Related papers: Cell-average based neural network method for high …

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…

This paper considers one of the fundamental parallel-in-time methods for the solution of ordinary differential equations, Parareal, and extends it by adopting a neural network as a coarse propagator. We provide a theoretical analysis of the…

The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…

In this paper, we introduce a tensor neural network based machine learning method for solving the elliptic partial differential equations with random coefficients in a bounded physical domain. With the help of tensor product structure, we…

Despite a lack of theoretical understanding, deep neural networks have achieved unparalleled performance in a wide range of applications. On the other hand, shallow representation learning with component analysis is associated with rich…

We present a subspace method based on neural networks for solving the partial differential equation in weak form with high accuracy. The basic idea of our method is to use some functions based on neural networks as base functions to span a…

A new penalty-free neural network method, PFNN-2, is presented for solving partial differential equations, which is a subsequent improvement of our previously proposed PFNN method [1]. PFNN-2 inherits all advantages of PFNN in handling the…

Modern computer vision (CV) is often based on convolutional neural networks (CNNs) that excel at hierarchical feature extraction. The previous generation of CV approaches was often based on conditional random fields (CRFs) that excel at…

We propose a novel method that trains a conditional Generative Adversarial Network (GAN) to generate visual interpretations of a Convolutional Neural Network (CNN). To comprehend a CNN, the GAN is trained with information on how the CNN…

Partial differential equations (PDEs) form a central component of scientific computing. Among recent advances in deep learning, evolutionary neural networks have been developed to successively capture the temporal dynamics of time-dependent…

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…

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, a class of high order numerical schemes is proposed to solve the nonlinear parabolic equations with variable coefficients. This method is based on our previous work [10] for convection-diffusion equations, which relies on a…

This paper proposes a new unsupervised domain adaptation approach called Collaborative and Adversarial Network (CAN), which uses the domain-collaborative and domain-adversarial learning strategy for training the neural network. The…

Solutions to differential equations are of significant scientific and engineering relevance. Recently, there has been a growing interest in solving differential equations with neural networks. This work develops a novel method for solving…

Recently, Deep Neural Networks (DNNs) have recorded great success in handling medical and other complex classification tasks. However, as the sizes of a DNN model and the available dataset increase, the training process becomes more complex…

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…

Different features have different relevance to a particular learning problem. Some features are less relevant; while some very important. Instead of selecting the most relevant features using feature selection, an algorithm can be given…

The numerical solution of high dimensional partial differential equations (PDEs) is severely constrained by the curse of dimensionality (CoD), rendering classical grid--based methods impractical beyond a few dimensions. In recent years,…

Randomized neural network (RaNN) methods have been proposed for solving various partial differential equations (PDEs), demonstrating high accuracy and efficiency. However, initializing the fixed parameters remains challenging. Additionally,…