相关论文: Least-Squares Linear Dilation-Erosion Regressor Tr…

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…

We propose a deep neural network (DNN) based least distance (LD) estimator (DNN-LD) for a multivariate regression problem, addressing the limitations of the conventional methods. Due to the flexibility of a DNN structure, both linear and…

A least-squares neural network (LSNN) method was introduced for solving scalar linear and nonlinear hyperbolic conservation laws (HCLs) in [7, 6]. This method is based on an equivalent least-squares (LS) formulation and uses ReLU neural…

Variational Physics-Informed Neural Networks often suffer from poor convergence when using stochastic gradient-descent-based optimizers. By introducing a Least Squares solver for the weights of the last layer of the neural network, we…

We present an error-neural-modeling-based strategy for approximating two-dimensional curvature in the level-set method. Our main contribution is a redesigned hybrid solver [Larios-C\'ardenas and Gibou, J. Comput. Phys. (May 2022),…

The extreme learning machine (ELM) method can yield highly accurate solutions to linear/nonlinear partial differential equations (PDEs), but requires the last hidden layer of the neural network to be wide to achieve a high accuracy. If the…

Proposed in 1991, Least Mean Square Error Reconstruction for self-organizing network, shortly Lmser, was a further development of the traditional auto-encoder (AE) by folding the architecture with respect to the central coding layer and…

We introduce the Neural Hodge Corrective Solver (NHCS), a hybrid iterative-neural framework for partial differential equations that embeds learned corrective operators within the Discrete Exterior Calculus (DEC) formulation. The method…

The scalability of Distributed Stochastic Gradient Descent (SGD) is today limited by communication bottlenecks. We propose a novel SGD variant: Communication-efficient SGD with Error Reset, or CSER. The key idea in CSER is first a new…

This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…

We introduce a recursive adaptive group lasso algorithm for real-time penalized least squares prediction that produces a time sequence of optimal sparse predictor coefficient vectors. At each time index the proposed algorithm computes an…

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…

We propose an efficient hybrid least squares/gradient descent method to accelerate DeepONet training. Since the output of DeepONet can be viewed as linear with respect to the last layer parameters of the branch network, these parameters can…

Extreme learning machine (ELM) is a methodology for solving partial differential equations (PDEs) using a single hidden layer feed-forward neural network. It presets the weight/bias coefficients in the hidden layer with random values, which…

In this paper, we investigate the use of single hidden-layer neural networks as a family of ansatz functions for the resolution of partial differential equations (PDEs). In particular, we train the network via Extreme Learning Machines…

Convolutional neural networks typically consist of many convolutional layers followed by one or more fully connected layers. While convolutional layers map between high-order activation tensors, the fully connected layers operate on…

This paper studies the convergence properties of a family of Relaxed $\ell$-Minimal Gradient Descent methods for quadratic optimization; the family includes the omnipresent Steepest Descent method, as well as the Minimal Gradient method.…

The recursive least-squares (RLS) algorithm is one of the most well-known algorithms used in adaptive filtering, system identification and adaptive control. Its popularity is mainly due to its fast convergence speed, which is considered to…

Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of…

We introduce an iterative scheme for discrete convex minimization problems of $p$-Laplace type such as variational graph $p$-Laplace problems and $\ell^p$ regression. In each iteration, the scheme solves only a weighted least-squares…