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A Tensor-Based Algorithm for the Optimal Model Reduction of High Dimensional Problems

Olivier Zahm , Marie Billaud-Friess , Anthony Nouy
2nd ECCOMAS Young Investigators Conference (YIC 2013), Sep 2013, Bordeaux, France
Communication dans un congrès hal-00855901v1

Optimal a priori Tensor Decomposition for the Solution of High Dimensional Problems

Anthony Nouy , Marie Billaud-Friess , Olivier Zahm
SIAM ALA, 2012, Valencia, Spain
Communication dans un congrès hal-01008617v1
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Approximation de faible rang d'un échantillon de solution d'une équation paramétrée

Loïc Giraldi , Anthony Nouy , Olivier Zahm
12e Colloque national en calcul des structures, CSMA, May 2015, Giens, France
Communication dans un congrès hal-01517284v1

Learning non-Gaussian graphical models via Hessian scores and triangular transport

Ricardo Baptista , Youssef Marzouk , Rebecca E. Morrison , Olivier Zahm
2022
Pré-publication, Document de travail hal-03528005v1

Greedy inference with structure-exploiting lazy maps

Michael Brennan , Daniele Bigoni , Olivier Zahm , Alessio Spantini , Youssef Marzouk
NeurIPS '20 - 34th International Conference on Neural Information Processing Systems, Dec 2020, Virtual, Canada. pp.8330-8342
Communication dans un congrès hal-02147706v1

Prior normalization for certified likelihood-informed subspace detection of Bayesian inverse problems

Tiangang Cui , Xin Tong , Olivier Zahm
Inverse Problems, 2022, 38 (12), pp.124002. ⟨10.1088/1361-6420/ac9582⟩
Article dans une revue hal-03877862v1
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Certified dimension reduction in nonlinear Bayesian inverse problems

Olivier Zahm , Tiangang Cui , Kody Law , Alessio Spantini , Youssef Marzouk
Mathematics of Computation, 2022, 91, pp.1789-1835. ⟨10.1090/mcom/3737⟩
Article dans une revue hal-01834039v2
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Méthode de réduction de modèle a priori basée sur des formulations idéales en minimum de résidu

Olivier Zahm , Marie Billaud-Friess , Anthony Nouy
11e colloque national en calcul des structures, CSMA, May 2013, Giens, France
Communication dans un congrès hal-01717098v1
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Optimal Riemannian metric for Poincaré inequalities and how to ideally precondition Langevin dymanics

Tiangang Cui , Xin Tong , Olivier Zahm
2024
Pré-publication, Document de travail hal-04526677v1

Méthode de réduction de modèles a priori basée sur des formulations idéales en minimum de résidu

Marie Billaud-Friess , Anthony Nouy , Olivier Zahm
Congrès d'Analyse NUMérique, 2012, Superbesse, France
Communication dans un congrès hal-01008424v1

Tensor-based methods for uncertainty propagation: alternative definitions and algorithms

Anthony Nouy , Marie Billaud-Friess , Mathilde Chevreuil , Prashant Rai , Olivier Zahm
SIAM Conference on Uncertainty Quantification, 2012, Raleigh, United States
Communication dans un congrès hal-01009008v1
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Diffeomorphism-based feature learning using Poincaré inequalities on augmented input space

Romain Verdière , Clémentine Prieur , Olivier Zahm
2023
Pré-publication, Document de travail hal-04364208v1

Tensor based methods for high dimensional parametric problems: optimal model reductions and their approximations

Anthony Nouy , Marie Billaud-Friess , Olivier Zahm
WCCM 2012, 2012, Sao Paulo, France
Communication dans un congrès hal-01009003v1

Principal Feature Detection via $\Phi$-Sobolev Inequalities

Matthew T. C. Li , Youssef Marzouk , Olivier Zahm
2023
Pré-publication, Document de travail hal-04216841v1
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Data-Free Likelihood-Informed Dimension Reduction of Bayesian Inverse Problems

Tiangang Cui , Olivier Zahm
Inverse Problems, 2021, 37 (4), pp.045009. ⟨10.1088/1361-6420/abeafb⟩
Article dans une revue hal-02938064v2
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Application of hierarchical matrix techniques to the homogenization of composite materials

Paul Cazeaux , Olivier Zahm
2013
Pré-publication, Document de travail hal-00922827v1

Projection based model order reduction methods for the estimation of vector-valued variables of interest

Olivier Zahm , Marie Billaud-Friess , Anthony Nouy
SIAM Journal on Scientific Computing, 2017, 39 (4), pp.A1647-A1674. ⟨10.1137/16M106385X⟩
Article dans une revue hal-01387236v1

A tensor approximation method based on ideal minimal residual formulations for the solution of high-dimensional problems

Marie Billaud-Friess , Anthony Nouy , Olivier Zahm
ESAIM: Mathematical Modelling and Numerical Analysis, 2014, 48, pp.1777-1806. ⟨10.1051/m2an/2014019⟩
Article dans une revue hal-00861914v1

Gradient-based data and parameter dimension reduction for Bayesian models: an information theoretic perspective

Ricardo Baptista , Youssef Marzouk , Olivier Zahm
2022
Pré-publication, Document de travail hal-03877649v1
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Gradient-based dimension reduction of multivariate vector-valued functions

Olivier Zahm , Paul Constantine , Clémentine Prieur , Youssef Marzouk
SIAM Journal on Scientific Computing, 2020, 42 (1), pp.A929-A956. ⟨10.1137/18M1221837⟩
Article dans une revue hal-01701425v3

Interpolation of inverse operators for preconditioning parameter-dependent equations

Olivier Zahm , Anthony Nouy
SIAM Journal on Scientific Computing, 2016, 38 (2), pp.A1044-A1074. ⟨10.1137/15M1019210⟩
Article dans une revue hal-01262424v1
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Model order reduction methods for parameter-dependent equations -- Applications in Uncertainty Quantification.

Olivier Zahm
Mathematics [math]. Ecole Centrale de Nantes (ECN), 2015. English. ⟨NNT : ⟩
Thèse tel-01256411v1
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Interpolation d'inverses d'opérateurs pour la réduction de modèles paramétrés.

Olivier Zahm , Anthony Nouy
12e Colloque national en calcul des structures, CSMA, May 2015, Giens, France
Communication dans un congrès hal-01515065v1

Self-reinforced polynomial approximation methods for concentrated probability densities

Tiangang Cui , Sergey Dolgov , Olivier Zahm
2023
Pré-publication, Document de travail hal-04216842v1

Certified coordinate selection for high-dimensional Bayesian inversion with Laplace prior

Rafael Flock , Yiqiu Dong , Felipe Uribe , Olivier Zahm
2023
Pré-publication, Document de travail hal-04273681v1

Scalable conditional deep inverse Rosenblatt transports using tensor trains and gradient-based dimension reduction

Tiangang Cui , Sergey Dolgov , Olivier Zahm
Journal of Computational Physics, 2023, pp.112103. ⟨10.1016/j.jcp.2023.112103⟩
Article dans une revue hal-03527999v1
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On the representation and learning of monotone triangular transport maps

Ricardo Baptista , Youssef Marzouk , Olivier Zahm
Foundations of Computational Mathematics, 2023, ⟨10.1007/s10208-023-09630-x⟩
Article dans une revue hal-03060198v1

A tensor-based algorithm for solving stochastic PDEs

Marie Billaud-Friess , Anthony Nouy , Olivier Zahm
SIAM Computational Sciences and Engineering, 2013, Boston, United States
Communication dans un congrès hal-01007814v1

Minimizing rational functions: a hierarchy of approximations via pushforward measures

Jean-Bernard Lasserre , Victor Magron , Swann Marx , Olivier Zahm
SIAM Journal on Optimization, 2021, 31 (3), pp.2285-2306. ⟨10.1137/20M138541X⟩
Article dans une revue hal-03053386v1
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Nonlinear dimension reduction for surrogate modeling using gradient information

Daniele Bigoni , Youssef Marzouk , Clémentine Prieur , Olivier Zahm
Information and Inference, 2022
Article dans une revue hal-03146362v1