Related papers: Multigrid-Augmented Deep Learning Preconditioners …

Convolutional Neural Networks (CNNs) have demonstrated their superiority in image classification, and evolutionary computation (EC) methods have recently been surging to automatically design the architectures of CNNs to save the tedious…

In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative algorithms have emerged as the standard approach to ill-posed inverse problems in the…

Hyperbolic graph convolutional networks (HGCNs) have demonstrated significant potential in extracting information from hierarchical graphs. However, existing HGCNs are limited to shallow architectures due to the computational expense of…

Lossy compression introduces complex compression artifacts, particularly blocking artifacts, ringing effects and blurring. Existing algorithms either focus on removing blocking artifacts and produce blurred output, or restore sharpened…

In this research, we address Darcy flow problems with random permeability using iterative solvers, enhanced by a two-grid preconditioner based on a generalized multiscale prolongation operator, which has been demonstrated to be stable for…

The omnipresence of deep learning architectures such as deep convolutional neural networks (CNN)s is fueled by the synergistic combination of ever-increasing labeled datasets and specialized hardware. Despite the indisputable success, the…

Deep neural networks, in particular convolutional neural networks, have become highly effective tools for compressing images and solving inverse problems including denoising, inpainting, and reconstruction from few and noisy measurements.…

Relying on either deep models or physical models are two mainstream approaches for solving inverse sample reconstruction problems in programmable illumination computational microscopy. Solutions based on physical models possess strong…

The joint optimization of the reconstruction and classification error is a hard non convex problem, especially when a non linear mapping is utilized. In order to overcome this obstacle, a novel optimization strategy is proposed, in which a…

Convolutional neural networks (CNNs) have demonstrated their capability to solve different kind of problems in a very huge number of applications. However, CNNs are limited for their computational and storage requirements. These limitations…

In this paper, we investigate the combination of multigrid methods and neural networks, starting from a Finite Element discretization of an elliptic PDE. Multigrid methods use interpolation operators to transfer information between…

This work presents a multigrid preconditioned high order immersed finite difference solver to accurately and efficiently solve the Poisson equation on complex 2D and 3D domains. The solver employs a low order Shortley-Weller multigrid…

Deep learning's great success motivates many practitioners and students to learn about this exciting technology. However, it is often challenging for beginners to take their first step due to the complexity of understanding and applying…

In this paper we propose solving localized multiple kernel learning (LMKL) using LMKL-Net, a feedforward deep neural network. In contrast to previous works, as a learning principle we propose {\em parameterizing} both the gating function…

Deep learning, e.g., convolutional neural networks (CNNs), has achieved great success in image processing and computer vision especially in high level vision applications such as recognition and understanding. However, it is rarely used to…

The novel contribution of this paper relies in the proposal of a fully implicit numerical method designed for nonlinear degenerate parabolic equations, in its convergence/stability analysis, and in the study of the related computational…

Image classification is a difficult machine learning task, where Convolutional Neural Networks (CNNs) have been applied for over 20 years in order to solve the problem. In recent years, instead of the traditional way of only connecting the…

This letter presents a novel high impedance fault (HIF) detection approach using a convolutional neural network (CNN). Compared to traditional artificial neural networks, a CNN offers translation invariance and it can accurately detect HIFs…

Autoregressive sequence models based on deep neural networks, such as RNNs, Wavenet and the Transformer attain state-of-the-art results on many tasks. However, they are difficult to parallelize and are thus slow at processing long…

The use of implicit time-stepping schemes for the numerical approximation of solutions to stiff nonlinear time-evolution equations brings well-known advantages including, typically, better stability behaviour and corresponding support of…