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Comptes Rendus. Mécanique

Numerical experiments on unsupervised manifold learning applied to mechanical modeling of materials and structures
Comptes Rendus. Mécanique, Tome 348 (2020) no. 10-11, pp. 937-958.

Article du numéro thématique : Contributions in mechanics of materials
[Contributions en mécanique des matériaux]

The present work aims at analyzing issues related to the data manifold dimensionality. The interest of the study is twofold: (i) first, when too many measurable variables are considered, manifold learning is expected to extract useless variables; (ii) second, and more important, the same technique, manifold learning, could be utilized for identifying the necessity of employing latent extra variables able to recover single-valued outputs. Both aspects are discussed in the modeling of materials and structural systems by using unsupervised manifold learning strategies.

Première publication :
Publié le :
DOI : https://doi.org/10.5802/crmeca.53
Mots clés : Nonsupervised manifold learning, State variables, Dimensionality reduction, k-PCA, Structural analysis, Material constitutive equations
@article{CRMECA_2020__348_10-11_937_0,
     author = {Ruben Ibanez and Pierre Gilormini and Elias Cueto and Francisco Chinesta},
     title = {Numerical experiments on unsupervised manifold learning applied to mechanical modeling of materials and structures},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {937--958},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {348},
     number = {10-11},
     year = {2020},
     doi = {10.5802/crmeca.53},
     language = {en},
}
Ruben Ibanez; Pierre Gilormini; Elias Cueto; Francisco Chinesta. Numerical experiments on unsupervised manifold learning applied to mechanical modeling of materials and structures. Comptes Rendus. Mécanique, Tome 348 (2020) no. 10-11, pp. 937-958. doi : 10.5802/crmeca.53. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.53/

[1] T. Kirchdoerfer; M. Ortiz Data-driven computational mechanics, Comput. Methods Appl. Mech. Eng., Volume 304 (2016), pp. 81-101 | Article | MR 3486310 | Zbl 1425.74503

[2] M. A. Bessa; R. Bostanabad; Z. Liu; A. Hu; D. W. Apley; C. Brinson; W. Chen; W. K. Liu A framework for data-driven analysis of materials under uncertainty: countering the curse of dimensionality, Comput. Methods Appl. Mech. Eng., Volume 320 (2017), pp. 633-667 | Article | MR 3646368 | Zbl 1439.74014

[3] Z. Liu; M. Fleming; W. K. Liu Microstructural material database for self-consistent clustering analysis of elastoplastic strain softening materials, Comput. Methods Appl. Mech. Eng., Volume 330 (2018), pp. 547-577 | Article | MR 3759108 | Zbl 1439.74063

[4] D. Gonzalez; F. Chinesta; E. Cueto Thermodynamically consistent data-driven computational mechanics, Contin. Mech. Thermodyn., Volume 31 (2019), pp. 239-253 | Article | MR 3908344

[5] R. Ibanez; E. Abisset-Chavanne; J.V. Aguado; D. Gonzalez; E. Cueto; F. Chinesta A manifold learning approach to data-driven computational elasticity and inelasticity, Arch. Comput. Methods Eng., Volume 25 (2018) no. 1, pp. 47-57 | Article | MR 3736475 | Zbl 1390.74195

[6] M. Latorre; F.J. Montans What-you-prescribe-is-what-you-get orthotropic hyperelasticity, Comput. Mech., Volume 53 (2014) no. 6, pp. 1279-1298 | Article | MR 3201940 | Zbl 1398.74028

[7] P. Ladeveze; D. Neron; P-W. Gerbaud Data-driven computation for history-dependent materials, C. R. Méc., Volume 347 (2019) no. 11, pp. 831-844 | Article

[8] J. A. Lee; M. Verleysen Nonlinear Dimensionality Reduction, Springer, New York, 2007 | Zbl 1128.68024

[9] L. Maaten; G. Hinton Visualizing data using t-SNE, J. Mach. Learn Res., Volume 9 (2008), pp. 2579-2605 | Zbl 1225.68219

[10] S. T. Roweis; L. K. Saul Nonlinear dimensionality reduction by locally linear embedding, Science, Volume 290 (2000) no. 5500, pp. 2323-2326 | Article

[11] N. Kambhatla; T.K. Leen Dimension reduction by local principal component analysis, Neural Comput., Volume 9 (1997) no. 7, pp. 1493-1516 | Article

[12] Z. Zhang; H. Zha Principal manifolds and nonlinear dimensionality reduction via tangent space alignment, SIAM J. Sci. Comput., Volume 26 (2005) no. 1, pp. 313-338 | Article | MR 2114346 | Zbl 1077.65042

[13] A. Badias; S. Curtit; D. Gonzalez; I. Alfaro; F. Chinesta; E. Cueto An augmented reality platform for interactive aerodynamic design and analysis, Int. J. Numer. Methods Eng., Volume 120 (2019) no. 1, pp. 125-138 | Article | MR 4007832

[14] D. Gonzalez; J.V. Aguado; E. Cueto; E. Abisset-Chavanne; F. Chinesta kPCA-based parametric solutions within the PGD framework, Arch. Comput. Methods Eng., Volume 25 (2018) no. 1, pp. 69-86 | Article | MR 3736477 | Zbl 06887320

[15] E. Lopez; D. Gonzalez; J. V. Aguado; E. Abisset-Chavanne; E. Cueto; C. Binetruy; F. Chinesta A manifold learning approach for integrated computational materials engineering, Arch. Comput. Methods Eng., Volume 25 (2018) no. 1, pp. 59-68 | Article | MR 3736476 | Zbl 1390.74196

[16] E. Lopez; A. Scheuer; E. Abisset-Chavanne; F. Chinesta On the effect of phase transition on the manifold dimensionality: application to the Ising model, Math. Mech. Complex Syst., Volume 6 (2018) no. 3, pp. 251-265 | Article | MR 3858778 | Zbl 06945830