composable Multi-Agent Framework for Automating CFD Simulation in OpenFOAM,”arXiv preprint arXiv:2509.18178, 2025. 30

    arXiv 2025

  20. [20]

    Automating Computational Fluid Dynamics with LLM-based Multi-Agent Systems,

    Pan, S., Yue, L., Somasekharan, N., Zhang, T., Cao, Y., Chen, Z., and Di, S., “Automating Computational Fluid Dynamics with LLM-based Multi-Agent Systems,” 2026

    2026

  21. [21]

    FoamGPT: Fine-Tuning Large Language Model for Agentic Automation of CFD Simulations with OpenFOAM,

    Yue, L., Xu, P., Zhang, T., Somasekharan, N., and Pan, S., “FoamGPT: Fine-Tuning Large Language Model for Agentic Automation of CFD Simulations with OpenFOAM,”San Diego, CA, 2025

    2025

  22. [22]

    CFDAgent: A language-guided, zero-shot multi-agent system for complex flow simulation,

    Xu, Z., Wang, L., Wang, C., Chen, Y., Luo, Q., Yao, H.-D., Wang, S., and He, G., “CFDAgent: A language-guided, zero-shot multi-agent system for complex flow simulation,”Physics of Fluids, Vol. 37, No. 11, 2025

    2025

  23. [23]

    ChatCFD: An LLM-Driven Agent for End-to-End CFD Automation with Domain-Specific Structured Reasoning,

    Fan, E., Hu, K., Wu, Z., Ge, J., Miao, J., Zhang, Y., Sun, H., Wang, W., and Zhang, T., “ChatCFD: An LLM-Driven Agent for End-to-End CFD Automation with Domain-Specific Structured Reasoning,”arXiv preprint arXiv:2506.02019, 2025

    arXiv 2025

  24. [24]

    Towards LLM-enabled autonomous combustion research: A literature-aware agent for self-corrective modeling workflows,

    Xiao, K., Zhang, H., Mao, R., Li, H., and Chen, Z. X., “Towards LLM-enabled autonomous combustion research: A literature-aware agent for self-corrective modeling workflows,”arXiv preprint arXiv:2601.01357, 2026

    arXiv 2026

  25. [25]

    From Natural-Language to Simulation: An Intermediate Representation for Computational Fluid Dynamics,

    Shenoy, D. V., and Frankel, S. H., “From Natural-Language to Simulation: An Intermediate Representation for Computational Fluid Dynamics,” 2026

    2026

  26. [26]

    Aerodynamic Design and Optimization via a Specialized Agentic Generative AI Framework,

    Lee, C., Cinar, G., and Martins, J. R., “Aerodynamic Design and Optimization via a Specialized Agentic Generative AI Framework,” 2025

    2025

  27. [27]

    AirfoilAgent: Airfoil aerodynamics optimization design via large language model multi-agent collaborations,

    Fan, Y., Zhan, H., Zhang, M., and Mi, B., “AirfoilAgent: Airfoil aerodynamics optimization design via large language model multi-agent collaborations,”Advanced Engineering Informatics, Vol. 71, 2026, p. 104246

    2026

  28. [28]

    Agentic AI for Conversational Aerodynamic Analysis and Optimization of Airfoils and Wings,

    Fang, L., and He, P., “Agentic AI for Conversational Aerodynamic Analysis and Optimization of Airfoils and Wings,”AIAA SCITECH 2026 Forum, 2026, p. 2395

    2026

  29. [29]

    A Multidisciplinary Design and Optimization (MDO) Agent Driven by Large Language Models,

    Guo, B., Li, W., Liu, X., Luo, J., Yu, Z., Dong, D., Zhang, S., and Zhang, Y., “A Multidisciplinary Design and Optimization (MDO) Agent Driven by Large Language Models,”arXiv preprint arXiv:2511.17511, 2025

    arXiv 2025

  30. [30]

    Fromconcepttomanufacturing: Evaluating vision-language models for engineering design,

    Picard, C., Edwards, K.M., Doris, A.C., Man, B., Giannone, G., Alam, M.F., andAhmed, F., “Fromconcepttomanufacturing: Evaluating vision-language models for engineering design,”Artificial Intelligence Review, Vol. 58, No. 9, 2025, p. 288

    2025

  31. [31]

    AI agents in engineering design: a multi-agent framework for aesthetic and aerodynamic car design,

    Elrefaie, M., Qian, J., Wu, R., Chen, Q., Dai, A., and Ahmed, F., “AI agents in engineering design: a multi-agent framework for aesthetic and aerodynamic car design,”International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Vol. 89237, American Society of Mechanical Engineers, 2025, p. V03BT03A048

    2025

  32. [32]

    Agentic Risk-Aware Set-Based Engineering Design,

    Kumar, V., and Karniadakis, G. E., “Agentic Risk-Aware Set-Based Engineering Design,”arXiv preprint arXiv:2604.16687, 2026

    Pith/arXiv arXiv 2026

  33. [33]

    AutoTurb: Using large language models for automatic algebraic turbulence model discovery,

    Zhang, Y., Zheng, K., Liu, F., Zhang, Q., and Wang, Z., “AutoTurb: Using large language models for automatic algebraic turbulence model discovery,”Physics of Fluids, Vol. 37, No. 1, 2025. 31

    2025

  34. [34]

    Large language model driven development of turbulence models,

    Yang, Z., Bin, Y., Shi, Y., and Yang, X. I., “Large language model driven development of turbulence models,”Flow, Vol. 5, 2025, p. E40

    2025

  35. [35]

    Code2MCP: Transforming Code Repositories into MCP Services,

    Ouyang, C., Yue, L., Di, S., Zheng, L., Yue, L., Pan, S., Yin, J., and Zhang, M.-L., “Code2MCP: Transforming Code Repositories into MCP Services,”arXiv preprint arXiv:2509.05941, 2025

    arXiv 2025

  36. [36]

    Toolrosetta: Bridging open- source repositories and large language model agents through automated tool standardization,

    Di, S., Yuan, X., Guo, H., Ouyang, C., Chen, Z., Yue, L., Zheng, L., Zhu, J., Pan, S., Yin, J., et al., “Toolrosetta: Bridging open- source repositories and large language model agents through automated tool standardization,”arXiv preprint arXiv:2603.09290, 2026

    Pith/arXiv arXiv 2026

  37. [37]

    From static templates to dynamic runtime graphs: A survey of workflow optimization for llm agents,

    Yue, L., Bhandari, K. R., Ko, C.-Y., Patel, D., Lin, S., Zhou, N., Gao, J., Chen, P.-Y., and Pan, S., “From static templates to dynamic runtime graphs: A survey of workflow optimization for llm agents,”arXiv preprint arXiv:2603.22386, 2026

    arXiv 2026

  38. [38]

    Agentic Exploration of PDE Spaces using Latent Foundation Models for Parameterized Simulations,

    Vishwasrao, A., Giral, F., Golestanian, M., Tonti, F., Ramo, A. A., Lozano-Duran, A., Brunton, S. L., Hoyas, S., Clainche, S. L., Gomez, H., et al., “Agentic Exploration of PDE Spaces using Latent Foundation Models for Parameterized Simulations,”arXiv preprint arXiv:2604.09584, 2026

    Pith/arXiv arXiv 2026

  39. [39]

    ALiutex-basedsubgridstressmodelforlarge-eddy simulation,

    Ding, Y., Pang, B.-y., Yan, B.-w., Wang, Y.-q., Chen, Y.-x., andQian, Y.-h., “ALiutex-basedsubgridstressmodelforlarge-eddy simulation,”Journal of Hydrodynamics, Vol. 34, No. 6, 2022, pp. 1145–1150

    2022

  40. [40]

    Liutex-Based Sub-Grid Model for Large Eddy Simulation of Turbulent Flow,

    Hossen, E., Yu, Y., Chaoqun, L., Chen, J., Liu, Z., Yan, Y., Shah, V., and Alvarez, O., “Liutex-Based Sub-Grid Model for Large Eddy Simulation of Turbulent Flow,”AIAA SCITECH 2025 Forum, 2025, p. 0073

    2025

  41. [41]

    Near-Wall Scaling and Separation Prediction of a Rotation-Based Subgrid-Scale Stress Model,

    Chen, J., Yu, Y., Hossen, E., and Liu, C., “Near-Wall Scaling and Separation Prediction of a Rotation-Based Subgrid-Scale Stress Model,”arXiv preprint arXiv:2507.20043, 2025

    Pith/arXiv arXiv 2025

  42. [42]

    A Relative Liutex Method for Vortex Identification,

    Chen, J., Yu, Y., and Liu, C., “A Relative Liutex Method for Vortex Identification,”arXiv preprint arXiv:2512.23857, 2025

    arXiv 2025

  43. [43]

    A Dynamic Subgrid-Scale Model Based on Liutex Theory for Wall-Bounded Turbulent Flows,

    Chen, J., Yu, Y., and Liu, C., “A Dynamic Subgrid-Scale Model Based on Liutex Theory for Wall-Bounded Turbulent Flows,” arXiv preprint arXiv:2512.14953, 2025

    arXiv 2025

  44. [44]

    OpenFOAM:AC++libraryforcomplexphysicssimulations,

    Jasak,H.,Jemcov,A.,Tukovic,Z.,etal.,“OpenFOAM:AC++libraryforcomplexphysicssimulations,”Internationalworkshop on coupled methods in numerical dynamics, Vol. 1000, Dubrovnik, Croatia), 2007, pp. 1–20

    2007

  45. [45]

    Explicit formula for the Liutex vector and physical meaning of vorticity based on the Liutex-Shear decomposition,

    Wang, Y.-q., Gao, Y.-s., Liu, J.-m., and Liu, C., “Explicit formula for the Liutex vector and physical meaning of vorticity based on the Liutex-Shear decomposition,”Journal of Hydrodynamics, Vol. 31, No. 3, 2019, pp. 464–474

    2019

  46. [46]

    Identifying the tangle of vortex tubes in homogeneous isotropic turbulence,

    Xiong, S., and Yang, Y., “Identifying the tangle of vortex tubes in homogeneous isotropic turbulence,”Journal of Fluid Mechanics, Vol. 874, 2019, pp. 952–978

    2019

  47. [47]

    A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers,

    Deardorff, J. W., “A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers,”Journal of Fluid Mechanics, Vol. 41, No. 2, 1970, pp. 453–480. 32

    1970