Related papers: Multigrid-Augmented Deep Learning Preconditioners …

Large-scale or high-resolution geologic models usually comprise a huge number of grid blocks, which can be computationally demanding and time-consuming to solve with numerical simulators. Therefore, it is advantageous to upscale geologic…

Deep learning methods have been shown to be effective in representing ground-state wave functions of quantum many-body systems. Existing methods use convolutional neural networks (CNNs) for square lattices due to their image-like…

Solving time-harmonic wave propagation problems by iterative methods is a difficult task, and over the last two decades, an important research effort has gone into developing preconditioners for the simplest representative of such wave…

The development of scalable and wavenumber-robust iterative solvers for Helmholtz problems is challenging but also relevant for various application fields. In this work, two-level Schwarz domain decomposition preconditioners are enhanced by…

Efficient resource allocation with hybrid precoder design is essential for massive MIMO systems operating in millimeter wave (mmW) domain. Owing to a higher energy efficiency and a lower complexity of a partially connected hybrid…

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…

The multigrid algorithm is a multilevel approach to accelerate the numerical solution of discretized differential equations in physical problems involving long-range interactions. Multiresolution analysis of wavelet theory provides an…

Deep learning has been shown to be able to recognize data patterns better than humans in specific circumstances or contexts. In parallel, quantum computing has demonstrated to be able to output complex wave functions with a few number of…

We present an efficient matrix-free geometric multigrid method for the elastic Helmholtz equation, and a suitable discretization. Many discretization methods had been considered in the literature for the Helmholtz equations, as well as many…

The excellent performance of deep neural networks has enabled us to solve several automatization problems, opening an era of autonomous devices. However, current deep net architectures are heavy with millions of parameters and require…

This paper focuses on addressing challenges posed by non-homogeneous unstructured grids, commonly used in Computational Fluid Dynamics (CFD). Their prevalence in CFD scenarios has motivated the exploration of innovative approaches for…

Accurate classification of fine-grained images remains a challenge in backbones based on convolutional operations or self-attention mechanisms. This study proposes novel dual-current neural networks (DCNN), which combine the advantages of…

Deep convolutional neural networks (ConvNets) of 3-dimensional kernels allow joint modeling of spatiotemporal features. These networks have improved performance of video and volumetric image analysis, but have been limited in size due to…

A neural network architecture is presented that exploits the multilevel properties of high-dimensional parameter-dependent partial differential equations, enabling an efficient approximation of parameter-to-solution maps, rivaling…

In this paper, we introduce deep learning technology to tackle two traditional low-level image processing problems, companding and inverse halftoning. We make two main contributions. First, to the best knowledge of the authors, this is the…

Convolution Neural Networks (CNN) have performed well in many applications such as object detection, pattern recognition, video surveillance and so on. CNN carryout feature extraction on labelled data to perform classification. Multi-label…

Over the past decade, deep learning research has been accelerated by increasingly powerful hardware, which facilitated rapid growth in the model complexity and the amount of data ingested. This is becoming unsustainable and therefore…

This paper investigates multilevel initialization strategies for training very deep neural networks with a layer-parallel multigrid solver. The scheme is based on the continuous interpretation of the training problem as a problem of optimal…

Scattering networks are a class of designed Convolutional Neural Networks (CNNs) with fixed weights. We argue they can serve as generic representations for modelling images. In particular, by working in scattering space, we achieve…

This paper aims to accelerate the test-time computation of deep convolutional neural networks (CNNs). Unlike existing methods that are designed for approximating linear filters or linear responses, our method takes the nonlinear units into…