Related papers: Least-Squares Neural Network (LSNN) Method For Sca…

We introduce a novel meshless method called the Constrained Least-Squares Ghost Sample Points (CLS-GSP) method for solving partial differential equations on irregular domains or manifolds represented by randomly generated sample points. Our…

We propose a least-squares method involving the recovery of the gradient and possibly the Hessian for elliptic equation in nondivergence form. As our approach is based on the Lax--Milgram theorem with the curl-free constraint built into the…

We address the problem of sparse recovery in an online setting, where random linear measurements of a sparse signal are revealed sequentially and the objective is to recover the underlying signal. We propose a reweighted least squares (RLS)…

Shuffled linear regression (SLR) seeks to estimate latent features through a linear transformation, complicated by unknown permutations in the measurement dimensions. This problem extends traditional least-squares (LS) and Least Absolute…

We propose an algorithm, semismooth Newton coordinate descent (SNCD), for the elastic-net penalized Huber loss regression and quantile regression in high dimensional settings. Unlike existing coordinate descent type algorithms, the SNCD…

Ordinary differential equations provide an attractive framework for modeling temporal dynamics in a variety of scientific settings. We show how consistent estimation for parameters in ODE models can be obtained by modifying a direct…

Deep hedging represents a cutting-edge approach to risk management for financial derivatives by leveraging the power of deep learning. However, existing methods often face challenges related to computational inefficiency, sensitivity to…

Physics-Informed Neural Networks (PINNs) have shown promise in solving partial differential equations (PDEs), including the frequency-domain Helmholtz equation. However, standard training of PINNs using gradient descent (GD) suffers from…

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…

In this paper, we investigate neural networks applied to multiscale simulations and discuss a design of a novel deep neural network model reduction approach for multiscale problems. Due to the multiscale nature of the medium, the fine-grid…

In this paper, we propose a novel deep neural network framework embedded with low-level features (LCNN) for salient object detection in complex images. We utilise the advantage of convolutional neural networks to automatically learn the…

Network pruning is a widely used technique to reduce computation cost and model size for deep neural networks. However, the typical three-stage pipeline significantly increases the overall training time. In this paper, we develop a…

A novel hybrid deep neural network architecture is designed to capture the spatial-temporal features of unsteady flows around moving boundaries directly from high-dimensional unsteady flow fields data. The hybrid deep neural network is…

Super-resolution (SR) techniques based on deep learning have recently emerged as a promising approach to enhance the spatial resolution of computational fluid dynamics simulations while containing computational cost. In this paper, we…

High-order nodal space-time flux reconstruction (STFR) methods have been developed to solve hyperbolic conservation laws on curvilinear moving grids. Unlike the method-of-lines approach for moving domain simulation, the grid velocity is…

In this paper we propose a {\it discontinuous} plane wave neural network (DPWNN) method with $hp-$refinement for approximately solving Helmholtz equation and time-harmonic Maxwell equations. In this method, we define a quadratic functional…

We introduce the implicitly constrained least squares (ICLS) classifier, a novel semi-supervised version of the least squares classifier. This classifier minimizes the squared loss on the labeled data among the set of parameters implied by…

We propose a new randomized algorithm for solving convex optimization problems that have a large number of constraints (with high probability). Existing methods like interior-point or Newton-type algorithms are hard to apply to such…

We present fourth-order conservative non-splitting semi-Lagrangian (SL) Hermite essentially non-oscillatory (HWENO) schemes for linear transport equations with applications for nonlinear problems including the Vlasov-Poisson system, the…

With the rapid development of science and technology, the problem of energy load monitoring and decomposition of electrical equipment has been receiving widespread attention from academia and industry. For the purpose of improving the…