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

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.

Reçu le :
Révisé le :
Accepté le :
Première publication :
Publié le :
DOI : 10.5802/crmeca.53
Mots clés : Nonsupervised manifold learning, State variables, Dimensionality reduction, $k$-PCA, Structural analysis, Material constitutive equations
Ruben Ibanez 1 ; Pierre Gilormini 1 ; Elias Cueto 2 ; Francisco Chinesta 1

1 PIMM lab, Arts et Metiers Institute of Technology, 151 Boulevard de Hôpital, 75013 Paris, France
2 Aragon Institute of Engineering Research, Universidad de Zaragoza, Maria de Luna s/n, 50018 Zaragoza, Spain
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
@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},
}
TY  - JOUR
AU  - Ruben Ibanez
AU  - Pierre Gilormini
AU  - Elias Cueto
AU  - Francisco Chinesta
TI  - Numerical experiments on unsupervised manifold learning applied to mechanical modeling of materials and structures
JO  - Comptes Rendus. Mécanique
PY  - 2020
SP  - 937
EP  - 958
VL  - 348
IS  - 10-11
PB  - Académie des sciences, Paris
DO  - 10.5802/crmeca.53
LA  - en
ID  - CRMECA_2020__348_10-11_937_0
ER  - 
%0 Journal Article
%A Ruben Ibanez
%A Pierre Gilormini
%A Elias Cueto
%A Francisco Chinesta
%T Numerical experiments on unsupervised manifold learning applied to mechanical modeling of materials and structures
%J Comptes Rendus. Mécanique
%D 2020
%P 937-958
%V 348
%N 10-11
%I Académie des sciences, Paris
%R 10.5802/crmeca.53
%G en
%F CRMECA_2020__348_10-11_937_0
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, Volume 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 | DOI | MR | Zbl

[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 | DOI | MR | Zbl

[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 | DOI | MR | Zbl

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

[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 | DOI | MR | Zbl

[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 | DOI | MR | Zbl

[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 | DOI

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

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

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

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

[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 | DOI | MR | Zbl

[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 | DOI | MR

[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 | DOI | MR | Zbl

[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 | DOI | MR | Zbl

[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 | DOI | MR | Zbl

Cité par Sources :

Commentaires - Politique


Ces articles pourraient vous intéresser

Conciliating accuracy and efficiency to empower engineering based on performance: a short journey

Francisco Chinesta; Elias Cueto

C. R. Méca (2023)


Code2vect: An efficient heterogenous data classifier and nonlinear regression technique

Clara Argerich Martín; Ruben Ibáñez Pinillo; Anais Barasinski; ...

C. R. Méca (2019)


Data-driven model based on the simulation of cracking process in brittle material using the phase-field method in application

Yosra Kriaa; Amine Ammar; Bassem Zouari

C. R. Méca (2020)