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

Searching for numerical methods that combine facility and efficiency, while remaining accurate and versatile, is critical. Often, irregular geometries challenge traditional methods that rely on structured or body-fitted meshes. Meshless…

Convolutional neural networks (CNNs) have succeeded in many practical applications. However, their high computation and storage requirements often make them difficult to deploy on resource-constrained devices. In order to tackle this issue,…

Sum-of-squares objective functions are very popular in computer vision algorithms. However, these objective functions are not always easy to optimize. The underlying assumptions made by solvers are often not satisfied and many problems are…

Wave equation techniques have been an integral part of geophysical imaging workflows to investigate the Earth's subsurface. Least-squares reverse time migration (LSRTM) is a linearized inversion problem that iteratively minimizes a misfit…

We propose a discontinuous least squares finite element method for solving the linear elasticity. The approximation space is obtained by patch reconstruction with only one unknown per element. We apply the L 2 norm least squares principle…

This work develops robust diffusion recursive least squares algorithms to mitigate the performance degradation often experienced in networks of agents in the presence of impulsive noise. The first algorithm minimizes an exponentially…

Classical reduced models are low-rank approximations using a fixed basis designed to achieve dimensionality reduction of large-scale systems. In this work, we introduce reduced deep networks, a generalization of classical reduced models…

We introduce new second-order adaptive low-dissipation central-upwind (LDCU) schemes for the one- and two-dimensional hyperbolic systems of conservation laws. The new adaptive LDCU schemes employ the LDCU numerical fluxes (recently proposed…

Deep Neural Network (DNN)-based image reconstruction, despite many successes, often exhibits uneven fidelity between high and low spatial frequency bands. In this paper we propose the Learning Synthesis by DNN (LS-DNN) approach where two…

Recurrent Spiking Neural Networks (RSNNs) have emerged as a computationally efficient and brain-inspired learning model. The design of sparse RSNNs with fewer neurons and synapses helps reduce the computational complexity of RSNNs.…

High-resolution (HR) information of fluid flows, although preferable, is usually less accessible due to limited computational or experimental resources. In many cases, fluid data are generally sparse, incomplete, and possibly noisy. How to…

We developed a Nonlinear Level-set Learning (NLL) method for dimensionality reduction in high-dimensional function approximation with small data. This work is motivated by a variety of design tasks in real-world engineering applications,…

This article introduces a novel methodology that integrates singular value decomposition (SVD) with a shallow linear neural network for forecasting high resolution fluid mechanics data. The method, termed LC-SVD-DLinear, combines a low-cost…

The emerging Learned Compression (LC) replaces the traditional codec modules with Deep Neural Networks (DNN), which are trained end-to-end for rate-distortion performance. This approach is considered as the future of image/video…

We study the total least squares (TLS) problem that generalizes least squares regression by allowing measurement errors in both dependent and independent variables. TLS is widely used in applied fields including computer vision, system…

Least-squares programming is a popular tool in robotics due to its simplicity and availability of open-source solvers. However, certain problems like sparse programming in the $\ell_0$- or $\ell_1$-norm for time-optimal control are not…

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…

This paper studies the asymptotic properties of the adaptive elastic net in ultra-high dimensional sparse linear regression models and proposes a new method called SSLS (Separate Selection from Least Squares) to improve prediction accuracy.…

Fault detection and diagnosis is significant for reducing maintenance costs and improving health and safety in chemical processes. Convolution neural network (CNN) is a popular deep learning algorithm with many successful applications in…

Solving compressible flows containing discontinuities remains a major challenge for numerical methods especially on unstructured grids. Thus in this work, we make contributions to shock capturing schemes on unstructured grids with aim of…