Related papers: Rank adaptive tensor recovery based model reductio…

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…

We study the role of numerical quadrature in residual-minimisation methods for neural network approximation of partial differential equations. We first present an abstract error framework that separates approximation, quadrature and…

In this manuscript we discuss weighted reduced order methods for stochastic partial differential equations. Random inputs (such as forcing terms, equation coefficients, boundary conditions) are considered as parameters of the equations. We…

We consider the multivariate response regression problem with a regression coefficient matrix of low, unknown rank. In this setting, we analyze a new criterion for selecting the optimal reduced rank. This criterion differs notably from the…

In this paper we consider high dimension models based on dependent observations defined through autoregressive processes. For such models we develop an adaptive efficient estimation method via the robust sequential model selection…

Low-rank methods have emerged as a promising strategy for reducing the memory footprint and computational cost of discrete-ordinates discretizations of the radiative transfer equation (RTE). However, most existing rank-adaptive approaches…

We study the low-rank phase retrieval problem, where the objective is to recover a sequence of signals (typically images) given the magnitude of linear measurements of those signals. Existing solutions involve recovering a matrix…

For finite-dimensional problems, stochastic approximation methods have long been used to solve stochastic optimization problems. Their application to infinite-dimensional problems is less understood, particularly for nonconvex objectives.…

Suppose we are given an $n$-dimensional order-3 symmetric tensor $T \in (\mathbb{R}^n)^{\otimes 3}$ that is the sum of $r$ random rank-1 terms. The problem of recovering the rank-1 components is possible in principle when $r \lesssim n^2$…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs). However, their performance heavily relies on the strategy used to select training points. Conventional adaptive…

Low-rank tensor approximation approaches have become an important tool in the scientific computing community. The aim is to enable the simulation and analysis of high-dimensional problems which cannot be solved using conventional methods…

The high-dimensional rank lasso (hdr lasso) model is an efficient approach to deal with high-dimensional data analysis. It was proposed as a tuning-free robust approach for the high-dimensional regression and was demonstrated to enjoy…

Joint probability mass function (PMF) estimation is a fundamental machine learning problem. The number of free parameters scales exponentially with respect to the number of random variables. Hence, most work on nonparametric PMF estimation…

In this work we propose and analyze a weighted proper orthogonal decomposition method to solve elliptic partial differential equations depending on random input data, for stochastic problems that can be transformed into parametric systems.…

Tensor decomposition of high-dimensional data often struggles to capture semantically or physically meaningful structures, particularly when relying on reconstruction objectives and fixed-rank constraints. We introduce a no-rank tensor…

In this paper, we propose a novel low-tubal-rank tensor recovery model, which directly constrains the tubal rank prior for effectively removing the mixed Gaussian and sparse noise in hyperspectral images. The constraints of tubal-rank and…

Many popular statistical models, such as factor and random effects models, give arise a certain type of covariance structures that is a summation of low rank and sparse matrices. This paper introduces a penalized approximation framework to…

Uncertainty quantification based on stochastic spectral methods suffers from the curse of dimensionality. This issue was mitigated recently by low-rank tensor methods. However, there exist two fundamental challenges in low-rank tensor-based…

We present two effective methods for solving high-dimensional partial differential equations (PDE) based on randomized neural networks. Motivated by the universal approximation property of this type of networks, both methods extend the…

To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of…