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Anthony Nouy

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Publications

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⟩
Journal articles hal-03919920v1

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⟩
Journal articles hal-04385174v1

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
Journal articles hal-04385142v1

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⟩
Journal articles hal-03919916v1
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Boosted optimal weighted least-squares

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

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⟩
Journal articles hal-03139679v1

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⟩
Journal articles hal-03919932v1

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⟩
Journal articles hal-01899835v1

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⟩
Journal articles hal-02889655v1

Principal bundle structure of matrix manifolds

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

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⟩
Journal articles hal-02458048v1

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⟩
Journal articles hal-02562161v1

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⟩
Journal articles hal-02909881v1

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⟩
Journal articles hal-01899833v1

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⟩
Journal articles hal-02562141v1

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⟩
Journal articles hal-01521759v1

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⟩
Journal articles hal-01457079v1
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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⟩
Journal articles hal-01668316v2

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⟩
Journal articles hal-01899836v1

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⟩
Journal articles hal-01899838v1

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⟩
Journal articles hal-01899830v1
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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⟩
Journal articles hal-01507489v2

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⟩
Journal articles hal-01387231v1

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⟩
Journal articles hal-01387236v1

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⟩
Journal articles hal-01262424v1

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⟩
Journal articles hal-01899842v1

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⟩
Journal articles hal-00861913v1
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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⟩
Journal articles hal-00945639v1

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⟩
Journal articles hal-01007458v1
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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⟩
Journal articles hal-00733733v1

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⟩
Journal articles hal-00861914v1
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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⟩
Journal articles hal-00952496v1

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
SIAM Journal on Scientific Computing, 2014, 36 (6), pp.A2720 - A2744. ⟨10.1137/130942802⟩
Journal articles hal-01899841v1
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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⟩
Journal articles hal-00762845v1
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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⟩
Journal articles hal-00733739v1

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⟩
Journal articles hal-00609108v1
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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⟩
Journal articles hal-00603342v1
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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⟩
Journal articles hal-00662564v1
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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
Journal articles hal-00461094v2
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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⟩
Journal articles hal-00521932v1
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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⟩
Journal articles hal-00455635v1
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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⟩
Journal articles hal-00461099v1
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eXtended Stochastic Finite Element Method for the numerical simulation of heterogenous materials with random material interfaces

Anthony Nouy , Alexandre Clement
International Journal for Numerical Methods in Engineering, 2010, 83 (10), pp.1312-1344. ⟨10.1002/nme.2865⟩
Journal articles hal-00455646v1
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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⟩
Journal articles hal-01005279v1
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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⟩
Journal articles hal-02163502v1
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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⟩
Journal articles hal-00366630v1
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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
Journal articles hal-00366636v1
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Identification of random shapes from images through polynomial chaos expansion of random level-set functions

G. Stefanou , Anthony Nouy , Alexandre Clement
International Journal for Numerical Methods in Engineering, 2009, 79 (2), pp.127-155. ⟨10.1002/nme.2546⟩
Journal articles hal-00366640v1
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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⟩
Journal articles hal-00366617v1
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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⟩
Journal articles hal-00366613v1
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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⟩
Journal articles hal-00366619v2
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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⟩
Journal articles hal-01007031v1
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X-SFEM, a computational technique based on X-FEM to deal with random shapes

Anthony Nouy , Franck Schoefs , Nicolas Moës
Revue Européenne de Mécanique Numérique/European Journal of Computational Mechanics, 2007, 16 (2), pp.277-293. ⟨10.3166/remn.16.277-293⟩
Journal articles hal-00368060v1
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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⟩
Journal articles hal-01006890v1
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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⟩
Journal articles hal-00368058v1
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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⟩
Journal articles hal-00366648v1
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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⟩
Journal articles hal-00366657v1
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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⟩
Journal articles hal-00368145v1

Stochastic Methods for Solving High-Dimensional Partial Differential Equations

Marie Billaud-Friess , Arthur Macherey , Anthony Nouy , Clémentine Prieur
Monte Carlo and Quasi-Monte Carlo Methods, 324, Springer International Publishing, pp.125-141, 2020, Springer Proceedings in Mathematics & Statistics, ⟨10.1007/978-3-030-43465-6_6⟩
Book sections hal-03919877v1

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
Book sections hal-01262422v1

Low-rank tensor methods for model order reduction

Anthony Nouy
R. Ghanem; D. Higdon; H. Owhadi. Handbook of Uncertainty Quantification, 2016
Book sections hal-01262403v1

Dictionary-based model reduction for state estimation

Anthony Nouy , Alexandre Pasco
2023
Preprints, Working Papers, ... hal-04069442v1

Weighted sparsity and sparse tensor networks for least squares approximation

Philipp Trunschke , Anthony Nouy , Martin Eigel
2023
Preprints, Working Papers, ... hal-04385061v1

Approximation Theory of Tree Tensor Networks: Tensorized Multivariate Functions

Mazen Ali , Anthony Nouy
2023
Preprints, Working Papers, ... hal-04385183v1

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

Oleg Balabanov , Anthony Nouy
2023
Preprints, Working Papers, ... hal-03919901v1
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A moment approach for entropy solutions of parameter-dependent hyperbolic conservation laws

Clément Cardoen , Swann Marx , Anthony Nouy , Nicolas Seguin
2023
Preprints, Working Papers, ... hal-04218591v1

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

Anthony Nouy , Bertrand Michel
2023
Preprints, Working Papers, ... hal-04385090v1

Moment-SoS Methods for Optimal Transport Problems

Olga Mula , Anthony Nouy
2022
Preprints, Working Papers, ... hal-03919946v1

Approximation with Tensor Networks. Part I: Approximation Spaces

Mazen Ali , Anthony Nouy
2020
Preprints, Working Papers, ... hal-02889656v1

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

Mazen Ali , Anthony Nouy
2020
Preprints, Working Papers, ... hal-02889657v1

Learning with tree-based tensor formats

Erwan Grelier , Anthony Nouy , Mathilde Chevreuil
2019
Preprints, Working Papers, ... hal-02283004v1
Image document

Geometric Structures in Tensor Representations (Final Release)

Antonio Falco , Wolfgang Hackbusch , Anthony Nouy
2016
Preprints, Working Papers, ... hal-00861916v2

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
Preprints, Working Papers, ... hal-00859536v1
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Constrained Tensor Product Approximations based on Penalized Best Approximations

Anthony Nouy , Antonio Falco
2011
Preprints, Working Papers, ... hal-00577942v1