72 citations · 536 across the 51 of their papers we have counts for
5 papers · 1 filter
Learning with tree-based tensor formats
Erwan Grelier, Anthony Nouy, Mathilde Chevreuil
This paper is concerned with the approximation of high-dimensional functions in a statistical learning setting, by empirical risk minimization over model classes of functions in tr…
Tree-based tensor formats
Antonio Falco, Wolfgang Hackbusch, Anthony Nouy
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 Hierarchical Tucker forma…
Singular Value Decomposition in Sobolev Spaces: Part I
Mazen Ali, Anthony Nouy
A well known result from functional analysis states that any compact operator between Hilbert spaces admits a singular value decomposition (SVD). This decomposition is a powerful t…
Tensor-based numerical method for stochastic homogenisation
Quentin Ayoul-Guilmard, Anthony Nouy, Christophe Binetruy
This paper addresses the complexity reduction of stochastic homogenisation of a class of random materials for a stationary diffusion equation. A cost-efficient approximation of the…
Randomized linear algebra for model reduction. Part I: Galerkin methods and error estimation
Oleg Balabanov, Anthony Nouy
We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is…