Anthony Nouy

Mazen Ali, Anthony Nouy. Singular Value Decomposition in Sobolev Spaces: Part I. Zeitschrift für Analysis und ihre Anwendungen, European Mathematical Society, 2020, 39, pp.349-369. ⟨10.4171/ZAA/1663⟩. ⟨hal-01899833⟩

Anthony Nouy, Mazen Ali. Singular Value Decomposition in Sobolev Spaces: Part II. Zeitschrift für Analysis und ihre Anwendungen, European Mathematical Society, 2020. ⟨hal-02562141⟩

Thomas Boiveau, Virginie Ehrlacher, Alexandre Ern, Anthony Nouy. Low-rank approximation of linear parabolic equations by space-time tensor Galerkin methods. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2019, 53 (2), pp.635-658. ⟨10.1051/m2an/2018073⟩. ⟨hal-01668316v2⟩

Anthony Nouy. Higher-order principal component analysis for the approximation of tensors in tree-based low-rank formats. Numerische Mathematik, Springer Verlag, 2019, 141 (3), pp.743-789. ⟨10.1007/s00211-018-1017-8⟩. ⟨hal-01521759⟩

Loïc Giraldi, Anthony Nouy. Weakly intrusive low-rank approximation method for nonlinear parameter-dependent equations. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2019, 41 (3), pp.A1777-A1792. ⟨10.1137/17M1136924⟩. ⟨hal-01899838⟩

Oleg Balabanov, Anthony Nouy. Randomized linear algebra for model reduction. Part I: Galerkin methods and error estimation. Advances in Computational Mathematics, Springer Verlag, 2019, 45, pp.2969-3019. ⟨hal-01899836⟩

Antonio Falcó, Wolfgang Hackbusch, Anthony Nouy. Tree-based tensor formats. SeMA Journal: Boletin de la Sociedad Española de Matemática Aplicada, Springer, 2018, ⟨10.1007/s40324-018-0177-x⟩. ⟨hal-01899830⟩

Anthony Nouy, Florent Pled. A multiscale method for semi-linear elliptic equations with localized uncertainties and non-linearities. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2018, 52 (5), pp.1763-1802. ⟨10.1051/m2an/2018025⟩. ⟨hal-01507489v2⟩

Quentin Ayoul-Guilmard, Anthony Nouy, Christophe Binetruy. Tensor-based multiscale method for diffusion problems in quasi-periodic heterogeneous media. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2018, 52 (3), pp.869-891. ⟨10.08307⟩. ⟨hal-01899837⟩

A. Falcó, W. Hackbusch, Anthony Nouy. On the Dirac-Frenkel Variational Principle on Tensor Banach Spaces. Foundations of Computational Mathematics, Springer Verlag, 2018, ⟨10.1007/s10208-018-9381-4⟩. ⟨hal-01457079⟩

Olivier Zahm, Marie Billaud-Friess, Anthony Nouy. Projection based model order reduction methods for the estimation of vector-valued variables of interest. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2017, 39 (4), pp.A1647-A1674. ⟨10.1137/16M106385X⟩. ⟨hal-01387236⟩

Marie Billaud-Friess, Anthony Nouy. Dynamical model reduction method for solving parameter-dependent dynamical systems. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2017, 39 (4), pp.A1766-A1792. ⟨10.1137/16M1071493⟩. ⟨hal-01387231⟩

Olivier Zahm, Anthony Nouy. Interpolation of inverse operators for preconditioning parameter-dependent equations. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2016, 38 (2), pp.A1044--A1074. ⟨hal-01262424⟩

Mathilde Chevreuil, Régis Lebrun, Anthony Nouy, Prashant Rai. A least-squares method for sparse low rank approximation of multivariate functions. SIAM/ASA Journal on Uncertainty Quantification, ASA, American Statistical Association, 2015, 3 (1), pp.897--921. ⟨hal-00861913⟩

Loïc Giraldi, Dishi Liu, Hermann Matthies, Anthony Nouy. To Be or Not to be Intrusive? The Solution of Parametric and Stochastic Equations---Proper Generalized Decomposition. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2015, 37 (1), pp.A347 - A368. ⟨10.1137/140969063⟩. ⟨hal-01899842⟩

Lucas Boucinha, Amine Ammar, Anthony Gravouil, Anthony Nouy. Ideal minimal residual-based proper generalized decomposition for non-symmetric multi-field models - Application to transient elastodynamics in space-time domain. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2014, 273, pp.56-76. ⟨10.1016/j.cma.2014.01.019⟩. ⟨hal-00952496⟩

Anthony Nouy, Christian Soize. Random fields representations for stochastic elliptic boundary value problems and statistical inverse problems. European Journal of Applied Mathematics, Cambridge University Press (CUP), 2014, 25 (3), pp.339-373. ⟨10.1017/S0956792514000072⟩. ⟨hal-00945639⟩

Marie Billaud-Friess, Anthony Nouy, Olivier Zahm. A tensor approximation method based on ideal minimal residual formulations for the solution of high-dimensional problems. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2014, 48, pp.1777-1806. ⟨10.1051/m2an/2014019⟩. ⟨hal-00861914⟩

Loïc Giraldi, Alexander Litvinenko, Dishi Liu, Hermann G. Matthies, Anthony Nouy, et al.. To Be or Not to Be Intrusive? The Solution of Parametric and Stochastic Equations---the “Plain Vanilla” Galerkin Case. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2014, 36 (6), pp.A2720 - A2744. ⟨10.1137/130942802⟩. ⟨hal-01899841⟩

Lorenzo Tamellini, Olivier Le Maitre, Anthony Nouy. Model reduction based on Proper Generalized Decomposition for the Stochastic steady incompressible Navier-Stokes equations. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2014, 36 (3), pp.A1089-A1117. ⟨10.1137/120878999⟩. ⟨hal-00733733⟩

Loïc Giraldi, Anthony Nouy, Grégory Legrain. Low-rank approximate inverse for preconditioning tensor-structured linear systems. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2014, 36 (4), pp.A1850-A1870. ⟨10.1137/130918137⟩. ⟨hal-01007458⟩

Loïc Giraldi, Anthony Nouy, Grégory Legrain, Patrice Cartraud. Tensor-based methods for numerical homogenization from high-resolution images. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2013, 254, pp.154-169. ⟨10.1016/j.cma.2012.10.012⟩. ⟨hal-00762845⟩

Mathilde Chevreuil, Anthony Nouy, Elias Safatly. A multiscale method with patch for the solution of stochastic partial differential equations with localized uncertainties. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2013, 255, pp.255-274. ⟨10.1016/j.cma.2012.12.003⟩. ⟨hal-00733739⟩

Mathilde Chevreuil, Anthony Nouy. Model Order Reduction based on Proper Generalized Decomposition for the Propagation of Uncertainties in Structural Dynamics. International Journal for Numerical Methods in Engineering, Wiley, 2012, 89, pp.241--268. ⟨10.1002/nme.3249⟩. ⟨hal-00603342⟩

Antonio Falco, Anthony Nouy. Proper Generalized Decomposition for Nonlinear Convex Problems in Tensor Banach Spaces. Numerische Mathematik, Springer Verlag, 2012, 121 (3), pp.503-530. ⟨10.1007/s00211-011-0437-5⟩. ⟨hal-00609108⟩

Antonio Falco, Anthony Nouy. A Proper Generalized Decomposition for the solution of elliptic problems in abstract form by using a functional Eckart-Young approach. Journal of Mathematical Analysis and Applications, Elsevier, 2011, 376 (2), pp.469-480. ⟨hal-00461094v2⟩

Anthony Nouy, Mathilde Chevreuil, Elias Safatly. Fictitious domain method and separated representations for the solution of boundary value problems on uncertain parameterized domains. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2011, 200 (45-46), pp.3066-3082. ⟨10.1016/j.cma.2011.07.002⟩. ⟨hal-00662564⟩

Anthony Nouy. A priori model reduction through Proper Generalized Decomposition for solving time-dependent partial differential equations. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2010, 199 (23-24), pp.1603-1626. ⟨10.1016/j.cma.2010.01.009⟩. ⟨hal-00455635⟩

Anthony Nouy, Alexandre Clement. eXtended Stochastic Finite Element Method for the numerical simulation of heterogenous materials with random material interfaces. International Journal for Numerical Methods in Engineering, Wiley, 2010, 83 (10), pp.1312-1344. ⟨10.1002/nme.2865⟩. ⟨hal-00455646⟩

Anthony Nouy. Proper Generalized Decompositions and separated representations for the numerical solution of high dimensional stochastic problems. Archives of Computational Methods in Engineering, Springer Verlag, 2010, 17 (4), pp.403-434. ⟨10.1007/s11831-010-9054-1⟩. ⟨hal-00461099⟩

Anthony Nouy. Identification of multi-modal random variables through mixtures of polynomial chaos expansions. Comptes Rendus Mécanique, Elsevier Masson, 2010, 338 (12), pp.698-703. ⟨10.1016/j.crme.2010.09.003⟩. ⟨hal-00521932⟩

G. Stefanou, Anthony Nouy, Alexandre Clement. Identification of random shapes from images through polynomial chaos expansion of random level-set functions. International Journal for Numerical Methods in Engineering, Wiley, 2009, 79 (2), pp.127-155. ⟨10.1002/nme.2546⟩. ⟨hal-00366640⟩

Anthony Nouy, Pierre Ladevèze. On a Computational Strategy with Time-Space Homogenization for Heterogeneous Materials. Journal of the Mechanical Behavior of Materials, De Gruyter, 2009, 19 (2-3), pp.115-124. ⟨10.1515/JMBM.2009.19.2-3.151⟩. ⟨hal-02163502⟩

Anthony Nouy. Recent developments in spectral stochastic methods for the numerical solution of stochastic partial differential equations. Archives of Computational Methods in Engineering, Springer Verlag, 2009, 16 (3), pp.251-285. ⟨hal-00366636⟩

Franck Schoefs, Alexandre Clément, Anthony Nouy. Assessment of ROC curves for inspection of random fields. Structural Safety, Elsevier, 2009, 31 (5), pp.409-419. ⟨10.1016/j.strusafe.2009.01.004⟩. ⟨hal-01005279⟩

Anthony Nouy, Olivier Le Maitre. Generalized Spectral Decomposition for Stochastic Non Linear Problems. Journal of Computational Physics, Elsevier, 2009, 228 (1), pp.202-235. ⟨10.1016/j.jcp.2008.09.010⟩. ⟨hal-00366630⟩

Anthony Nouy. Generalized spectral decomposition method for solving stochastic finite element equations: invariant subspace problem and dedicated algorithms. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2008, 197 (51-52), pp.4718-4736. ⟨10.1016/j.cma.2008.06.012⟩. ⟨hal-00366613⟩

Anthony Nouy, Alexandre Clement, Franck Schoefs, N. Moes. An eXtended Stochastic Finite Element Method for solving stochastic partial differential equations on random domains. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2008, 197 (51-52), pp.4663-4682. ⟨10.1016/j.cma.2008.06.010⟩. ⟨hal-00366617⟩

Anthony Nouy. Méthode de construction de bases spectrales généralisées pour l'approximation de problèmes stochastiques. Mechanics & Industry, EDP Sciences, 2007, 8 (3), pp.283-288. ⟨10.1051/meca:2007050⟩. ⟨hal-01007031⟩

Anthony Nouy. A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2007, 196 (45-48), pp.4521-4537. ⟨10.1016/j.cma.2007.05.016⟩. ⟨hal-00366619v2⟩

Anthony Nouy, Franck Schoefs, Nicolas Moës. X-SFEM, a computational technique based on X-FEM to deal with random shapes. Revue Européenne de Mécanique Numérique/European Journal of Computational Mechanics, Hermès / Paris : Lavoisier 2007, 16 (2), pp.277-293. ⟨10.3166/remn.16.277-293⟩. ⟨hal-00368060⟩

Humberto Yáñez-Godoy, Franck Schoefs, Anthony Nouy, Pascal Casari. Extreme storm loading on in-service wharf structures: Interest of monitoring for reliability updating. Revue Européenne de Génie Civil, Ed. Lavoisier, 2006, 10 (5), pp.565-581. ⟨10.1080/17747120.2006.9692845⟩. ⟨hal-01006890⟩

Anthony Nouy, Pierre Ladevèze. Multiscale Computational Strategy With Time and Space Homogenization: A Radial-Type Approximation Technique for Solving Microproblems. International Journal for Multiscale Computational Engineering, Begell House, 2004, 2 (4), ⟨10.1615/IntJMultCompEng.v2.i4.40⟩. ⟨hal-00368058⟩

Pierre Ladevèze, Anthony Nouy. On a Multiscale Computational Strategy with Time and Space Homogenization for Structural Mechanics. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2003, 192 (28-30), pp.3061-3087. ⟨10.1016/S0045-7825(03)00341-4⟩. ⟨hal-00366648⟩

Pierre Ladevèze, Anthony Nouy. A multiscale computational method with time and space homogenization. Comptes Rendus Mécanique, Elsevier Masson, 2002, 330 (10), pp.683-689. ⟨10.1016/S1631-0721(02)01514-0⟩. ⟨hal-00368145⟩

Pierre Ladevèze, Anthony Nouy, O. Loiseau. A Multiscale Computational Approach for Contact Problems. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2002, 191 (43), pp.4869-4891. ⟨10.1016/S0045-7825(02)00406-1⟩. ⟨hal-00366657⟩

Anthony Nouy. Low-rank methods for high-dimensional approximation and model order reduction. P. Benner; A. Cohen; M. Ohlberger; K. Willcox. Model Reduction and Approximation: Theory and Algorithms, SIAM, Philadelphia, 2017. ⟨hal-01262422⟩

Anthony Nouy. Low-rank tensor methods for model order reduction. R. Ghanem; D. Higdon; H. Owhadi. Handbook of Uncertainty Quantification, 2016. ⟨hal-01262403⟩

Bertrand Michel, Anthony Nouy. Learning with tree tensor networks: complexity estimates and model selection. 2020. ⟨hal-02889655⟩

Mazen Ali, Anthony Nouy. Approximation with Tensor Networks. Part II: Approximation Rates for Smoothness Classes. 2020. ⟨hal-02889657⟩

Oleg Balabanov, Anthony Nouy. Randomized linear algebra for model reduction. Part II: minimal residual methods and dictionary-based approximation. 2020. ⟨hal-02562161⟩

Marie Billaud Friess, Antonio Falco, Anthony Nouy. A geometry based algorithm for dynamical low-rank approximation. 2020. ⟨hal-02458048⟩

Mazen Ali, Anthony Nouy. Approximation with Tensor Networks. Part I: Approximation Spaces. 2020. ⟨hal-02889656⟩

Mazen Ali, Anthony Nouy. Approximation of Smoothness Classes by Deep ReLU Networks. 2020. ⟨hal-02909881⟩

Cécile Haberstich, Anthony Nouy, Guillaume Perrin. Boosted optimal weighted least-squares. 2020. ⟨hal-02562188⟩

Erwan Grelier, Anthony Nouy, Mathilde Chevreuil. Learning with tree-based tensor formats. 2019. ⟨hal-02283004⟩

Marie Billaud Friess, Arthur Macherey, Anthony Nouy, Clémentine Prieur. Stochastic methods for solving high-dimensional partial differential equations. 2019. ⟨hal-02140703⟩

Quentin Ayoul-Guilmard, Anthony Nouy, Christophe Binetruy. Tensor-based numerical method for stochastic homogenisation. 2018. ⟨hal-01899835⟩

Marie Billaud-Friess, Antonio Falco, Anthony Nouy. Principal bundle structure of matrix manifolds. 2017. ⟨hal-01521748⟩

Antonio Falco, Wolfgang Hackbusch, Anthony Nouy. Geometric Structures in Tensor Representations (Final Release). 2016. ⟨hal-00861916v2⟩

Loïc Giraldi, Alexander Litvinenko, Dishi Liu, Hermann G. Matthies, Anthony Nouy. To be or not to be intrusive? The solution of parametric and stochastic equations - the "plain vanilla" Galerkin case. 2013. ⟨hal-00859536⟩

Anthony Nouy, Antonio Falco. Constrained Tensor Product Approximations based on Penalized Best Approximations. 2011. ⟨hal-00577942⟩