Matthieu Dolbeault
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View article: Iterative thresholding low-rank time integration
Iterative thresholding low-rank time integration Open
We develop time integration methods in low-rank representation that can adaptively adjust approximation ranks to achieve a prescribed accuracy, while ensuring that these ranks remain proportional to the corresponding best approximation ran…
View article: State estimation of urban air pollution with statistical, physical, and super-learning graph models
State estimation of urban air pollution with statistical, physical, and super-learning graph models Open
We consider the problem of real-time reconstruction of urban air pollution maps. The task is challenging due to the heterogeneous sources of available data, the scarcity of direct measurements, the presence of noise, and the large surfaces…
View article: State estimation of urban air pollution with statistical, physical, and super-learning graph models
State estimation of urban air pollution with statistical, physical, and super-learning graph models Open
We consider the problem of real-time reconstruction of urban air pollution maps. The task is challenging due to the heterogeneous sources of available data, the scarcity of direct measurements, the presence of noise, and the large surfaces…
View article: Spectrally accurate fully discrete schemes for some nonlocal and nonlinear integrable PDEs via explicit formulas
Spectrally accurate fully discrete schemes for some nonlocal and nonlinear integrable PDEs via explicit formulas Open
We construct fully-discrete schemes for the Benjamin-Ono, Calogero-Sutherland DNLS, and cubic Szegő equations on the torus, which are $\textit{exact in time}$ with $\textit{spectral accuracy}$ in space. We prove spectral convergence for th…
View article: Échantillonnage optimal et réduction de modèle
Échantillonnage optimal et réduction de modèle Open
This thesis is concerned, on the one hand, with the design of reduced order models that optimally approximate complex classes of functions, and on the other hand with the use of such reduced models to recover functions from a limited amoun…
View article: Randomized least-squares with minimal oversampling and interpolation in general spaces
Randomized least-squares with minimal oversampling and interpolation in general spaces Open
In approximation of functions based on point values, least-squares methods provide more stability than interpolation, at the expense of increasing the sampling budget. We show that near-optimal approximation error can nevertheless be achie…
View article: Reduced order modeling for elliptic problems with high contrast diffusion coefficients
Reduced order modeling for elliptic problems with high contrast diffusion coefficients Open
We consider a parametric elliptic PDE with a scalar piecewise constant diffusion coefficient taking arbitrary positive values on fixed subdomains. This problem is not uniformly elliptic, as the contrast can be arbitrarily high, contrary to…
View article: Reduced order modeling for elliptic problems with high contrast diffusion coefficients
Reduced order modeling for elliptic problems with high contrast diffusion coefficients Open
We consider the parametric elliptic PDE $-{\rm div} (a(y)\nabla u)=f$ on a spatial domain $Ω$, with $a(y)$ a scalar piecewise constant diffusion coefficient taking any positive values $y=(y_1, \dots, y_d)\in ]0,\infty[^d$ on fixed subdomai…
View article: A sharp upper bound for sampling numbers in L2
A sharp upper bound for sampling numbers in L2 Open
View article: Nonlinear approximation spaces for inverse problems
Nonlinear approximation spaces for inverse problems Open
This paper is concerned with the ubiquitous inverse problem of recovering an unknown function u from finitely many measurements, possibly affected by noise. In recent years, inversion methods based on linear approximation spaces were intro…
View article: Nonlinear approximation spaces for inverse problems
Nonlinear approximation spaces for inverse problems Open
This paper is concerned with the ubiquitous inverse problem of recovering an unknown function u from finitely many measurements possibly affected by noise. In recent years, inversion methods based on linear approximation spaces were introd…
View article: Projet SNCF maths-entreprises AMIES.
Projet SNCF maths-entreprises AMIES. Open
View article: Optimal pointwise sampling for $L^2$ approximation
Optimal pointwise sampling for $L^2$ approximation Open
Given a function $u\in L^2=L^2(D,μ)$, where $D\subset \mathbb R^d$ and $μ$ is a measure on $D$, and a linear subspace $V_n\subset L^2$ of dimension $n$, we show that near-best approximation of $u$ in $V_n$ can be computed from a near-optim…
View article: Optimal sampling and Christoffel functions on general domains
Optimal sampling and Christoffel functions on general domains Open
We consider the problem of reconstructing an unknown function $u\in L^2(D,μ)$ from its evaluations at given sampling points $x^1,\dots,x^m\in D$, where $D\subset \mathbb R^d$ is a general domain and $μ$ a probability measure. The approxima…