Publications
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Preprints Journal papers Book chapters Technical reports
Optimal sampling for stochastic and natural gradient descent. arXiv preprint arXiv:2402.03113, 2024.
Weighted least-squares approximation with determinantal point processes and generalized volume sampling. arXiv preprint arXiv:2312.14057, 2023.
Weighted sparsity and sparse tensor networks for least squares approximation. arXiv preprint arXiv:2310.08942, 2023.
A moment approach for entropy solutions of parameter-dependent hyperbolic conservation. arXiv preprint arXiv:2307.10043, 2023.
A probabilistic reduced basis method for parameter-dependent problems. arXiv preprint arXiv:2304.08784, 2023.
Dictionary-based model reduction for state estimation. arXiv preprint arXiv:2303.10771, 2023.
Moment-SoS Methods for Optimal Transport Problems. arXiv preprint arXiv:2211.10742, 2022.
Preconditioners for model order reduction by interpolation and random sketching of operators. arXiv preprint arXiv:2104.12177, 2021.
Approximation Theory of Tree Tensor Networks: Tensorized Multivariate Functions. arXiv preprint arXiv:2101.11932, 2021.
Learning with tree-based tensor formats. ArXiv e-prints, arXiv:1811.04455, November 2018.
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.
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.
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.
Geometry of tree-based tensor formats in tensor Banach spaces.
Annali di Matematica Pura ed Applicata, March 2023.
Learning with tree tensor networks: complexity estimates and model selection.
Bernoulli, 28(2):910--936, 2022.
Learning high-dimensional probability distributions using tree tensor
networks. International Journal for Uncertainty Quantification. Volume 12, Issue 5, pp. 47-69, 2022.
Boosted optimal weighted least-squares.
Mathematics of Computation, 2022.
A PAC algorithm in relative precision for bandit problem with costly sampling.
Mathematical Methods of Operations Research, volume 96, pages 161–185, 2022.
Tensor-based numerical method for stochastic homogenisation.
SIAM Multiscale Modeling & Simulation, volume 20, issue 1, 2022.
Approximation of smoothness classes by deep rectifier networks.
SIAM Journal on Numerical Analysis, 59(6):3032–3051, 2021.
A new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of matrix manifolds. BIT Numerical Mathematics, 2021.
Randomized linear algebra for model reduction. part II: minimal
residual methods and dictionary-based approximation.
Advances in Computational Mathematics. 47, 26, 2021.
Principal bundle structure of matrix manifolds.
Mathematics, 9:1669, 2021.
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.
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.
Singular Value Decomposition in Sobolev Spaces: Part I.
Zeitschrift für Analysis und ihre Anwendungen. 39(3):349-369, 2020.
Singular Value Decomposition in Sobolev Spaces: Part II.
Zeitschrift für Analysis und ihre Anwendungen. 39(4):371–394, 2020.
Randomized linear algebra for model reduction. Part I: Galerkin methods and error estimation. Advances in Computational Mathematics. 45(5-6):2969--3019,
2019.
Low-rank approximation of linear parabolic equations by space-time tensor Galerkin methods. ESAIM: M2AN, 53(2):635-658, 2019.
Weakly intrusive low-rank approximation method for nonlinear parameter-dependent equations. SIAM Journal on Scientific Computing, Volume 41, Issue 3, 2019.
Higher-order principal component analysis for the approximation of tensors in tree-based low rank formats.
Numerische Mathematik, 141(3):743--789, Mar 2019.
On the Dirac-Frenkel Variational Principle on Tensor Banach Spaces.
Foundations of Computational Mathematics, 19(1):159--204, Feb
2019.
Tree-based tensor formats.
SeMA Journal, pp 1-15, Oct 2018.
A multiscale method for semi-linear elliptic equations with localized
uncertainties and non-linearities.
ESAIM: M2AN, 52(5):1763--1802, 2018.
Tensor-based multiscale method for diffusion problems in quasi-periodic heterogeneous media.
ESAIM: M2AN, 52(3):869--891, 2018.
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.
Interpolation of inverse operators for preconditioning
parameter-dependent equations.
SIAM Journal on Scientific Computing, 38(2):A1044--A1074, 2016.
Dynamical model reduction method for solving parameter-dependent
dynamical systems.
SIAM Journal on Scientific Computing, 39(4):A1766--A1792, 2017.
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.
A least-squares method for sparse low rank approximation of multivariate functions.
SIAM/ASA Journal on Uncertainty Quantification, 3(1):897--921,
2015.
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.
Low-rank approximate inverse for preconditioning tensor-structured linear systems.
SIAM Journal on Scientific Computing, 36(4):A1850--A1870, 2014.
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.
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.
Random fields representations for stochastic elliptic boundary value problems and statistical inverse problems. European J. of Applied Mathematics, 25(3):339-373, 2014.
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.
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.
Tensor-based methods for numerical homogenization from high-resolution images. Computer Methods in Applied Mechanics and Engineering, 254(0):154-169, 2013.
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.
Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces. Numerische Mathematik, 121:503-530, 2012.
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 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,
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 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.
Identification of multi-modal random variables through mixtures of
polynomial chaos expansions. Comptes Rendus Mécanique,
338(12):698--703, 2010.
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.
Generalized spectral
decomposition method for stochastic non linear problems.
Journal of Computational Physics, 228(1):202--235, 2009.
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.
Proper Generalized Decomposition in Extreme Simulations: Towards a Change
of Paradigm in Computational Mechanics? IACM expressions, 26,
December 2009.
Assessment
of roc curves for inspection of random fields. Structural Safety,
31(5):409--419, 2009.
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.
On a
computational strategy with time-space homogenization for
heterogeneous materials. Journal of the mechanical behaviour Of
materials, 19(2-3):151--158, 2009.
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.
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 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.
Méthode de construction de bases spectrales
généralisées pour l'approximation de problemes stochastiques.
Mécanique & Industries, 8(3):283--288, 2007.
X-SFEM, a computational technique based on
X-FEM to deal with random shapes.
European Journal of Computational Mechanics, 16(2):277--293, 2007.
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.
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.
On a multiscale computational strategy with
time and space homogenization for structural mechanics. Comput.
Meth. App. Mech. Eng., 192:3061--3087, 2003.
A multiscale computational approach for contact problems. Comput. Meth. App.
Mech. Eng., 191:4869--4891, 2002.
A multiscale computational method with
time and space homogenization. C. R. Mécanique, 330(10):683--689,
2002.