相关论文: Local Feature Filtering for Scalable and Well-Cond…

Aiming to enhance Face Recognition (FR) on Low-Quality (LQ) inputs, recent studies suggest incorporating synthetic LQ samples into training. Although promising, the quality factors that are considered in these works are general rather than…

We propose and test the first Reduced Radial Basis Function Method (R$^2$BFM) for solving parametric partial differential equations on irregular domains. The two major ingredients are a stable Radial Basis Function (RBF) solver that has an…

Optimization problems constrained by partial differential equations (PDEs) naturally arise in scientific computing, as those constraints often model physical systems or the simulation thereof. In an implicitly constrained approach, the…

Reduced-order modeling (ROM) commonly refers to the construction, based on a few solutions (referred to as snapshots) of an expensive discretized partial differential equation (PDE), and the subsequent application of low-dimensional…

Rational filter functions can be used to improve convergence of contour-based eigensolvers, a popular family of algorithms for the solution of the interior eigenvalue problem. We present a framework for the optimization of rational filters…

This article presents matrix backpropagation algorithms for the QR decomposition of matrices $A_{m, n}$, that are either square (m = n), wide (m < n), or deep (m > n), with rank $k = min(m, n)$. Furthermore, we derive novel matrix…

Randomized algorithms for low-rank matrix approximation are investigated, with the emphasis on the fixed-precision problem and computational efficiency for handling large matrices. The algorithms are based on the so-called QB factorization,…

Extreme Learning Machine (ELM) is an efficient and effective least-square-based learning algorithm for classification, regression problems based on single hidden layer feed-forward neural network (SLFN). It has been shown in the literature…

We propose a prediction procedure for the functional linear quantile regression model by using partial quantile covariance techniques and develop a simple partial quantile regression (SIMPQR) algorithm to efficiently extract partial…

This paper addresses the efficient solution of linear systems arising from curl-conforming finite element discretizations of $H(\mathrm{curl})$ elliptic problems with heterogeneous coefficients. We first employ the discrete form of a…

CholeskyQR is a simple and fast QR decomposition via Cholesky decomposition, while it has been considered highly sensitive to the condition number. In this paper, we provide a randomized preconditioner framework for CholeskyQR algorithm.…

Distributional assumptions have been shown to be necessary for the robust learnability of concept classes when considering the exact-in-the-ball robust risk and access to random examples by Gourdeau et al. (2019). In this paper, we study…

Parameter-efficient fine-tuning for pre-trained Vision Transformers aims to adeptly tailor a model to downstream tasks by learning a minimal set of new adaptation parameters while preserving the frozen majority of pre-trained parameters.…

The simulation of complex systems, such as gas transport in large pipeline networks, often involves solving PDEs posed on intricate graph structures. Such problems require considerable computational and memory resources. The Random Batch…

A multi-preconditioned LBFGS (MP-LBFGS) algorithm is introduced for training finite-basis physics-informed neural networks (FBPINNs). The algorithm is motivated by the nonlinear additive Schwarz method and exploits the…

Kernel power $k$-means (KPKM) leverages a family of means to mitigate local minima issues in kernel $k$-means. However, KPKM faces two key limitations: (1) the computational burden of the full kernel matrix restricts its use on extensive…

Vision problems ranging from image clustering to motion segmentation to semi-supervised learning can naturally be framed as subspace segmentation problems, in which one aims to recover multiple low-dimensional subspaces from noisy and…

We present a reduced order modeling (ROM) technique for subsurface multi-phase flow problems building on the recently introduced deep residual recurrent neural network (DR-RNN) [1]. DR-RNN is a physics aware recurrent neural network for…

Variational Quantum Algorithms (VQAs) have gained prominence as a viable framework for exploiting near-term quantum devices in applications ranging from optimization and chemistry simulation to machine learning. However, the effectiveness…

Randomized neural networks (RaNNs) are attractive for partial differential equations (PDEs) because they replace expensive end-to-end training with a linear least-squares solve over randomized hidden features. Their practical performance,…