Open Access
Issue |
Mechanics & Industry
Volume 25, 2024
|
|
---|---|---|
Article Number | 9 | |
Number of page(s) | 12 | |
DOI | https://doi.org/10.1051/meca/2024001 | |
Published online | 15 March 2024 |
- O. Cecil Zienkiewicz, P.B. Morice, The finite element method in engineering science, Vol. 1977, McGraw-Hill London, 1971 [Google Scholar]
- F. Chinesta, P. Ladeveze, E. Cueto, A short review on model order reduction based on proper generalized Decomposition, Arch. Comput. Methods Eng. 18, 395 (2011) [CrossRef] [Google Scholar]
- M. Verleysen, D. François, The curse of dimensionality in data mining and time series prediction, in Computational Intelligence and Bioinspired Systems: 8th International Work-Conference on Artificial Neural Networks, IWANN 2005, Vilanova i la GeltrU, Barcelona, Spain, June 8–10, 2005, Proceedings 8. Springer, 2005, pp. 758–770 [Google Scholar]
- A. Belloni, V. Chernozhukov, L1-penalized quantile regression in high-dimensional sparse models, 2011 [Google Scholar]
- G. Yi, J.Q. Shi, T. Choi, Penalized Gaussian process regression and classification for high-dimensional nonlinear data, Biometrics 67, 1285–1294 (2011) [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- A. Sancarlos, V. Champaney, J.-L. Duval, E. Cueto, F. Chinesta, Pgd-based advanced nonlinear multiparametric regressions for constructing metamodels at the scarce-data limit, [arXiv:2103.05358], 2021 [Google Scholar]
- U. Wilensky, Paradox, programming, and learning probability: a case study in a connected mathematics framework, J. Math. Behav. 14, 253–280 (1995) [CrossRef] [Google Scholar]
- C. Villani et al., Optimal transport: old and new, Vol. 338, Springer, 2009 [CrossRef] [Google Scholar]
- Y. Rubner, C. Tomasi, L.J. Guibas, The earth mover’s distance as a metric for image retrieval, Int. J. Comput. Vis. 40, 99 (2000) [CrossRef] [Google Scholar]
- M. Perrot, N. Courty, R. Flamary, A. Habrard, Mapping estimation for discrete optimal transport, Adv. Neural Inform. Process. Syst. 29, 4197–4205 (2016) [Google Scholar]
- M. Cuturi, A. Doucet, Fast computation of wasserstein barycenters, in: International Conference on Machine Learning, PMLR, 2014, 685–693 [Google Scholar]
- P.A Knight, The sinkhorn-knopp algorithm: convergence and applications, SIAM J. Matrix Anal. Applic. 30, 261–275 (2008) [CrossRef] [Google Scholar]
- P. Dvurechensky, A. Gasnikov, A. Kroshnin, Computational optimal transport: complexity by accelerated gradient descent is better than by sinkhorn’s algorithm, in: International Conference on Machine Learning, PMLR, 2018, 1367–1376 [Google Scholar]
- X. Bian, Z. Li, G.E. Karniadakis, Multi-resolution flow simulations by smoothed particle hydrodynamics via domain decomposition, J. Comput. Phys. 297, 132–155 (2015) [CrossRef] [MathSciNet] [Google Scholar]
- J. Weed, F. Bach, Sharp asymptotic and finite-sample rates of convergence of empirical measures in wasserstein distance, 2019 [Google Scholar]
- M. Jacot, V. Champaney, F. Chinesta, J. Cortial, Parametric damage mechanics empowering structural health monitoring of 3D woven composites, Sensors 23, 1946 (2023) [CrossRef] [PubMed] [Google Scholar]
- S. Torregrosa, V. Champaney, A. Ammar, V. Herbert, F. Chinesta, Surrogate parametric metamodel based on optimal transport, Math. Comput. Simul. 194, 36–63 (2022) [CrossRef] [Google Scholar]
- J. Rabin, G. Peyre, J. Delon, M. Bernot, Wasserstein barycenter and its application to texture mixing, in: Scale Space and Variational Methods in Computer Vision: Third International Conference, SSVM 2011, Ein-Gedi, Israel, May 29-June 2, 2011, Revised Selected Papers 3. Springer, 2012, pp. 435–446 [Google Scholar]
- N. Deb, P. Ghosal, B. Sen, Rates of estimation of optimal transport maps using plug-in estimators via barycen-tric projections, Adv. Neural Inform. Process. Syst. 34, 29736–29753 (2021) [Google Scholar]
- G. Peyré, M. Cuturi, et al., Computational optimal transport, Center for Research in Economics and Statistics Working Papers, 2017–86, 2017 [Google Scholar]
- G. Peyré, M. Cuturi, et al., Computational optimal transport: with applications to data science, Found. Trends Mach. Learn. 11, 355–607 (2019) [CrossRef] [Google Scholar]
- C. Villani, Topics in optimal transportation, Vol. 58, American Mathematical Society, 2021 [Google Scholar]
- N. Bonneel, M.V. De Panne, S. Paris, W. Heidrich, Displacement interpolation using lagrangian mass transport, in: Proceedings of the 2011 SIGGRAPH Asia Conference, 2011, pp. 1–12 [Google Scholar]
- R. Flamary, N. Courty, A. Gramfort, M.Z. Alaya, A. Boisbunon, S. Chambon, L. Chapel, A. Corenflos, K. Fatras, N. Fournier, et al., Pot: Python optimal transport, J. Mach. Learn. Res. 22, 3571–3578 (2021) [Google Scholar]
- R.J. McCann, A convexity principle for interacting gases, Adv. Math. 128, 153–179 (1997) [CrossRef] [MathSciNet] [Google Scholar]
- M. El Fallaki Idrissi, F. Praud, V. Champaney, F. Chinesta, F. Meraghni, Multiparametric modeling of composite materials based on non-intrusive pgd informed by multi-scale analyses: application for real-time stiffness prediction of woven composites, Composite Struct. 302, 116228 (2022). [CrossRef] [Google Scholar]
- R. Ibáñez, E. Abisset-Chavanne, A. Ammar, D. González, E. Cueto, A. Huerta, J.L. Duval, F. Chinesta, et al., A multidimensional data-driven sparse identification technique: the sparse proper generalized decomposition, Complexity 2018 (2018). [Google Scholar]
- I. Torre, Diffusive solver: a diffusion-equations solver based on fenics, [arXiv:2011.04351], 2020 [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.