Related papers: Least-Squares ReLU Neural Network (LSNN) Method Fo…
The deep-learning-based least squares method has shown successful results in solving high-dimensional non-linear partial differential equations (PDEs). However, this method usually converges slowly. To speed up the convergence of this…
In the field of localization the linear least square solution is frequently used. This solution is compared to nonlinear solvers more effected by noise, but able to provide a position estimation without the knowledge of any starting…
In this paper, we study the problem of multipath channel estimation for direct sequence spread spectrum signals. To resolve multipath components arriving within a short interval, we propose a new algorithm called the least-squares based…
We propose a deep learning approach to the obstacle problem inspired by the first-order system least-squares (FOSLS) framework. This method reformulates the problem as a convex minimization task; by simultaneously approximating the…
This document is an introduction to the Matlab package SDLS (Semi-Definite Least-Squares) for solving least-squares problems over convex symmetric cones. The package is shortly presented through the addressed problem, a sketch of the…
This is a brief tutorial on the least square estimation technique that is straightforward yet effective for parameter estimation. The tutorial is focused on the linear LSEs instead of nonlinear versions, since most nonlinear LSEs can be…
This paper presents a first-order {distributed continuous-time algorithm} for computing the least-squares solution to a linear equation over networks. Given the uniqueness of the solution, with nonintegrable and diminishing step size,…
Motivated by renal imaging studies that combine renogram curves with pharmacokinetic and demographic covariates, we propose Hybrid partial least squares (Hybrid PLS) for simultaneous supervised dimension reduction and regression in the…
For hyperbolic conservation laws, traditional methods and physics-informed neural networks (PINNs) often encounter difficulties in capturing sharp discontinuities and maintaining temporal consistency. To address these challenges, we…
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…
This work addresses weight optimization problem for fully-connected feed-forward neural networks. Unlike existing approaches that are based on back-propagation (BP) and chain rule gradient-based optimization (which implies iterative…
Neural networks are predominantly trained using gradient-based methods, yet in many applications their final predictions remain far from the accuracy attainable within the model's expressive capacity. We introduce Linearized Subspace…
Deploying deep learning models, comprising of non-linear combination of millions, even billions, of parameters is challenging given the memory, power and compute constraints of the real world. This situation has led to research into model…
We investigate to what extent it is possible to solve linear inverse problems with $ReLu$ networks. Due to the scaling invariance arising from the linearity, an optimal reconstruction function $f$ for such a problem is positive homogeneous,…
This paper considers the problem of learning a single ReLU neuron with squared loss (a.k.a., ReLU regression) in the overparameterized regime, where the input dimension can exceed the number of samples. We analyze a Perceptron-type…
A growing body of literature has been leveraging techniques of machine learning (ML) to build novel approaches to approximating the solutions to partial differential equations. Noticeably absent from the literature is a systematic…
This paper proposes an Adaptive-Growth Randomized Neural Network (AG-RaNN) method for computing multivalued solutions of nonlinear first-order PDEs with hyperbolic characteristics, including quasilinear hyperbolic balance laws and…
A new method is proposed for the problem of solving chi-square minimization with a positive solution. This method is embodied in an evolution of the popular NNLS algorithm. Its efficiency with respect to residue minimization is illustrated…
This paper studies an unsupervised deep learning-based numerical approach for solving partial differential equations (PDEs). The approach makes use of the deep neural network to approximate solutions of PDEs through the compositional…
We introduce new adaptive schemes for the one- and two-dimensional hyperbolic systems of conservation laws. Our schemes are based on an adaption strategy recently introduced in [{\sc S. Chu, A. Kurganov, and I. Menshov}, Appl. Numer. Math.,…