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08/31/2023
Dynamical low-rank tensor approximations to high-dimensional parabolic problems: existence and convergence of spatial discretizations
We consider dynamical low-rank approximations to parabolic problems on h...
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02/03/2023
A space-time adaptive low-rank method for high-dimensional parabolic partial differential equations
An adaptive method for parabolic partial differential equations that com...
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12/02/2021
Approximation by tree tensor networks in high dimensions: Sobolev and compositional functions
This paper is concerned with convergence estimates for fully discrete tr...
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09/30/2021
Polynomial Approximation of Symmetric Functions
We study the polynomial approximation of symmetric multivariate function...
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09/19/2021
An adaptive stochastic Galerkin method based on multilevel expansions of random fields: Convergence and optimality
The subject of this work is a new stochastic Galerkin method for second-...
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04/27/2021
Particle Number Conservation and Block Structures in Matrix Product States
The eigenvectors of the particle number operator in second quantization ...
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11/13/2020
Multilevel Representations of Isotropic Gaussian Random Fields on the Sphere
Series expansions of isotropic Gaussian random fields on 𝕊^2 with indepe...
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02/27/2020
Existence of dynamical low-rank approximations to parabolic problems
The existence of weak solutions of dynamical low-rank evolution for para...
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11/08/2019
Approximation of Potential Energy Surfaces with Spherical Harmonics
In this note we detail a framework to systematically derive polynomial b...
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10/15/2019
Adaptive Low-Rank Approximations for Operator Equations: Accuracy Control and Computational Complexity
The challenge of mastering computational tasks of enormous size tends to...
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05/31/2019
Unified Analysis of Periodization-Based Sampling Methods for Matérn Covariances
The periodization of a stationary Gaussian random field on a sufficientl...
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05/28/2018