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

A unified deep neural network, denoted the multi-scale CNN (MS-CNN), is proposed for fast multi-scale object detection. The MS-CNN consists of a proposal sub-network and a detection sub-network. In the proposal sub-network, detection is…

Recent works have shown that deep neural networks can be employed to solve partial differential equations, giving rise to the framework of physics informed neural networks. We introduce a generalization for these methods that manifests as a…

In this paper, we propose forward and backward stochastic differential equations (FBSDEs) based deep neural network (DNN) learning algorithms for the solution of high dimensional quasilinear parabolic partial differential equations (PDEs),…

Salient object detection is a fundamental problem and has been received a great deal of attentions in computer vision. Recently deep learning model became a powerful tool for image feature extraction. In this paper, we propose a multi-scale…

We combine concepts from multilevel solvers for partial differential equations (PDEs) with neural network based deep learning and propose a new methodology for the efficient numerical solution of high-dimensional parametric PDEs. An…

A neural network is essentially a high-dimensional complex mapping model by adjusting network weights for feature fitting. However, the spectral bias in network training leads to unbearable training epochs for fitting the high-frequency…

In this paper, a multi-scale Fourier neural operator (MscaleFNO) is proposed to reduce the spectral bias of the FNO in learning the mapping between highly oscillatory functions, with application to the nonlinear mapping between the…

Discrete tensor train decomposition is widely employed to mitigate the curse of dimensionality in solving high-dimensional PDEs through traditional methods. However, the direct application of the tensor train method typically requires…

Backward stochastic differential equation (BSDE) provides probabilistic solutions for a class of parabolic partial differential equations (PDEs). DeepBSDE and FBSNN are two deep learning approaches for solving high-dimensional PDEs through…

Beyond the scope of conventional metasurface which necessitates plenty of computational resources and time, an inverse design approach using machine learning algorithms promises an effective way for metasurfaces design. In this paper,…

To overcome these obstacles and improve computational accuracy and efficiency, this paper presents the Randomized Radial Basis Function Neural Network (RRNN), an innovative approach explicitly crafted for solving multiscale elliptic…

Recently, machine learning methods have gained significant traction in scientific computing, particularly for solving Partial Differential Equations (PDEs). However, methods based on deep neural networks (DNNs) often lack convergence…

This paper proposes a Kolmogorov high order deep neural network (K-HOrderDNN) for solving high-dimensional partial differential equations (PDEs), which improves the high order deep neural networks (HOrderDNNs). HOrderDNNs have been…

The purpose of this article is to develop a machinery to study the capacity of deep neural networks (DNNs) to approximate high-dimensional functions. In particular, we show that DNNs have the expressive power to overcome the curse of…

Spectral methods are an important part of scientific computing's arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the…

Solving high-dimensional partial differential equations (PDEs) efficiently requires handling multi-scale features across varying resolutions. To address this challenge, we present the Multiwavelet-based Multigrid Neural Operator (M2NO), a…

We studied the use of deep neural networks (DNNs) in the numerical solution of the oscillatory Fredholm integral equation of the second kind. It is known that the solution of the equation exhibits certain oscillatory behaviors due to the…

Reconstruction of PET images is an ill-posed inverse problem and often requires iterative algorithms to achieve good image quality for reliable clinical use in practice, at huge computational costs. In this paper, we consider the PET…

Deep Neural Networks (DNNs) have the potential to improve the quality of image-based 3D reconstructions. However, the use of DNNs in the context of 3D reconstruction from large and high-resolution image datasets is still an open challenge,…

The recent success of Deep Neural Networks (DNNs) has drastically improved the state of the art for many application domains. While achieving high accuracy performance, deploying state-of-the-art DNNs is a challenge since they typically…