Search Results - "Nouy, Anthony"

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

“…Over the past years, model reduction techniques have become a necessary path for the reduction of computational requirements in the numerical simulation of…”
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Generalized spectral decomposition method for solving stochastic finite element equations: Invariant subspace problem and dedicated algorithms by Nouy, Anthony

“…Stochastic Galerkin methods have become a significant tool for the resolution of stochastic partial differential equations (SPDE). However, they suffer from…”
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Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations by Nouy, Anthony

“…Uncertainty quantification appears today as a crucial point in numerous branches of science and engineering. In the last two decades, a growing interest has…”
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Approximation Theory of Tree Tensor Networks: Tensorized Univariate Functions by Ali, Mazen, Nouy, Anthony

“…We study the approximation of univariate functions by combining tensorization of functions with tensor trains (TTs)—a commonly used type of tensor networks…”
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Moment-SoS methods for optimal transport problems by Mula, Olga, Nouy, Anthony

“…Most common optimal transport (OT) solvers are currently based on an approximation of underlying measures by discrete measures. However, it is sometimes…”
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Randomized linear algebra for model reduction—part II: minimal residual methods and dictionary-based approximation by Balabanov, Oleg, Nouy, Anthony

“…A methodology for using random sketching in the context of model order reduction for high-dimensional parameter-dependent systems of equations was introduced…”
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Dictionary-based model reduction for state estimation by Nouy, Anthony, Pasco, Alexandre

“…We consider the problem of state estimation from a few linear measurements, where the state to recover is an element of the manifold M of solutions of a…”
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A moment approach for entropy solutions of parameter-dependent hyperbolic conservation laws by Cardoen, Clément, Marx, Swann, Nouy, Anthony, Seguin, Nicolas

“…We propose a numerical method to solve parameter-dependent scalar hyperbolic partial differential equations (PDEs) with a moment approach, based on a previous…”
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Geometry of tree-based tensor formats in tensor Banach spaces by Falcó, Antonio, Hackbusch, Wolfgang, Nouy, Anthony

“…In the paper ‘On the Dirac–Frenkel Variational Principle on Tensor Banach Spaces’ , we provided a geometrical description of manifolds of tensors in Tucker…”
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A probabilistic reduced basis method for parameter-dependent problems by Billaud-Friess, Marie, Macherey, Arthur, Nouy, Anthony, Prieur, Clémentine

“…Probabilistic variants of model order reduction (MOR) methods have recently emerged for improving stability and computational performance of classical…”
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A new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of matrix manifolds by Billaud-Friess, Marie, Falcó, Antonio, Nouy, Anthony

“…In this paper, we propose a new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of the set of fixed rank…”
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Tree-based tensor formats by Falcó, Antonio, Hackbusch, Wolfgang, Nouy, Anthony

“…The main goal of this paper is to study the topological properties of tensors in tree-based Tucker format. These formats include the Tucker format and the…”
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Principal Bundle Structure of Matrix Manifolds by Billaud-Friess, Marie, Falcó, Antonio, Nouy, Anthony

“…In this paper, we introduce a new geometric description of the manifolds of matrices of fixed rank. The starting point is a geometric description of the…”
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A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations by Nouy, Anthony

“…We propose a new robust technique for solving a class of linear stochastic partial differential equations. The solution is approximated by a series of terms,…”
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Higher-order principal component analysis for the approximation of tensors in tree-based low-rank formats by Nouy, Anthony

“…This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition…”
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Proper Generalized Decompositions and Separated Representations for the Numerical Solution of High Dimensional Stochastic Problems by Nouy, Anthony

“…Uncertainty quantification and propagation in physical systems appear as a critical path for the improvement of the prediction of their response. Galerkin-type…”
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Randomized linear algebra for model reduction. Part I: Galerkin methods and error estimation by Balabanov, Oleg, Nouy, Anthony

“…We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A…”
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Foreword to the Proceedings of the CEMRACS 2013 by Champagnat, Nicolas, Lelièvre, Tony, Nouy, Anthony

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Model order reduction based on proper generalized decomposition for the propagation of uncertainties in structural dynamics by Chevreuil, Mathilde, Nouy, Anthony

“…SUMMARY A priori model reduction methods based on separated representations are introduced for the prediction of the low frequency response of uncertain…”
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Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces by Falcó, Antonio, Nouy, Anthony

“…Tensor-based methods are receiving a growing interest in scientific computing for the numerical solution of problems defined in high dimensional tensor product…”
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