Related papers: A tensor approximation method based on ideal minim…

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, can be exploited. A relevant tool for analysing sparse…

This work introduces an empirical quadrature-based hyperreduction procedure and greedy training algorithm to effectively reduce the computational cost of solving convection-dominated problems with limited training. The proposed approach…

We propose a low-rank tensor approach to approximate linear transport and nonlinear Vlasov solutions and their associated flow maps. The approach takes advantage of the fact that the differential operators in the Vlasov equation is tensor…

In this paper, we propose a novel adaptive-rank method for simulating multi-scale BGK equations, based on a greedy sampling strategy. The method adaptively selects important rows and columns of the solution matrix and updates them using a…

We propose a projection-based model order reduction method for the solution of parameter-dependent dynamical systems. The proposed method relies on the construction of time-dependent reduced spaces generated from evaluations of the solution…

The proximal Galerkin finite element method is a high-order, low-iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of point-wise bound constraints in infinite-dimensional function spaces.…

In this paper, we take a step towards developing efficient hard thresholding methods for low-rank tensor recovery from memory-efficient linear measurements with tensorial structure. Theoretical guarantees for many standard iterative…

Parameter-dependent models arise in many contexts such as uncertainty quantification, sensitivity analysis, inverse problems or optimization. Parametric or uncertainty analyses usually require the evaluation of an output of a model for many…

Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to…

Tensors, especially higher-order tensors, are typically represented in low-rank formats to preserve the main information of the high-dimensional data while saving memory space. In practice, only a small fraction elements in high-dimensional…

This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…

In the fields of control theory and machine learning, the dynamic low-rank approximation for large-scale matrices has received substantial attention. Considering large-scale semilinear stiff matrix differential equations, we propose…

Within the tensor singular value decomposition (T-SVD) framework, existing robust low-rank tensor completion approaches have made great achievements in various areas of science and engineering. Nevertheless, these methods involve the T-SVD…

Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries…

This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a…

In low-rank tensor completion tasks, due to the underlying multiple large-scale singular value decomposition (SVD) operations and rank selection problem of the traditional methods, they suffer from high computational cost and high…

This paper proposes an efficient algorithm (HOLRR) to handle regression tasks where the outputs have a tensor structure. We formulate the regression problem as the minimization of a least square criterion under a multilinear rank…

We study an iterative low-rank approximation method for the solution of the steady-state stochastic Navier--Stokes equations with uncertain viscosity. The method is based on linearization schemes using Picard and Newton iterations and…

In this paper, we propose three approaches for the estimation of the Tucker decomposition of multi-way arrays (tensors) from partial observations. All approaches are formulated as convex minimization problems. Therefore, the minimum is…

In this paper, we consider the Poisson equation on a "long" domain which is the Cartesian product of a one-dimensional long interval with a (d-1)-dimensional domain. The right-hand side is assumed to have a rank-1 tensor structure. We will…