Anthony Nouy

77
Documents

Publications

Publications

Moment-SoS Methods for Optimal Transport Problems

Olga Mula , Anthony Nouy
Numerische Mathematik, 2024, 156 (4), pp.1541-1578. ⟨10.1007/s00211-024-01422-x⟩
Article dans une revue hal-03919946 v1
Image document

A moment approach for entropy solutions of parameter-dependent hyperbolic conservation laws

Clément Cardoen , Swann Marx , Anthony Nouy , Nicolas Seguin
Numerische Mathematik, 2024, 156, pp.1289-1324. ⟨10.1007/s00211-024-01428-5⟩
Article dans une revue hal-04218591 v3

Dictionary-based model reduction for state estimation

Anthony Nouy , Alexandre Pasco
Advances in Computational Mathematics, 2024, 50 (3), pp.32. ⟨10.1007/s10444-024-10129-4⟩
Article dans une revue hal-04069442 v1

Approximation by tree tensor networks in high dimensions: Sobolev and compositional functions

Markus Bachmayr , Anthony Nouy , Reinhold Schneider
Pure and Applied Functional Analysis, 2023, 8 (2), pp.405-428. ⟨10.48550/arXiv.2112.01474⟩
Article dans une revue hal-04385142 v1

Approximation Theory of Tree Tensor Networks: Tensorized Univariate Functions

Mazen Ali , Anthony Nouy
Constructive Approximation, 2023, 58 (2), pp.463-544. ⟨10.1007/s00365-023-09620-w⟩
Article dans une revue hal-04385174 v1

Active learning of tree tensor networks using optimal least-squares

Cécile Haberstich , Anthony Nouy , Guillaume Perrin
SIAM/ASA Journal on Uncertainty Quantification, 2023, 11 (3), pp.848-876. ⟨10.1137/21M1415911⟩
Article dans une revue hal-03919916 v1
Image document

Geometry of tree-based tensor formats in tensor Banach spaces

Antonio Falcó , Wolfgang Hackbusch , Anthony Nouy
Annali di Matematica Pura ed Applicata, 2023, 202 (5), pp.2127-2144. ⟨10.1007/s10231-023-01315-0⟩
Article dans une revue hal-03919920 v2

A PAC algorithm in relative precision for bandit problem with costly sampling

Marie Billaud-Friess , Arthur Macherey , Anthony Nouy , Clémentine Prieur
Mathematical Methods of Operations Research, 2022, 96, pp.161-185. ⟨10.1007/s00186-022-00769-x⟩
Article dans une revue hal-03139679 v1
Image document

Boosted optimal weighted least-squares

Cécile Haberstich , Anthony Nouy , Guillaume Perrin
Mathematics of Computation, 2022, 91, pp.1281-1315. ⟨10.1090/mcom/3710⟩
Article dans une revue hal-02562188 v1

Tensor-based numerical method for stochastic homogenisation

Quentin Ayoul-Guilmard , Anthony Nouy , Christophe Binetruy
Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2022, 20 (1), pp.36-71. ⟨10.1137/18M1191221⟩
Article dans une revue hal-01899835 v1

Learning with tree tensor networks: complexity estimates and model selection

Bertrand Michel , Anthony Nouy
Bernoulli, 2022, 28 (2), pp.910 - 936. ⟨10.3150/21-BEJ1371⟩
Article dans une revue hal-02889655 v1
Image document

LEARNING HIGH-DIMENSIONAL PROBABILITY DISTRIBUTIONS USING TREE TENSOR NETWORKS

Erwan Grelier , Anthony Nouy , Regis Lebrun
International Journal for Uncertainty Quantification, 2022, 12 (5), pp.47-69. ⟨10.1615/Int.J.UncertaintyQuantification.2022034340⟩
Article dans une revue hal-03919932 v1

Randomized linear algebra for model reduction. Part II: minimal residual methods and dictionary-based approximation

Oleg Balabanov , Anthony Nouy
Advances in Computational Mathematics, 2021, 47 (26), ⟨10.1007/s10444-020-09836-5⟩
Article dans une revue hal-02562161 v1

Approximation of Smoothness Classes by Deep Rectifier Networks

Mazen Ali , Anthony Nouy
SIAM Journal on Numerical Analysis, 2021, 59 (6), pp.3032-3051. ⟨10.1137/20M1360657⟩
Article dans une revue hal-02909881 v1
Image document

Principal bundle structure of matrix manifolds

Marie Billaud-Friess , Antonio Falco , Anthony Nouy
Mathematics , 2021, 9 (14), pp.1669. ⟨10.3390/math9141669⟩
Article dans une revue hal-01521748 v1

A new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of matrix manifolds

Marie Billaud Friess , Antonio Falco , Anthony Nouy
BIT Numerical Mathematics, 2021, ⟨10.1007/s10543-021-00884-x⟩
Article dans une revue hal-02458048 v1

Singular Value Decomposition in Sobolev Spaces: Part I

Mazen Ali , Anthony Nouy
Zeitschrift für Analysis und ihre Anwendungen, 2020, 39, pp.349-369. ⟨10.4171/ZAA/1663⟩
Article dans une revue hal-01899833 v1

Singular Value Decomposition in Sobolev Spaces: Part II

Mazen Ali , Anthony Nouy
Zeitschrift für Analysis und ihre Anwendungen, 2020, 39 (4), pp.371-394. ⟨10.4171/ZAA/1664⟩
Article dans une revue hal-02562141 v1
Image document

Low-rank approximation of linear parabolic equations by space-time tensor Galerkin methods

Thomas Boiveau , Virginie Ehrlacher , Alexandre Ern , Anthony Nouy
ESAIM: Mathematical Modelling and Numerical Analysis, 2019, 53 (2), pp.635-658. ⟨10.1051/m2an/2018073⟩
Article dans une revue hal-01668316 v2

Randomized linear algebra for model reduction. Part I: Galerkin methods and error estimation

Oleg Balabanov , Anthony Nouy
Advances in Computational Mathematics, 2019, 45 (5-6), pp.2969-3019. ⟨10.1007/s10444-019-09725-6⟩
Article dans une revue hal-01899836 v1

Higher-order principal component analysis for the approximation of tensors in tree-based low-rank formats

Anthony Nouy
Numerische Mathematik, 2019, 141 (3), pp.743-789. ⟨10.1007/s00211-018-1017-8⟩
Article dans une revue hal-01521759 v1

On the Dirac-Frenkel Variational Principle on Tensor Banach Spaces

A. Falcó , W. Hackbusch , Anthony Nouy
Foundations of Computational Mathematics, 2019, 19, pp.159-204. ⟨10.1007/s10208-018-9381-4⟩
Article dans une revue hal-01457079 v1

Weakly intrusive low-rank approximation method for nonlinear parameter-dependent equations

Loïc Giraldi , Anthony Nouy
SIAM Journal on Scientific Computing, 2019, 41 (3), pp.A1777-A1792. ⟨10.1137/17M1136924⟩
Article dans une revue hal-01899838 v1

Tree-based tensor formats

Antonio Falcó , Wolfgang Hackbusch , Anthony Nouy
SeMA Journal: Boletin de la Sociedad Española de Matemática Aplicada, 2018, ⟨10.1007/s40324-018-0177-x⟩
Article dans une revue hal-01899830 v1
Image document

A multiscale method for semi-linear elliptic equations with localized uncertainties and non-linearities

Anthony Nouy , Florent Pled
ESAIM: Mathematical Modelling and Numerical Analysis, 2018, 52 (5), pp.1763-1802. ⟨10.1051/m2an/2018025⟩
Article dans une revue hal-01507489 v2
Image document

Dynamical model reduction method for solving parameter-dependent dynamical systems

Marie Billaud-Friess , Anthony Nouy
SIAM Journal on Scientific Computing, 2017, 39 (4), pp.A1766-A1792. ⟨10.1137/16M1071493⟩
Article dans une revue hal-01387231 v1
Image document

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-01387236 v1

Calcul en fiabilité d’un quai sur pieux à partir de données d’instrumentation

Humberto Yáñez-Godoy , Franck Schoefs , Anthony Nouy
Revue française de Géotechnique, 2017, 133, pp.51-57. ⟨10.1051/geotech/2010133051⟩
Article dans une revue hal-04985561 v1
Image document

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-01262424 v1
Image document

To Be or Not to be Intrusive? The Solution of Parametric and Stochastic Equations---Proper Generalized Decomposition

Loïc Giraldi , Dishi Liu , Hermann G. Matthies , Anthony Nouy
SIAM Journal on Scientific Computing, 2015, 37 (1), pp.A347 - A368. ⟨10.1137/140969063⟩
Article dans une revue hal-01899842 v1
Image document

A least-squares method for sparse low rank approximation of multivariate functions

Mathilde Chevreuil , Régis Lebrun , Anthony Nouy , Prashant Rai
SIAM/ASA Journal on Uncertainty Quantification, 2015, 3 (1), pp.897-921. ⟨10.1137/13091899X⟩
Article dans une revue hal-00861913 v1
Image document

Model reduction based on Proper Generalized Decomposition for the Stochastic steady incompressible Navier-Stokes equations

Lorenzo Tamellini , Olivier Le Maitre , Anthony Nouy
SIAM Journal on Scientific Computing, 2014, 36 (3), pp.A1089-A1117. ⟨10.1137/120878999⟩
Article dans une revue hal-00733733 v1
Image document

Ideal minimal residual-based proper generalized decomposition for non-symmetric multi-field models - Application to transient elastodynamics in space-time domain

Lucas Boucinha , Amine Ammar , Anthony Gravouil , Anthony Nouy
Computer Methods in Applied Mechanics and Engineering, 2014, 273, pp.56-76. ⟨10.1016/j.cma.2014.01.019⟩
Article dans une revue hal-00952496 v1
Image document

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-00861914 v1

Low-rank approximate inverse for preconditioning tensor-structured linear systems

Loïc Giraldi , Anthony Nouy , Grégory Legrain
SIAM Journal on Scientific Computing, 2014, 36 (4), pp.A1850-A1870. ⟨10.1137/130918137⟩
Article dans une revue hal-01007458 v1
Image document

Random fields representations for stochastic elliptic boundary value problems and statistical inverse problems

Anthony Nouy , Christian Soize
European Journal of Applied Mathematics, 2014, 25 (3), pp.339-373. ⟨10.1017/S0956792514000072⟩
Article dans une revue hal-00945639 v1

To Be or Not to Be Intrusive? The Solution of Parametric and Stochastic Equations---the “Plain Vanilla” Galerkin Case

Loïc Giraldi , Alexander Litvinenko , Dishi Liu , Hermann G. Matthies , Anthony Nouy et al.
SIAM Journal on Scientific Computing, 2014, 36 (6), pp.A2720 - A2744. ⟨10.1137/130942802⟩
Article dans une revue hal-01899841 v1
Image document

Tensor-based methods for numerical homogenization from high-resolution images

Loïc Giraldi , Anthony Nouy , Grégory Legrain , Patrice Cartraud
Computer Methods in Applied Mechanics and Engineering, 2013, 254, pp.154-169. ⟨10.1016/j.cma.2012.10.012⟩
Article dans une revue hal-00762845 v1
Image document

A multiscale method with patch for the solution of stochastic partial differential equations with localized uncertainties

Mathilde Chevreuil , Anthony Nouy , Elias Safatly
Computer Methods in Applied Mechanics and Engineering, 2013, 255, pp.255-274. ⟨10.1016/j.cma.2012.12.003⟩
Article dans une revue hal-00733739 v1
Image document

Proper Generalized Decomposition for Nonlinear Convex Problems in Tensor Banach Spaces

Antonio Falco , Anthony Nouy
Numerische Mathematik, 2012, 121 (3), pp.503-530. ⟨10.1007/s00211-011-0437-5⟩
Article dans une revue hal-00609108 v1
Image document

Model Order Reduction based on Proper Generalized Decomposition for the Propagation of Uncertainties in Structural Dynamics

Mathilde Chevreuil , Anthony Nouy
International Journal for Numerical Methods in Engineering, 2012, 89, pp.241--268. ⟨10.1002/nme.3249⟩
Article dans une revue istex hal-00603342 v1
Image document

Fictitious domain method and separated representations for the solution of boundary value problems on uncertain parameterized domains

Anthony Nouy , Mathilde Chevreuil , Elias Safatly
Computer Methods in Applied Mechanics and Engineering, 2011, 200 (45-46), pp.3066-3082. ⟨10.1016/j.cma.2011.07.002⟩
Article dans une revue hal-00662564 v1
Image document

A Proper Generalized Decomposition for the solution of elliptic problems in abstract form by using a functional Eckart-Young approach

Antonio Falco , Anthony Nouy
Journal of Mathematical Analysis and Applications, 2011, 376 (2), pp.469-480
Article dans une revue hal-00461094 v2
Image document

Identification of multi-modal random variables through mixtures of polynomial chaos expansions

Anthony Nouy
Comptes Rendus Mécanique, 2010, 338 (12), pp.698-703. ⟨10.1016/j.crme.2010.09.003⟩
Article dans une revue hal-00521932 v1
Image document

A priori model reduction through Proper Generalized Decomposition for solving time-dependent partial differential equations

Anthony Nouy
Computer Methods in Applied Mechanics and Engineering, 2010, 199 (23-24), pp.1603-1626. ⟨10.1016/j.cma.2010.01.009⟩
Article dans une revue hal-00455635 v1
Image document

Proper Generalized Decompositions and separated representations for the numerical solution of high dimensional stochastic problems

Anthony Nouy
Archives of Computational Methods in Engineering, 2010, 17 (4), pp.403-434. ⟨10.1007/s11831-010-9054-1⟩
Article dans une revue hal-00461099 v1
Image document

eXtended Stochastic Finite Element Method for the numerical simulation of heterogenous materials with random material interfaces

Anthony Nouy , Alexandre Clément
International Journal for Numerical Methods in Engineering, 2010, 83 (10), pp.1312-1344. ⟨10.1002/nme.2865⟩
Article dans une revue istex hal-00455646 v1
Image document

Assessment of ROC curves for inspection of random fields

Franck Schoefs , Alexandre Clément , Anthony Nouy
Structural Safety, 2009, 31 (5), pp.409-419. ⟨10.1016/j.strusafe.2009.01.004⟩
Article dans une revue hal-01005279 v1
Image document

Generalized Spectral Decomposition for Stochastic Non Linear Problems

Anthony Nouy , Olivier Le Maitre
Journal of Computational Physics, 2009, 228 (1), pp.202-235. ⟨10.1016/j.jcp.2008.09.010⟩
Article dans une revue hal-00366630 v1
Image document

On a Computational Strategy with Time-Space Homogenization for Heterogeneous Materials

Anthony Nouy , Pierre Ladevèze
Journal of the Mechanical Behavior of Materials, 2009, 19 (2-3), pp.115-124. ⟨10.1515/JMBM.2009.19.2-3.151⟩
Article dans une revue hal-02163502 v1
Image document

Identification of random shapes from images through polynomial chaos expansion of random level-set functions

Ioannis Stefanou , Anthony Nouy , Alexandre Clément
International Journal for Numerical Methods in Engineering, 2009, 79 (2), pp.127-155. ⟨10.1002/nme.2546⟩
Article dans une revue hal-00366640 v1
Image document

Recent developments in spectral stochastic methods for the numerical solution of stochastic partial differential equations

Anthony Nouy
Archives of Computational Methods in Engineering, 2009, 16 (3), pp.251-285
Article dans une revue hal-00366636 v1
Image document

Generalized spectral decomposition method for solving stochastic finite element equations: invariant subspace problem and dedicated algorithms

Anthony Nouy
Computer Methods in Applied Mechanics and Engineering, 2008, 197 (51-52), pp.4718-4736. ⟨10.1016/j.cma.2008.06.012⟩
Article dans une revue hal-00366613 v1
Image document

An eXtended Stochastic Finite Element Method for solving stochastic partial differential equations on random domains

Anthony Nouy , Alexandre Clément , Franck Schoefs , Nicolas Moes
Computer Methods in Applied Mechanics and Engineering, 2008, 197 (51-52), pp.4663-4682. ⟨10.1016/j.cma.2008.06.010⟩
Article dans une revue hal-00366617 v1
Image document

Méthode de construction de bases spectrales généralisées pour l'approximation de problèmes stochastiques

Anthony Nouy
Mechanics & Industry, 2007, 8 (3), pp.283-288. ⟨10.1051/meca:2007050⟩
Article dans une revue hal-01007031 v1
Image document

X-SFEM, a computational technique based on X-FEM to deal with random shapes

Anthony Nouy , Franck Schoefs , Nicolas Moes
Revue Européenne de Mécanique Numérique/European Journal of Computational Mechanics, 2007, 16 (2), pp.277-293. ⟨10.3166/remn.16.277-293⟩
Article dans une revue hal-00368060 v1
Image document

A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations

Anthony Nouy
Computer Methods in Applied Mechanics and Engineering, 2007, 196 (45-48), pp.4521-4537. ⟨10.1016/j.cma.2007.05.016⟩
Article dans une revue hal-00366619 v2
Image document

Extreme storm loading on in-service wharf structures

Humberto Yáñez-Godoy , Franck Schoefs , Anthony Nouy , Pascal Casari
Revue Européenne de Génie Civil, 2006, 10 (5), pp.565-581. ⟨10.1080/17747120.2006.9692845⟩
Article dans une revue hal-01006890 v1
Image document

Multiscale Computational Strategy With Time and Space Homogenization: A Radial-Type Approximation Technique for Solving Microproblems

Anthony Nouy , Pierre Ladevèze
International Journal for Multiscale Computational Engineering, 2004, 2 (4), ⟨10.1615/IntJMultCompEng.v2.i4.40⟩
Article dans une revue hal-00368058 v1
Image document

On a Multiscale Computational Strategy with Time and Space Homogenization for Structural Mechanics

Pierre Ladevèze , Anthony Nouy
Computer Methods in Applied Mechanics and Engineering, 2003, 192 (28-30), pp.3061-3087. ⟨10.1016/S0045-7825(03)00341-4⟩
Article dans une revue hal-00366648 v1
Image document

A multiscale computational method with time and space homogenization

Pierre Ladevèze , Anthony Nouy
Comptes Rendus Mécanique, 2002, 330 (10), pp.683-689. ⟨10.1016/S1631-0721(02)01514-0⟩
Article dans une revue hal-00368145 v1
Image document

A Multiscale Computational Approach for Contact Problems

Pierre Ladevèze , Anthony Nouy , O. Loiseau
Computer Methods in Applied Mechanics and Engineering, 2002, 191 (43), pp.4869-4891. ⟨10.1016/S0045-7825(02)00406-1⟩
Article dans une revue hal-00366657 v1

Low-rank methods for high-dimensional approximation and model order reduction

Anthony Nouy
P. Benner; A. Cohen; M. Ohlberger; K. Willcox. Model Reduction and Approximation: Theory and Algorithms, SIAM, Philadelphia, 2017
Chapitre d'ouvrage hal-01262422 v1

Low-rank tensor methods for model order reduction

Anthony Nouy
R. Ghanem; D. Higdon; H. Owhadi. Handbook of Uncertainty Quantification, 2016
Chapitre d'ouvrage hal-01262403 v1

Almost-sure quasi-optimal approximation in reproducing kernel Hilbert spaces

Philipp Trunschke , Anthony Nouy
2024
Pré-publication, Document de travail hal-04785505 v1

Optimal sampling for stochastic and natural gradient descent

Robert Gruhlke , Anthony Nouy , Philipp Trunschke
2024
Pré-publication, Document de travail hal-04785511 v1

Optimal sampling for least squares approximation with general dictionaries

Philipp Trunschke , Anthony Nouy
2024
Pré-publication, Document de travail hal-04785502 v1

Preconditioners for model order reduction by interpolation and random sketching of operators

Oleg Balabanov , Anthony Nouy
2023
Pré-publication, Document de travail hal-03919901 v1

Weighted sparsity and sparse tensor networks for least squares approximation

Philipp Trunschke , Anthony Nouy , Martin Eigel
2023
Pré-publication, Document de travail hal-04385061 v1

Approximation Theory of Tree Tensor Networks: Tensorized Multivariate Functions

Mazen Ali , Anthony Nouy
2023
Pré-publication, Document de travail hal-04385183 v1

Weighted least-squares approximation with determinantal point processes and generalized volume sampling

Anthony Nouy , Bertrand Michel
2023
Pré-publication, Document de travail hal-04385090 v1

Approximation with Tensor Networks. Part I: Approximation Spaces

Mazen Ali , Anthony Nouy
2020
Pré-publication, Document de travail hal-02889656 v1

Approximation with Tensor Networks. Part II: Approximation Rates for Smoothness Classes

Mazen Ali , Anthony Nouy
2020
Pré-publication, Document de travail hal-02889657 v1

Learning with tree-based tensor formats

Erwan Grelier , Anthony Nouy , Mathilde Chevreuil
2019
Pré-publication, Document de travail hal-02283004 v1
Image document

Geometric Structures in Tensor Representations (Final Release)

Antonio Falco , Wolfgang Hackbusch , Anthony Nouy
2016
Pré-publication, Document de travail hal-00861916 v2

To be or not to be intrusive? The solution of parametric and stochastic equations - the "plain vanilla" Galerkin case

Loïc Giraldi , Alexander Litvinenko , Dishi Liu , Hermann G. Matthies , Anthony Nouy
2013
Pré-publication, Document de travail hal-00859536 v1
Image document

Constrained Tensor Product Approximations based on Penalized Best Approximations

Anthony Nouy , Antonio Falco
2011
Pré-publication, Document de travail hal-00577942 v1