相关论文: Error estimates of deep learning methods for the n…

Energy and resource efficient training of DNNs will greatly extend the applications of deep learning. However, there are three major obstacles which mandate accurate calculation in high precision. In this paper, we tackle two of them…

In this work, we propose a new deep learning-based scheme for solving high dimensional nonlinear backward stochastic differential equations (BSDEs). The idea is to reformulate the problem as a global optimization, where the local loss…

The incompressible magnetohydrodynamic (MHD) equations are fundamental in many scientific and engineering applications. However, their strong nonlinearity and dual divergence-free constraints make them highly challenging for conventional…

We perform a comprehensive numerical study of the effect of approximation-theoretical results for neural networks on practical learning problems in the context of numerical analysis. As the underlying model, we study the…

Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…

Machine learning-based neural network potentials have the ability to provide ab initio-level predictions while reaching large length and time scales often limited to empirical force fields. Traditionally, neural network potentials rely on a…

Deep neural networks (DNNs) are efficient solvers for ill-posed problems and have been shown to outperform classical optimization techniques in several computational imaging problems. DNNs are trained by solving an optimization problem…

Recent developments on deep learning established some theoretical properties of deep neural networks estimators. However, most of the existing works on this topic are restricted to bounded loss functions or (sub)-Gaussian or bounded input.…

Deep Learning (DL) has made remarkable achievements in computer vision and adopted in safety critical domains such as medical imaging or autonomous drive. Thus, it is necessary to understand the uncertainty of the model to effectively…

We propose a deep neural network (DNN) as a fast surrogate model for local stress (and in principle strain) calculation in inhomogeneous non-linear material systems. We show that the DNN predicts the local stresses with about 3.8% mean…

Albeit worryingly underrated in the recent literature on machine learning in general (and, on deep learning in particular), multivariate density estimation is a fundamental task in many applications, at least implicitly, and still an open…

We describe and analyze a hybrid finite element/neural network method for predicting solutions of partial differential equations. The methodology is designed for obtaining fine scale fluctuations from neural networks in a local manner. The…

This paper presents a deep learning approach to aid dead-reckoning (DR) navigation using a limited sensor suite. A Recurrent Neural Network (RNN) was developed to predict the relative horizontal velocities of an Autonomous Underwater…

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…

In-memory deep learning computes neural network models where they are stored, thus avoiding long distance communication between memory and computation units, resulting in considerable savings in energy and time. In-memory deep learning has…

In this proceeding, we will briefly review our recent progress on implementing deep learning to relativistic hydrodynamics. We will demonstrate that a successfully designed and trained deep neural network, called {\tt stacked U-net}, can…

We present a novel approach to compute three-dimensional Magnetohydrodynamic equilibria by parametrizing Fourier modes with artificial neural networks and compare it to equilibria computed by conventional solvers. The full nonlinear global…

Using the nonlinear shallow water equations as benchmark, we demonstrate that a simulation with the ICON-O ocean model with a 20km resolution that is frequently corrected by a U-net-type neural network can achieve discretization errors of a…

Deep neural networks (DNN) with a huge number of adjustable parameters remain largely black boxes. To shed light on the hidden layers of DNN, we study supervised learning by a DNN of width $N$ and depth $L$ consisting of $NL$ perceptrons…

In this paper, we study Discretized Neural Networks (DNNs) composed of low-precision weights and activations, which suffer from either infinite or zero gradients due to the non-differentiable discrete function during training. Most…