Related papers: A Least-Squares-Based Neural Network (LS-Net) for …
In this paper, a physics-informed multiresolution wavelet neural network (PIMWNN) method is proposed for solving partial differential equations (PDEs). This method uses the multiresolution wavelet neural network (MWNN) to approximate…
Deep neural networks have proved very successful on archetypal tasks for which large training sets are available, but when the training data are scarce, their performance suffers from overfitting. Many existing methods of reducing…
The a posteriori error estimator using the least-squares functional can be used for adaptive mesh refinement and error control even if the numerical approximations are not obtained from the corresponding least-squares method. This suggests…
The closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding method developed to solve a variety of partial differential equations (PDEs) on smooth surfaces, using a closest point representation…
We consider the least-squares finite element method (lsfem) for systems of nonlinear ordinary differential equations and establish an optimal error estimate for this method when piecewise linear elements are used. The main assumptions are…
We develop theoretical results that establish a connection across various regression methods such as the non-negative least squares, bounded variable least squares, simplex constrained least squares, and lasso. In particular, we show in…
Solving partial differential equations (PDEs) has been indispensable in scientific and engineering applications. Recently, deep learning methods have been widely used to solve high-dimensional problems, one of which is the physics-informed…
There are many practical applications based on the Least Square Error (LSE) approximation. It is based on a square error minimization 'on a vertical' axis. The LSE method is simple and easy also for analytical purposes. However, if data…
We study the problem of finding the best linear model that can minimize least-squares loss given a data-set. While this problem is trivial in the low dimensional regime, it becomes more interesting in high dimensions where the population…
We present a novel method for using Neural Networks (NNs) for finding solutions to a class of Partial Differential Equations (PDEs). Our method builds on recent advances in Neural Radiance Field research (NeRFs) and allows for a NN to…
Solving large-scale Partial Differential Equations (PDEs) on complex three-dimensional geometries represents a central challenge in scientific and engineering computing, often impeded by expensive pre-processing stages and substantial…
The present work deals with the rational model order reduction method based on the single-point Least-Square (LS) Pad\'e approximation technique introduced in [3]. Algorithmical aspects concerning the construction of the rational LS-Pad\'e…
Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…
In this work, we study the problem of non-blind image deconvolution and propose a novel recurrent network architecture that leads to very competitive restoration results of high image quality. Motivated by the computational efficiency and…
Surface partial differential equations arise in numerous scientific and engineering applications. Their numerical solution on static and evolving surfaces remains challenging due to geometric complexity and, for evolving geometries, the…
Many classical Computer Vision problems, such as essential matrix computation and pose estimation from 3D to 2D correspondences, can be tackled by solving a linear least-square problem, which can be done by finding the eigenvector…
We propose a framework for solving nonlinear partial differential equations (PDEs) by combining perturbation theory with one-shot transfer learning in Physics-Informed Neural Networks (PINNs). Nonlinear PDEs with polynomial terms are…
Partial Least Squares (PLS) is a widely used method for data integration, designed to extract latent components shared across paired high-dimensional datasets. Despite decades of practical success, a precise theoretical understanding of its…
The classical iteratively reweighted least-squares (IRLS) algorithm aims to recover an unknown signal from linear measurements by performing a sequence of weighted least squares problems, where the weights are recursively updated at each…
The method of ``Total Least Squares'' is proposed as a more natural way (than ordinary least squares) to approximate the data if both the matrix and and the right-hand side are contaminated by ``errors''. In this tutorial note, we give a…