Related papers: Multi-scale Deep Neural Networks for Solving High …

In this article, we present an efficient deep learning method called coupled deep neural networks (CDNNs) for coupled physical problems. Our method compiles the interface conditions of the coupled PDEs into the networks properly and can be…

We propose a two-scale neural network method for solving partial differential equations (PDEs) with small parameters using physics-informed neural networks (PINNs). We directly incorporate the small parameters into the architecture of…

We propose a finite-dimensional control-based method to approximate solution operators for evolutional partial differential equations (PDEs), particularly in high-dimensions. By employing a general reduced-order model, such as a deep neural…

In this paper, an innovative Physical Model-driven Neural Network (PMNN) method is proposed to solve time-fractional differential equations. It establishes a temporal iteration scheme based on physical model-driven neural networks which…

Accurate forecasting of long-term time series has important applications for decision making and planning. However, it remains challenging to capture the long-term dependencies in time series data. To better extract long-term dependencies,…

In this paper, the authors propose the utilization of Fibonacci Neural Networks (FNN) for solving arbitrary order differential equations. The FNN architecture comprises input, middle, and output layers, with various degrees of Fibonacci…

Signal dimension, defined here as the number of copies with different delays or angular shifts, is a prerequisite for many high-resolution delay estimation and direction-finding algorithms in sensing and communication systems. Thus,…

In this paper, we propose a multi-scale deep feature learning method for high-resolution satellite image classification. Specifically, we firstly warp the original satellite image into multiple different scales. The images in each scale are…

All-optical diffractive neural networks (DNNs) offer a promising alternative to electronics-based neural network processing due to their low latency, high throughput, and inherent spatial parallelism. However, the lack of reconfigurability…

With joint learning of sampling and recovery, the deep learning-based compressive sensing (DCS) has shown significant improvement in performance and running time reduction. Its reconstructed image, however, losses high-frequency content…

We develop a minimax rate analysis to describe the reason that deep neural networks (DNNs) perform better than other standard methods. For nonparametric regression problems, it is well known that many standard methods attain the minimax…

In this paper, we compute numerical approximations of the minimal surfaces, an essential type of Partial Differential Equation (PDE), in higher dimensions. Classical methods cannot handle it in this case because of the Curse of…

We propose a novel multi-stage depth super-resolution network, which progressively reconstructs high-resolution depth maps from explicit and implicit high-frequency features. The former are extracted by an efficient transformer processing…

Physics-informed neural networks (PINNs) have been demonstrated to be efficient in solving partial differential equations (PDEs) from a variety of experimental perspectives. Some recent studies have also proposed PINN algorithms for PDEs on…

Deep neural networks (DNNs) form the cornerstone of modern AI services, supporting a wide range of applications, including autonomous driving, chatbots, and recommendation systems. As models increase in size and complexity, DNN workloads…

In this paper, we propose a robust estimator for the location function from multi-dimensional functional data. The proposed estimators are based on the deep neural networks with ReLU activation function. At the meanwhile, the estimators are…

Image retrieval refers to finding relevant images from an image database for a query, which is considered difficult for the gap between low-level representation of images and high-level representation of queries. Recently further developed…

Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…

Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…

In recent years, a significant amount of attention has been paid to solve partial differential equations (PDEs) by deep learning. For example, deep Galerkin method (DGM) uses the PDE residual in the least-squares sense as the loss function…