Preprints

• A. Bensallah, A. Nouy and J. Soffo.
  Nonlinear manifold approximation using compositional polynomial networks. arXiv preprint arXiv:2502.05088 , 2025.
• P. Trunschke and A. Nouy.
  Optimal sampling for least squares approximation with general dictionaries. arXiv preprint arXiv:2407.07814, 2024.
• P. Trunschke and A. Nouy.
  Almost-sure quasi-optimal approximation in reproducing kernel Hilbert spaces. arXiv preprint arXiv:2407.06674, 2024.
• R. Gruhlke, A. Nouy and P. Trunschke.
  Optimal sampling for stochastic and natural gradient descent. arXiv preprint arXiv:2402.03113, 2024.
• A. Nouy and B. Michel.
  Weighted least-squares approximation with determinantal point processes and generalized volume sampling. arXiv preprint arXiv:2312.14057, 2023.
• P. Trunschke, A. Nouy, M. Eigel.
  Weighted sparsity and sparse tensor networks for least squares approximation. arXiv preprint arXiv:2310.08942, 2023.
• O. Balabanov and A. Nouy.
  Preconditioners for model order reduction by interpolation and random sketching of operators. arXiv preprint arXiv:2104.12177, 2021.
• M. Ali and A. Nouy.
  Approximation Theory of Tree Tensor Networks: Tensorized Multivariate Functions. arXiv preprint arXiv:2101.11932, 2021.
• E. Grelier, A. Nouy, and M. Chevreuil.
  Learning with tree-based tensor formats. ArXiv e-prints, arXiv:1811.04455, November 2018.

Journal papers

• C. Cardoen, S. Marx, A. Nouy, and N. Seguin.
  A moment approach for entropy solutions of parameter-dependent hyperbolic conservation. Numerische Mathematik, 2024. arXiv preprint arXiv:2307.10043v2.
• O. Mula, A. Nouy.
  Moment-SoS Methods for Optimal Transport Problems. Numerische Mathematik, 2024. arXiv preprint arXiv:2211.10742.
• A. Nouy and A. Pasco.
  Dictionary-based model reduction for state estimation. Adv. Comput. Math., 50(3):1–31, June 2024. arXiv preprint arXiv:2303.10771.
• M. Billaud-Friess, A. Macherey, A. Nouy, and C. Prieur.
  A probabilistic reduced basis method for parameter-dependent problems. Adv. Comput. Math., 50(2):1–26, Apr. 2024. arXiv preprint arXiv:2304.08784.
• C. Haberstich, A. Nouy, and G. Perrin.
  Active learning of tree tensor networks using optimal least-squares. SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 3, pp. 848--876, 2023. arXiv preprint arXiv:2104.13436.
• M. Bachmayr, A. Nouy, and R. Schneider.
  Approximation by tree tensor networks in high dimensions: Sobolev and compositional functions. Pure and Applied Functional Analysis, Volume 8, Number 2, pp. 405--428, 2023. arXiv preprint arXiv:2112.01474.
• M. Ali and A. Nouy.
  Approximation Theory of Tree Tensor Networks: Tensorized Univariate Functions. Constructive Approximation, March 2023. ArXiv e-prints in two parts: arXiv:2007.00118, arXiv:2007.00128.
• A. Falco, W. Hackbusch, A. Nouy.
  Geometry of tree-based tensor formats in tensor Banach spaces. Annali di Matematica Pura ed Applicata, March 2023.
• B. Michel and A. Nouy.
  Learning with tree tensor networks: complexity estimates and model selection. Bernoulli, 28(2):910--936, 2022.
• E. Grelier, A. Nouy, and R. Lebrun.
  Learning high-dimensional probability distributions using tree tensor networks. International Journal for Uncertainty Quantification. Volume 12, Issue 5, pp. 47-69, 2022.
• C. Haberstich, A. Nouy, and G. Perrin.
  Boosted optimal weighted least-squares. Mathematics of Computation, 2022.
• M. Billaud-Friess, A. Macherey, A. Nouy, and C. Prieur.
  A PAC algorithm in relative precision for bandit problem with costly sampling. Mathematical Methods of Operations Research, volume 96, pages 161–185, 2022.
• Q. Ayoul-Guilmard, A. Nouy, and C. Binetruy.
  Tensor-based numerical method for stochastic homogenisation. SIAM Multiscale Modeling & Simulation, volume 20, issue 1, 2022.
• M. Ali and A. Nouy.
  Approximation of smoothness classes by deep rectifier networks. SIAM Journal on Numerical Analysis, 59(6):3032–3051, 2021.
• M. Billaud-Friess, A. Falco, and A. Nouy.
  A new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of matrix manifolds. BIT Numerical Mathematics, 2021.
• O. Balabanov and A. Nouy.
  Randomized linear algebra for model reduction. part II: minimal residual methods and dictionary-based approximation. Advances in Computational Mathematics. 47, 26, 2021.
• M. Billaud-Friess, A. Falco, and A. Nouy.
  Principal bundle structure of matrix manifolds. Mathematics, 9:1669, 2021.
• G. Ducamp, P. Bonnard, A. Nouy, P.-H. Wuillemin.
  An Efficient Low-Rank Tensors Representation for Algorithms in Complex Probabilistic Graphical Models. Proceedings of the 10th International Conference on Probabilistic Graphical Models, PMLR 138, 2020.
• M. Billaud-Friess, A. Macherey, A. Nouy, and C. Prieur.
  Stochastic methods for solving high-dimensional partial differential equations.. In Monte Carlo and Quasi-Monte Carlo Methods, B. Tuffin and P. L'Ecuyer (Eds). Pages 125-141. Springer, Cham, 2020.
• M. Ali and A. Nouy.
  Singular Value Decomposition in Sobolev Spaces: Part I. Zeitschrift für Analysis und ihre Anwendungen. 39(3):349-369, 2020.
• M. Ali and A. Nouy.
  Singular Value Decomposition in Sobolev Spaces: Part II. Zeitschrift für Analysis und ihre Anwendungen. 39(4):371–394, 2020.
• O. Balabanov and A. Nouy.
  Randomized linear algebra for model reduction. Part I: Galerkin methods and error estimation. Advances in Computational Mathematics. 45(5-6):2969--3019, 2019.
• T. Boiveau, V. Ehrlacher, A. Ern, and A. Nouy.
  Low-rank approximation of linear parabolic equations by space-time tensor Galerkin methods. ESAIM: M2AN, 53(2):635-658, 2019.
• L. Giraldi and A. Nouy.
  Weakly intrusive low-rank approximation method for nonlinear parameter-dependent equations. SIAM Journal on Scientific Computing, Volume 41, Issue 3, 2019.
• A. Nouy.
  Higher-order principal component analysis for the approximation of tensors in tree-based low rank formats. Numerische Mathematik, 141(3):743--789, Mar 2019.
• A. Falco, W. Hackbusch and A. Nouy.
  On the Dirac-Frenkel Variational Principle on Tensor Banach Spaces. Foundations of Computational Mathematics, 19(1):159--204, Feb 2019.
• A. Falco, W. Hackbusch, and A. Nouy.
  Tree-based tensor formats. SeMA Journal, pp 1-15, Oct 2018.
• A. Nouy and F. Pled.
  A multiscale method for semi-linear elliptic equations with localized uncertainties and non-linearities. ESAIM: M2AN, 52(5):1763--1802, 2018.
• Q. Ayoul-Guilmard, A. Nouy, and C. Binetruy.
  Tensor-based multiscale method for diffusion problems in quasi-periodic heterogeneous media. ESAIM: M2AN, 52(3):869--891, 2018.
• O. Zahm, M. Billaud-Friess, and A. Nouy.
  Projection-based model order reduction methods for the estimation of vector-valued variables of interest. SIAM Journal on Scientific Computing, 39(4):A1647--A1674, 2017.
• O. Zahm and A. Nouy.
  Interpolation of inverse operators for preconditioning parameter-dependent equations. SIAM Journal on Scientific Computing, 38(2):A1044--A1074, 2016.
• M. Billaud-Friess and A. Nouy.
  Dynamical model reduction method for solving parameter-dependent dynamical systems. SIAM Journal on Scientific Computing, 39(4):A1766--A1792, 2017.
• L. Giraldi, D. Liu, H. G. Matthies, and A. Nouy.
  To be or not to be intrusive? The solution of parametric and stochastic equations --- Proper Generalized Decomposition. SIAM J. Sci. Comp., 37(1):A347-A368, 2015.
• M. Chevreuil, R. Lebrun, A. Nouy, and P. Rai.
  A least-squares method for sparse low rank approximation of multivariate functions. SIAM/ASA Journal on Uncertainty Quantification, 3(1):897--921, 2015.
• M. Billaud-Friess, A. Nouy and O. Zahm.
  A tensor approximation method based on ideal minimal residual formulations for the solution of high-dimensional problems. ESAIM: Mathematical Modelling and Numerical Analysis, 48:1777-1806, 2014.
• L. Giraldi, A. Nouy, and G. Legrain.
  Low-rank approximate inverse for preconditioning tensor-structured linear systems. SIAM Journal on Scientific Computing, 36(4):A1850--A1870, 2014.
• L. Giraldi, A. Litvinenko, D. Liu, H. G. Matthies, and A. Nouy.
  To be or not to be intrusive? The solution of parametric and stochastic equations - the "plain vanilla" Galerkin case. SIAM Journal on Scientific Computing. 36(6):A2720-A2744, 2014.
• L. Boucinha, A. Ammar, A. Gravouil and A. 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. 273:56-76, 2014.
• A. Nouy and C. Soize.
  Random fields representations for stochastic elliptic boundary value problems and statistical inverse problems. European J. of Applied Mathematics, 25(3):339-373, 2014.
• L. Tamellini, O. Le Maitre, and A. Nouy.
  Model reduction based on proper generalized decomposition for the stochastic steady incompressible Navier-Stokes equations. SIAM Journal on Scientific Computing, 36(3):A1089--A1117, 2014.
• M. Chevreuil, A. Nouy, and E. Safatly.
  A multiscale method with patch for the solution of stochastic partial differential equations with localized uncertainties. Computer Methods in Applied Mechanics and Engineering, 255(0):255-274, 2013.
• L. Giraldi, A. Nouy, G. Legrain, and P. Cartraud.
  Tensor-based methods for numerical homogenization from high-resolution images. Computer Methods in Applied Mechanics and Engineering, 254(0):154-169, 2013.
• M. Chevreuil and A. Nouy.
  Model order reduction based on proper generalized decomposition for the propagation of uncertainties in structural dynamics. Int. J. for Numerical Methods in Engineering, 89:241--268, 2012.
• A. Falcó and A. Nouy.
  Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces. Numerische Mathematik, 121:503-530, 2012.
• A. Nouy, M. Chevreuil, and E. 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, 200(45-46):3066--3082, 2011.
• A. Falco and A. 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, 376(2):469--480,
• A. Nouy.
  Proper Generalized Decompositions and separated representations for the numerical solution of high dimensional stochastic problems. Archives of Computational Methods in Engineering, 17(4):403--434, 2010.
• A. Nouy.
  A priori model reduction through proper generalized decomposition for solving time dependent partial differential equations. Computer Methods in Applied Mechanics and Engineering, 199(23-24):1603--1626, 2010.
• A. Nouy.
  Identification of multi-modal random variables through mixtures of polynomial chaos expansions. Comptes Rendus Mécanique, 338(12):698--703, 2010.
• A. Nouy and A. Clement.
  Extended stochastic finite element method for the numerical simulation of heterogenous materials with random material interfaces. Int. J. for Numerical Methods in Engineering, 83(10):127--155, 2010.
• A. Nouy and O.P. Le Maître.
  Generalized spectral decomposition method for stochastic non linear problems. Journal of Computational Physics, 228(1):202--235, 2009.
• A. Nouy.
  Recent developments in spectral stochastic methods for the numerical solution of stochastic partial differential equations. Archives of Computational Methods in Engineering, 16(3):251-- 285, 2009.
• F. Chinesta, P. Ladevèze, A. Ammar, E. Cueto, A. Nouy.
  Proper Generalized Decomposition in Extreme Simulations: Towards a Change of Paradigm in Computational Mechanics? IACM expressions, 26, December 2009.
• F. Schoefs, A. Clement, and A. Nouy.
  Assessment of roc curves for inspection of random fields. Structural Safety, 31(5):409--419, 2009.
• G. Stefanou, A. Nouy, and A. Clément.
  Identification of random shapes from images through polynomial chaos expansion of random level-set functions. Int. J. for Numerical Methods in Engineering, 79(2):127--155, 2009.
• A. Nouy and P. Ladevèze.
  On a computational strategy with time-space homogenization for heterogeneous materials. Journal of the mechanical behaviour Of materials, 19(2-3):151--158, 2009.
• A. Nouy.
  Generalized spectral decomposition method for solving stochastic finite element equations: invariant subspace problem and dedicated algorithms. Comput. Meth. App. Mech. Eng., 197:4718--4736, 2008.
• A. Nouy, A. Clément, F. Schoefs, and N. Moës.
  An extended stochastic finite element method for solving stochastic partial differential equations on random domains. Comput. Meth. App. Mech. Eng., 197:4663--4682, 2008.
• A. Nouy.
  A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations. Comput. Meth. App. Mech. Eng., 196(45- 48):4521--4537, 2007.
• A. Nouy.
  Méthode de construction de bases spectrales généralisées pour l'approximation de problemes stochastiques. Mécanique & Industries, 8(3):283--288, 2007.
• A. Nouy, F. Schoefs, and N. Moes.
  X-SFEM, a computational technique based on X-FEM to deal with random shapes. European Journal of Computational Mechanics, 16(2):277--293, 2007.
• H. Yanez-Godoy, F. Schoefs, A. Nouy, and P. Casari.
  Extreme storm loading on in-service wharf structures. interest of monitoring for reliability updating. European Journal of Environmental and Civil Engineering, 10(5):565--581, 2006.
• A. Nouy and P. Ladevèze.
  Multiscale computational strategy with time and space homogenization: a radial-type approximation technique for solving micro problems. International Journal for Multiscale Computational Engineering, 170(2):557--574, 2004.
• P. Ladevèze and A. Nouy.
  On a multiscale computational strategy with time and space homogenization for structural mechanics. Comput. Meth. App. Mech. Eng., 192:3061--3087, 2003.
• P. Ladevèze, A. Nouy, and O. Loiseau.
  A multiscale computational approach for contact problems. Comput. Meth. App. Mech. Eng., 191:4869--4891, 2002.
• P. Ladevèze and A. Nouy.
  A multiscale computational method with time and space homogenization. C. R. Mécanique, 330(10):683--689, 2002.

• A. Nouy. Low-rank methods for high-dimensional approximation and model order reduction. In P. Benner, A. Cohen, M. Ohlberger, and K. Willcox (eds.), Model Reduction and Approximation: Theory and Algorithms. SIAM, Philadelphia, PA, 2017.
• A. Nouy. Low-Rank Tensor Methods for Model Order Reduction. In R. Ghanem, D. Higdon, H. Owhadi (Eds), Handbook of Uncertainty Quantification. Springer International Publishing, Cham, 2017.

Technical reports

• A. Falcó, W. Hackbusch, and A. Nouy. Geometric structures in tensor representations (Final Release). arXiv:1505.03027.
• A. Nouy and A. Falco. Constrained tensor product approximations based on penalized best approximations. oai:hal.archives-ouvertes.fr:hal-00577942, 2011.