72 citations · 536 across the 51 of their papers we have counts for
40 papers · 1 filter
Surrogate to Poincaré inequalities on manifolds for structured dimension reduction in nonlinear feature spaces
Alexandre Pasco, Anthony Nouy
This paper is concerned with the approximation of continuously differentiable functions with high-dimensional input by a composition of two functions: a feature map that extracts f…
Approximation and learning with compositional tensor trains
Martin Eigel, Charles Miranda, Anthony Nouy +1
We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train form…
Surrogate to Poincaré inequalities on manifolds for dimension reduction in nonlinear feature spaces
Anthony Nouy, Alexandre Pasco
We aim to approximate a continuously differentiable function by a composition of functions where $g:\mathbb{R}^d \rightarrow \mat…
Nonlinear manifold approximation using compositional polynomial networks
Antoine Bensalah, Anthony Nouy, Joel Soffo
We consider the problem of approximating a subset of a Hilbert space by a low-dimensional manifold , using samples from . We propose a nonlinear approximation metho…
Optimal sampling for least squares approximation with general dictionaries
Philipp Trunschke, Anthony Nouy
We consider the problem of approximating an unknown function from point evaluations. This problem is a crucial subproblem in many modern (nonlinear) approximation schemes. When obt…
Sample-based almost-sure quasi-optimal approximation in reproducing kernel Hilbert spaces
Nando Hegemann, Anthony Nouy, Philipp Trunschke
This paper addresses the problem of approximating an unknown function from point evaluations. When obtaining these point evaluations is costly, minimising the required sample size…
Weighted least-squares approximation with determinantal point processes and generalized volume sampling
Anthony Nouy, Bertrand Michel
We consider the problem of approximating a function from by an element of a given -dimensional space , associated with some feature map , using evaluati…
Weighted sparsity and sparse tensor networks for least squares approximation
Philipp Trunschke, Anthony Nouy, Martin Eigel
Approximation of high-dimensional functions is a problem in many scientific fields that is only feasible if advantageous structural properties, such as sparsity in a given basis, c…
A moment approach for entropy solutions of parameter-dependent hyperbolic conservation laws
Clément Cardoen, Swann Marx, Anthony Nouy +1
We propose a numerical method to solve parameter-dependent hyperbolic partial differential equations (PDEs) with a moment approach, based on a previous work from Marx et al. (2020)…
A probabilistic reduced basis method for parameter-dependent problems
Marie Billaud-Friess, Arthur Macherey, Anthony Nouy +1
Probabilistic variants of Model Order Reduction (MOR) methods have recently emerged for improving stability and computational performance of classical approaches. In this paper, we…
Dictionary-based model reduction for state estimation
Anthony Nouy, Alexandre Pasco
We consider the problem of state estimation from a few linear measurements, where the state to recover is an element of the manifold of solutions of a parameter-depen…
Moment-SoS Methods for Optimal Transport Problems
Olga Mula, Anthony Nouy
Most common Optimal Transport (OT) solvers are currently based on an approximation of underlying measures by discrete measures. However, it is sometimes relevant to work only with…
Active learning of tree tensor networks using optimal least-squares
Cécile Haberstich, Anthony Nouy, Guillaume Perrin
In this paper, we propose new learning algorithms for approximating high-dimensional functions using tree tensor networks in a least-squares setting. Given a dimension tree or arch…
Random sketching of operators with application to learning preconditioners
Oleg Balabanov, Anthony Nouy, Alexandre Pasco
We propose a new random sketching approach for embedding high-dimensional Hilbert-Schmidt operators, using random input-output pairs. Such operator can then be approximated in a lo…
Geometry of tree-based tensor formats in tensor Banach spaces
Antonio Falcó, Wolfgang Hackbusch, Anthony Nouy
In the paper `On the Dirac-Frenkel Variational Principle on Tensor Banach Spaces', we provided a geometrical description of manifolds of tensors in Tucker format with fixed multili…
A new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of matrix manifolds
Marie Billaud-Friess, Antonio Falcó, Anthony Nouy
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 matrices. We first introdu…
Boosted optimal weighted least-squares
Cécile Haberstich, Anthony Nouy, Guillaume Perrin
This paper is concerned with the approximation of a function in a given approximation space of dimension from evaluations of the function at suitably chosen point…
Randomized linear algebra for model reduction. Part II: minimal residual methods and dictionary-based approximation
Oleg Balabanov, Anthony Nouy
A methodology for using random sketching in the context of model order reduction for high-dimensional parameter-dependent systems of equations was introduced in [Balabanov and Nouy…
Stochastic methods for solving high-dimensional partial differential equations
Marie Billaud-Friess, Arthur Macherey, Anthony Nouy +1
We propose algorithms for solving high-dimensional Partial Differential Equations (PDEs) that combine a probabilistic interpretation of PDEs, through Feynman-Kac representation, wi…
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…
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…
Low-rank approximation of linear parabolic equations by space-time tensor Galerkin methods
Thomas Boiveau, Virginie Ehrlacher, Alexandre Ern +1
We devise a space-time tensor method for the low-rank approximation of linear parabolic evolution equations. The proposed method is a stable Galerkin method, uniformly in the discr…
Tensor-based multiscale method for diffusion problems in quasi-periodic heterogeneous media
Quentin Ayoul-Guilmard, Anthony Nouy, Christophe Binetruy
This paper proposes to address the issue of complexity reduction for the numerical simulation of multiscale media in a quasi-periodic setting. We consider a stationary elliptic dif…