Related papers: Deep neural networks for solving large linear syst…

At present, deep learning based methods are being employed to resolve the computational challenges of high-dimensional partial differential equations (PDEs). But the computation of the high order derivatives of neural networks is costly,…

In this paper we use deep feedforward artificial neural networks to approximate solutions to partial differential equations in complex geometries. We show how to modify the backpropagation algorithm to compute the partial derivatives of the…

This article studies deep neural network expression rates for optimal stopping problems of discrete-time Markov processes on high-dimensional state spaces. A general framework is established in which the value function and continuation…

This paper addresses the problem of learning binary hash codes for large scale image search by proposing a novel hashing method based on deep neural network. The advantage of our deep model over previous deep model used in hashing is that…

In this paper, we introduce a type of tensor neural network based machine learning method to solve elliptic multiscale problems. Based on the special structure, we can do the direct and highly accurate high dimensional integrations for the…

In this work we apply deep neural networks to find the non-equilibrium steady state solution to correlated open quantum many-body systems. Motivated by the ongoing search to find more powerful representations of (mixed) quantum states, we…

Why do deep neural networks (DNNs) benefit from very high dimensional parameter spaces? Their huge parameter complexities vs stunning performance in practice is all the more intriguing and not explainable using the standard theory of model…

Complex networks are ubiquitous to several Computer Science domains. Centrality measures are an important analysis mechanism to uncover vital elements of complex networks. However, these metrics have high computational costs and…

Deep artificial neural networks are powerful tools with many possible applications in nanophotonics. Here, we demonstrate how a deep neural network can be used as a fast, general purpose predictor of the full near-field and far-field…

On complex problems, state of the art prediction accuracy of Deep Neural Networks (DNN) can be achieved using very large-scale models, consisting of billions of parameters. Such models can only be run on dedicated servers, typically…

Deep Neural Networks (DNNs) have become very popular for prediction in many areas. Their strength is in representation with a high number of parameters that are commonly learned via gradient descent or similar optimization methods. However,…

Deep neural networks (DNNs) are powerful machine learning models and have succeeded in various artificial intelligence tasks. Although various architectures and modules for the DNNs have been proposed, selecting and designing the…

Deep learning has become very popular for tasks such as predictive modeling and pattern recognition in handling big data. Deep learning is a powerful machine learning method that extracts lower level features and feeds them forward for the…

Training deep neural networks results in strong learned representations that show good generalization capabilities. In most cases, training involves iterative modification of all weights inside the network via back-propagation. In Extreme…

In this paper we present an approach for training deep generative models solely based on solving determined systems of linear equations. A network that uses this approach, called a StarNet, has the following desirable properties: 1)…

Neural network models can now recognise images, understand text, translate languages, and play many human games at human or superhuman levels. These systems are highly abstracted, but are inspired by biological brains and use only…

As demonstrated in many areas of real-life applications, neural networks have the capability of dealing with high dimensional data. In the fields of optimal control and dynamical systems, the same capability was studied and verified in many…

The success of deep learning has inspired recent interests in applying neural networks in statistical inference. In this paper, we investigate the use of deep neural networks for nonparametric regression with measurement errors. We propose…

Can neural networks learn to solve partial differential equations (PDEs)? We investigate this question for two (systems of) PDEs, namely, the Poisson equation and the steady Navier--Stokes equations. The contributions of this paper are…

Deep neural networks and other deep learning methods have very successfully been applied to the numerical approximation of high-dimensional nonlinear parabolic partial differential equations (PDEs), which are widely used in finance,…