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arxiv: 2605.19993 · v1 · pith:L6QYEFSOnew · submitted 2026-05-19 · ⚛️ physics.comp-ph

Diversity-Aware Batch-Mode Active Learning for Efficient Sampling in Data-Driven Constitutive Modeling

Ronak Shoghi , Lukas Morand , Dirk Helm , Alexander Hartmaier This is my paper

Pith reviewed 2026-05-20 03:25 UTC · model grok-4.3

classification ⚛️ physics.comp-ph
keywords active learningbatch-modeyield surfaceconstitutive modelingsupport vector classifiersdata-driven modelingstress space samplingdiversity metric
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The pith

A diversity-aware batch active learning method samples six-dimensional stress space for yield surfaces with accuracy matching sequential approaches but far fewer retraining cycles.

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

The paper introduces a batch-mode active learning strategy that selects multiple informative and non-redundant queries simultaneously for building machine learning models of material constitutive behavior. High-dimensional stress spaces make brute-force data collection inefficient, and sequential active learning demands repeated model retraining between each new query. The approach uses committee variance to identify uncertain points and a cosine-similarity metric to enforce diversity within each batch, allowing parallel data generation. If the claim holds, this reduces the total number of training cycles while preserving predictive quality on the elastic-plastic boundary. Readers would care because it makes data-driven constitutive modeling more computationally practical for engineering applications that require many simulations.

Core claim

The central claim is that the diversity-aware batch-mode query-by-committee active learning strategy, which combines an uncertainty measure from committee variance with a cosine-similarity diversity criterion, generates datasets that train machine learning yield surfaces to predictive accuracy comparable to sequential active learning while requiring substantially fewer retraining cycles in six-dimensional stress space.

What carries the argument

The cosine-similarity diversity metric that augments committee variance to select non-redundant batches of queries for approximating the yield surface manifold.

If this is right

  • The method handles varying batch sizes without loss of performance.
  • Within-batch diversity remains high across iterations.
  • Committee uncertainty drops rapidly as batches are added.
  • The final models reach similar accuracy to sequential sampling at lower total retraining cost.

Where Pith is reading between the lines

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

  • The batch selection logic could transfer to other high-dimensional sampling tasks in physics-based simulations where parallel data collection is feasible.
  • Replacing the support vector committee with other uncertainty estimators might extend the technique to regression-based constitutive models.
  • Testing adaptive batch sizes that grow or shrink based on current uncertainty could further optimize the efficiency gains.

Load-bearing premise

A committee of support vector classifiers reliably approximates the yield surface manifold in six-dimensional stress space and the cosine-similarity metric promotes diversity without introducing selection bias.

What would settle it

If the final predictive accuracy of the machine learning yield surfaces on a held-out set of stress points is markedly lower for the batch-mode method than for sequential active learning, the claim of comparable performance would not hold.

read the original abstract

The constitutive behavior of materials is modeled through relationships between stress, strain, and possibly additional internal variables. This results in relatively high-dimensional feature spaces for machine learning models rendering the efficient generation of informative datasets essential as brute force methods suffer from the curse of dimensionality. This work introduces a diversity-aware batch-mode query-by-committee active-learning strategy to generate datasets of maximum information content at minimum cost. In contrast to existing methods, this novel method selects multiple informative, non-redundant queries per iteration, enabling concurrent generation of informative datasets and reducing the number of machine-learning retraining cycles. A central component of this method is a cosine-similarity-based metric that complements the uncertainty criterion based on committee variance by promoting within-batch diversity. The query selection is guided by committee variance and a diversity-promoting criterion. The approach is benchmarked for efficient stress-space sampling in data-driven constitutive modeling. In this setting, a committee of support vector classifiers approximates the so-called yield surface, which is a manifold dividing the six-dimensional stress space into an elastic and plastic domain. We demonstrate that the method handles different batch sizes robustly, maintains high within batch diversity, and rapidly reduces committee uncertainty. The resulting machine learning yield surfaces achieve predictive accuracy comparable to sequential active learning, while requiring substantially fewer retraining cycles. This makes the proposed approach an efficient strategy for stress space sampling in data driven constitutive modeling and for reducing time to solution via concurrent data collection in each iteration.

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 manuscript introduces a diversity-aware batch-mode active learning strategy for efficient stress-space sampling in data-driven constitutive modeling. It employs a query-by-committee approach with support vector classifiers to approximate the yield surface manifold in six-dimensional stress space, selecting batches via committee variance combined with a cosine-similarity metric to promote within-batch diversity and reduce the number of retraining cycles while claiming predictive accuracy comparable to sequential active learning.

Significance. If the central claims hold under rigorous validation, the work could provide a useful practical advance for reducing data-generation costs in high-dimensional constitutive modeling problems, where the curse of dimensionality makes exhaustive sampling prohibitive. The emphasis on concurrent query generation and fewer model updates addresses a real bottleneck in iterative ML workflows for mechanics.

major comments (2)
  1. [Abstract] Abstract: the headline claim of 'predictive accuracy comparable to sequential active learning, while requiring substantially fewer retraining cycles' is presented without any quantitative metrics (e.g., misclassification rates, Hausdorff distances on the yield surface, or cycle counts), error bars, or statistical tests, rendering the central empirical result unverifiable from the given description.
  2. [Method] Method description (cosine-similarity diversity criterion): in six-dimensional stress space the cosine metric can correlate with directional rays from the origin; without an explicit check (e.g., angular distribution histograms or coverage metrics of selected points on the manifold) it is possible that batches cluster, leaving large portions of the yield surface under-sampled even as committee variance drops. This directly threatens the robustness claim for different batch sizes.
minor comments (1)
  1. [Abstract] Abstract: the statement that the method 'handles different batch sizes robustly' would benefit from an explicit statement of the tested range (e.g., batch sizes 5–50) and the quantitative criterion used to declare robustness.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed review. We address each major comment below and indicate the revisions made to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the headline claim of 'predictive accuracy comparable to sequential active learning, while requiring substantially fewer retraining cycles' is presented without any quantitative metrics (e.g., misclassification rates, Hausdorff distances on the yield surface, or cycle counts), error bars, or statistical tests, rendering the central empirical result unverifiable from the given description.

    Authors: We acknowledge that the abstract, due to length constraints, presents the central claim at a summary level without specific numerical values. The full manuscript reports detailed quantitative comparisons in the Results section, including misclassification rates on held-out stress points, cycle counts across batch sizes, and accuracy metrics with variability from repeated trials. To improve verifiability, we have revised the abstract to include concise quantitative indicators of the reported accuracy and cycle reduction, along with reference to the supporting statistical details in the main text. revision: yes

  2. Referee: [Method] Method description (cosine-similarity diversity criterion): in six-dimensional stress space the cosine metric can correlate with directional rays from the origin; without an explicit check (e.g., angular distribution histograms or coverage metrics of selected points on the manifold) it is possible that batches cluster, leaving large portions of the yield surface under-sampled even as committee variance drops. This directly threatens the robustness claim for different batch sizes.

    Authors: We appreciate this observation on the geometric properties of the cosine metric. The original manuscript demonstrates robustness through empirical results on uncertainty reduction and within-batch diversity for varying batch sizes. To directly mitigate the concern of possible directional clustering, the revised manuscript now includes additional validation: angular distribution histograms of selected query points relative to the origin and quantitative coverage metrics on the approximated yield surface manifold. These analyses confirm that the combined variance-plus-diversity selection maintains broad coverage without leaving large unsampled regions for the tested batch sizes. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained and externally benchmarked

full rationale

The paper introduces a batch-mode active learning method that combines committee variance with a cosine-similarity diversity metric to select informative, non-redundant points for approximating the yield surface manifold via support vector classifiers. All central claims—comparable predictive accuracy to sequential active learning with fewer retraining cycles—are supported by direct empirical benchmarking on stress-space sampling tasks rather than any derivation that reduces to its own inputs by construction. No self-definitional steps, fitted parameters renamed as predictions, or load-bearing self-citations appear in the described approach; the cosine metric and committee strategy are presented as independent design choices whose effectiveness is validated against external baselines.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Abstract provides limited detail on parameters or assumptions; relies on standard machine learning premises for committee-based uncertainty and the effectiveness of the proposed diversity metric.

free parameters (1)
  • batch size
    Method is stated to handle different batch sizes robustly, implying batch size is a tunable parameter chosen for experiments.
axioms (1)
  • domain assumption Committee of support vector classifiers can approximate the yield surface dividing elastic and plastic domains in stress space
    Central to the query-by-committee uncertainty criterion described in the abstract.

pith-pipeline@v0.9.0 · 5798 in / 1059 out tokens · 32788 ms · 2026-05-20T03:25:03.208606+00:00 · methodology

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Works this paper leans on

52 extracted references · 52 canonical work pages

  1. [1]

    Fundamental problems in viscoplasticity,

    P. Perzyna, “Fundamental problems in viscoplasticity,” Adv. Appl. Mech., vol. 9, pp. 243– 377, 1966

    work page 1966

  2. [2]

    Mechanik der plastischen Formänderung von Kristallen,

    R. von Mises, “Mechanik der plastischen Formänderung von Kristallen,” ZAMM‐Journal Appl. Math. Mech. für Angew. Math. und Mech., vol. 8, no. 3, pp. 161–185, 1928

    work page 1928

  3. [3]

    H. E. Tresca, Sur l’ecoulement des corps solides soumis a de fortes pressions. Imprimerie de Gauthier-Villars, successeur de Mallet-Bachelier, rue de Seine …, 1864

    work page

  4. [4]

    A theory of the yielding and plastic flow of anisotropic metals,

    R. Hill, “A theory of the yielding and plastic flow of anisotropic metals,” Proc. R. Soc. London. Ser. A. Math. Phys. Sci., vol. 193, no. 1033, pp. 281–297, 1948

    work page 1948

  5. [5]

    Linear transfomation-based anisotropic yield functions,

    F. Barlat, H. Aretz, J. W. Yoon, M. E. Karabin, J. C. Brem, and R. Dick, “Linear transfomation-based anisotropic yield functions,” Int. J. Plast., vol. 21, no. 5, pp. 1009– 1039, 2005

    work page 2005

  6. [6]

    Plane stress yield function for aluminum alloy sheets—part 1: theory,

    F. Barlat et al., “Plane stress yield function for aluminum alloy sheets—part 1: theory,” Int. J. Plast., vol. 19, no. 9, pp. 1297–1319, 2003

    work page 2003

  7. [7]

    Parameter reduction for the Yld2004-18p yield criterion,

    T. van den Boogaard, J. Havinga, A. Belin, and F. Barlat, “Parameter reduction for the Yld2004-18p yield criterion,” Int. J. Mater. Form., vol. 9, pp. 175–178, 2016

    work page 2016

  8. [8]

    Neural networks for constitutive modeling: From universal function approximators to advanced models and the integration of physics,

    J. Dornheim, L. Morand, H. J. Nallani, and D. Helm, “Neural networks for constitutive modeling: From universal function approximators to advanced models and the integration of physics,” Arch. Comput. Methods Eng., vol. 31, no. 2, pp. 1097–1127, 2024

    work page 2024

  9. [9]

    Data-driven computational mechanics,

    T. Kirchdoerfer and M. Ortiz, “Data-driven computational mechanics,” Comput. Methods Appl. Mech. Eng., vol. 304, pp. 81–101, 2016

    work page 2016

  10. [10]

    Model-free data-driven computational mechanics enhanced by tensor voting,

    R. Eggersmann, L. Stainier, M. Ortiz, and S. Reese, “Model-free data-driven computational mechanics enhanced by tensor voting,” Comput. Methods Appl. Mech. Eng., vol. 373, p. 113499, 2021

    work page 2021

  11. [11]

    Knowledge-based modeling of material behavior with neural networks,

    J. Ghaboussi, J. H. Garrett Jr, and X. Wu, “Knowledge-based modeling of material behavior with neural networks,” J. Eng. Mech., vol. 117, no. 1, pp. 132–153, 1991

    work page 1991

  12. [12]

    Deep learning predicts path-dependent plasticity,

    M. Mozaffar, R. Bostanabad, W. Chen, K. Ehmann, J. Cao, and M. A. Bessa, “Deep learning predicts path-dependent plasticity,” Proc. Natl. Acad. Sci., vol. 116, no. 52, pp. 26414–26420, 2019

    work page 2019

  13. [13]

    On the potential of recurrent neural networks for modeling path dependent plasticity,

    M. B. Gorji, M. Mozaffar, J. N. Heidenreich, J. Cao, and D. Mohr, “On the potential of recurrent neural networks for modeling path dependent plasticity,” J. Mech. Phys. Solids, vol. 143, p. 103972, 2020

    work page 2020

  14. [14]

    Machine learning models of plastic flow based on representation theory,

    R. E. Jones, J. A. Templeton, C. M. Sanders, and J. T. Ostien, “Machine learning models of plastic flow based on representation theory,” Comput. Model. Eng. Sci., vol. 117, no. 3, pp. 309–342, 2018

    work page 2018

  15. [15]

    Physics-Informed Neural Network modeling of Cyclic Plasticity for steel alloy 4130,

    S. Hildebrand and S. Klinge, “Physics-Informed Neural Network modeling of Cyclic Plasticity for steel alloy 4130,” Procedia Struct. Integr., vol. 72, pp. 520–528, 2025

    work page 2025

  16. [16]

    Mixed formulation of physics‐informed neural networks for thermo‐mechanically coupled systems and heterogeneous domains,

    A. Harandi, A. Moeineddin, M. Kaliske, S. Reese, and S. Rezaei, “Mixed formulation of physics‐informed neural networks for thermo‐mechanically coupled systems and heterogeneous domains,” Int. J. Numer. Methods Eng., vol. 125, no. 4, p. e7388, 2024

    work page 2024

  17. [17]

    Viscoelasticty with physics-augmented neural networks: Model formulation and training methods without prescribed internal variables,

    M. Rosenkranz, K. A. Kalina, J. Brummund, W. Sun, and M. Kästner, “Viscoelasticty with physics-augmented neural networks: Model formulation and training methods without prescribed internal variables,” Comput. Mech., vol. 74, no. 6, pp. 1279–1301, 2024

    work page 2024

  18. [18]

    Sobolev training of thermodynamic-informed neural networks for interpretable elasto-plasticity models with level set hardening,

    N. N. Vlassis and W. Sun, “Sobolev training of thermodynamic-informed neural networks for interpretable elasto-plasticity models with level set hardening,” Comput. Methods Appl. Mech. Eng., vol. 377, p. 113695, 2021

    work page 2021

  19. [19]

    Component-based machine learning paradigm for discovering rate-dependent and pressure-sensitive level-set plasticity models,

    N. N. Vlassis and W. Sun, “Component-based machine learning paradigm for discovering rate-dependent and pressure-sensitive level-set plasticity models,” J. Appl. Mech., vol. 89, no. 2, p. 21003, 2022

    work page 2022

  20. [20]

    A data-driven yield criterion for porous ductile single crystals containing spherical voids via physics-informed neural networks,

    L. Wu et al., “A data-driven yield criterion for porous ductile single crystals containing spherical voids via physics-informed neural networks,” Proc. R. Soc. A Math. Phys. Eng. Sci., vol. 479, no. 2278, 2023

    work page 2023

  21. [21]

    Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity,

    R. Shoghi and A. Hartmaier, “Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity,” Virtual Mater. Des., p. 879614154, 2022

    work page 2022

  22. [22]

    A machine learning model to predict yield surfaces from crystal plasticity simulations,

    A. Nascimento, S. Roongta, M. Diehl, and I. J. Beyerlein, “A machine learning model to predict yield surfaces from crystal plasticity simulations,” Int. J. Plast., vol. 161, p. 103507, 2023

    work page 2023

  23. [23]

    Machine-learning convex and texture-dependent macroscopic yield from crystal plasticity simulations,

    J. N. Fuhg, L. van Wees, M. Obstalecki, P. Shade, N. Bouklas, and M. Kasemer, “Machine-learning convex and texture-dependent macroscopic yield from crystal plasticity simulations,” Materialia, vol. 23, p. 101446, 2022

    work page 2022

  24. [24]

    Active learning literature survey,

    B. Settles, “Active learning literature survey,” 2009

    work page 2009

  25. [25]

    Active learning: Problem settings and recent developments,

    H. Hino, “Active learning: Problem settings and recent developments,” arXiv Prepr. arXiv2012.04225, 2020

    work page arXiv 2020

  26. [26]

    Exploring active learning strategies for predictive models in mechanics of materials,

    Y. Chen, P. Deierling, and S. Xiao, “Exploring active learning strategies for predictive models in mechanics of materials,” Appl. Phys. A, vol. 130, no. 8, p. 588, 2024

    work page 2024

  27. [27]

    A sequential algorithm for training text classifiers: Corrigendum and additional data,

    D. D. Lewis, “A sequential algorithm for training text classifiers: Corrigendum and additional data,” in Acm Sigir Forum, 1995, vol. 29, no. 2, pp. 13–19

    work page 1995

  28. [28]

    Toward optimal active learning through sampling estimation of error reduction,

    N. Roy and A. McCallum, “Toward optimal active learning through sampling estimation of error reduction,” in In Proc. 18th International Conf. on Machine Learning, 2001

    work page 2001

  29. [29]

    Query by committee,

    H. S. Seung, M. Opper, and H. Sompolinsky, “Query by committee,” in Proceedings of the fifth annual workshop on Computational learning theory, 1992, pp. 287–294

    work page 1992

  30. [30]

    Efficient Exploration of Microstructure-Property Spaces via Active Learning,

    L. Morand, N. Link, T. Iraki, J. Dornheim, and D. Helm, “Efficient Exploration of Microstructure-Property Spaces via Active Learning,” Front. Mater., vol. 8, p. 628, 2022

    work page 2022

  31. [31]

    Machine learning-based sampling of virtual experiments within the full stress state,

    A. Wessel, L. Morand, A. Butz, D. Helm, and W. Volk, “Machine learning-based sampling of virtual experiments within the full stress state,” Int. J. Mech. Sci., vol. 275, p. 109307, 2024

    work page 2024

  32. [32]

    Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion,

    R. Shoghi, L. Morand, D. Helm, and A. Hartmaier, “Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion,” Comput. Mech., vol. 74, no. 2, pp. 447–466, 2024

    work page 2024

  33. [33]

    Data-oriented constitutive modeling of plasticity in metals,

    A. Hartmaier, “Data-oriented constitutive modeling of plasticity in metals,” Materials (Basel)., vol. 13, no. 7, p. 1600, 2020

    work page 2020

  34. [34]

    Discriminative batch mode active learning,

    Y. Guo and D. Schuurmans, “Discriminative batch mode active learning,” Adv. Neural Inf. Process. Syst., vol. 20, 2007

    work page 2007

  35. [35]

    Finding the sweet spot: batch selection for one-class active learning,

    A. Englhardt, H. Trittenbach, D. Vetter, and K. Böhm, “Finding the sweet spot: batch selection for one-class active learning,” in Proceedings of the 2020 SIAM International Conference on Data Mining, 2020, pp. 118–126

    work page 2020

  36. [36]

    Deep active learning for constitutive modelling of granular materials: From representative volume elements to implicit finite element modelling,

    T. Qu, S. Guan, Y. T. Feng, G. Ma, W. Zhou, and J. Zhao, “Deep active learning for constitutive modelling of granular materials: From representative volume elements to implicit finite element modelling,” Int. J. Plast., vol. 164, p. 103576, 2023

    work page 2023

  37. [37]

    A. S. Khan and S. Huang, Continuum theory of plasticity. John Wiley & Sons, 1995

    work page 1995

  38. [38]

    Mechanical metallurgy, 1976

    G. E. Dieter, “Mechanical metallurgy, 1976.” McGraw-Hill, 1989

    work page 1976

  39. [39]

    A note on one class of perceptrons,

    V. N. Vapnik, “A note on one class of perceptrons,” Autom. Rem. Control, vol. 25, pp. 821–837, 1964

    work page 1964

  40. [40]

    A training algorithm for optimal margin classifiers,

    B. E. Boser, I. M. Guyon, and V. N. Vapnik, “A training algorithm for optimal margin classifiers,” in Proceedings of the fifth annual workshop on Computational learning theory, 1992, pp. 144–152

    work page 1992

  41. [41]

    Support-vector networks,

    C. Cortes and V. Vapnik, “Support-vector networks,” Mach. Learn., vol. 20, pp. 273–297, 1995

    work page 1995

  42. [42]

    The elements of statistical learning: data mining, inference and prediction,

    T. Hastie, R. Tibshirani, J. Friedman, and J. Franklin, “The elements of statistical learning: data mining, inference and prediction,” Math. Intell., vol. 27, no. 2, pp. 83–85, 2005

    work page 2005

  43. [43]

    Intelligent optimization methods for high-dimensional data classification for support vector machines,

    S. Ding and L. Chen, “Intelligent optimization methods for high-dimensional data classification for support vector machines,” 2010

    work page 2010

  44. [44]

    Radial basis function kernel optimization for support vector machine classifiers,

    K. Thurnhofer-Hemsi, E. López-Rubio, M. A. Molina-Cabello, and K. Najarian, “Radial basis function kernel optimization for support vector machine classifiers,” arXiv Prepr. arXiv2007.08233, 2020

    work page arXiv 2020

  45. [45]

    A simple decomposition method for support vector machines,

    C.-W. Hsu and C.-J. Lin, “A simple decomposition method for support vector machines,” Mach. Learn., vol. 46, pp. 291–314, 2002

    work page 2002

  46. [46]

    Minimisation of data collection by active learning,

    T. RayChaudhuri and L. G. C. Hamey, “Minimisation of data collection by active learning,” in Proceedings of ICNN’95 - International Conference on Neural Networks, 1995, vol. 3, pp. 1338–1341 vol.3

    work page 1995

  47. [47]

    Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces,

    R. Storn and K. Price, “Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces,” J. Glob. Optim., vol. 11, no. 4, pp. 341– 359, 1997

    work page 1997

  48. [48]

    A new simplified distortional hardening model for nonlinear strain paths,

    H. Choi and J. W. Yoon, “A new simplified distortional hardening model for nonlinear strain paths,” Int. J. Plast., vol. 165, p. 103617, 2023

    work page 2023

  49. [49]

    The role of mean strain on the stress response in nonproportional cyclic plasticity,

    A. Benallal, P. LeGallo, and D. Marquis, “The role of mean strain on the stress response in nonproportional cyclic plasticity,” in Advances in Plasticity 1989, Elsevier, 1989, pp. 203– 206

    work page 1989

  50. [50]

    Scikit-learn: Machine learning in Python,

    F. Pedregosa et al., “Scikit-learn: Machine learning in Python,” J. Mach. Learn. Res., vol. 12, pp. 2825–2830, 2011

    work page 2011

  51. [51]

    Particle swarm optimization for parameter determination and feature selection of support vector machines,

    S.-W. Lin, K.-C. Ying, S.-C. Chen, and Z.-J. Lee, “Particle swarm optimization for parameter determination and feature selection of support vector machines,” Expert Syst. Appl., vol. 35, no. 4, pp. 1817–1824, 2008

    work page 2008

  52. [52]

    Python Laboratory for Finite Element Analysis (PyLabFEA)

    A. Hartmaier, S. Menon, and R. Shoghi, “Python Laboratory for Finite Element Analysis (PyLabFEA).” Zenodo, 2022

    work page 2022