Related papers: A Deep Learning algorithm to accelerate Algebraic …

Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…

Traditionally, an artificial neural network (ANN) is trained slowly by a gradient descent algorithm such as the backpropagation algorithm since a large number of hyperparameters of the ANN need to be fine-tuned with many training epochs. To…

Isogeometric analysis (IgA) offers enhanced approximation capabilities for the discretization of elliptic boundary-value problems, yet it results in large, sparse, and increasingly ill-conditioned linear systems due to higher…

State-of-the-art training algorithms for deep learning models are based on stochastic gradient descent (SGD). Recently, many variations have been explored: perturbing parameters for better accuracy (such as in Extragradient), limiting SGD…

The widely used density matrix renormalization group (DRMG) method often fails to converge in systems with multiple length scales, such as lattice discretizations of continuum models and dilute or weakly doped lattice models. The local…

Graph Neural Networks (GNNs) are powerful techniques in representation learning for graphs and have been increasingly deployed in a multitude of different applications that involve node- and graph-wise tasks. Most existing studies solve…

NLP(natural language processsing) has achieved great success through the transformer model.However, the model has hundreds of millions or billions parameters,which is huge burden for its deployment on personal computer or small scale of…

During the last decade, Neural Networks (NNs) have proved to be extremely effective tools in many fields of engineering, including autonomous vehicles, medical diagnosis and search engines, and even in art creation. Indeed, NNs often…

One of the most common and universal problems in science is to investigate a function. The prediction can be made by an Artificial Neural Network (ANN) or a mathematical model. Both approaches have their advantages and disadvantages.…

Topology optimization for large scale problems continues to be a computational challenge. Several works exist in the literature to address this topic, and all make use of iterative solvers to handle the linear system arising from the Finite…

We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…

Exploring the expected quantizing scheme with suitable mixed-precision policy is the key point to compress deep neural networks (DNNs) in high efficiency and accuracy. This exploration implies heavy workloads for domain experts, and an…

We propose a path cover adaptive algebraic multigrid (PC-$\alpha$AMG) method for solving linear systems of weighted graph Laplacians and can also be applied to discretized second order elliptic partial differential equations. The…

Deep Neural Network (DNN) is powerful but computationally expensive and memory intensive, thus impeding its practical usage on resource-constrained front-end devices. DNN pruning is an approach for deep model compression, which aims at…

The choice of parameters, and the design of the network architecture are important factors affecting the performance of deep neural networks. However, there has not been much work on developing an established and systematic way of building…

Emerging technologies such as Reconfigurable Intelligent Surfaces (RIS) make it possible to optimize some parameters of wireless channels. Conventional approaches require relating the channel and its programmable parameters via a simple…

Motivated by extreme multi-label classification applications, we consider training deep learning models over sparse data in multi-GPU servers. The variance in the number of non-zero features across training batches and the intrinsic GPU…

Mixed-signal artificial neural networks (ANNs) that employ analog matrix-multiplication accelerators can achieve higher speed and improved power efficiency. Though analog computing is known to be susceptible to noise and device…

In this paper, we propose a deep learning-enhanced multigrid solver for high-frequency and heterogeneous Helmholtz equations. By applying spectral analysis, we categorize the iteration error into characteristic and non-characteristic…

A wide range of modern science and engineering applications are formulated as optimization problems with a system of partial differential equations (PDEs) as constraints. These PDE-constrained optimization problems are typically solved in a…