Related papers: Two-level overlapping additive Schwarz preconditio…

Multilayer transformer networks consist of interleaved self-attention and feedforward sublayers. Could ordering the sublayers in a different pattern lead to better performance? We generate randomly ordered transformers and train them with…

A symmetric and a nonsymmetric variant of the additive Schwarz preconditioner are proposed for the solution of a nonsymmetric system of algebraic equations arising from a general finite volume element discretization of symmetric elliptic…

We present and analyze a class of nonsymmetric preconditioners within a normal (weighted least-squares) matrix form for use in GMRES to solve nonsymmetric matrix problems that typically arise in finite element discretizations. An example of…

With the increasing computing power, using data-driven approaches to co-design a robot's morphology and controller has become a promising way. However, most existing data-driven methods require training the controller for each morphology to…

Many approaches to transform classification problems from non-linear to linear by feature transformation have been recently presented in the literature. These notably include sparse coding methods and deep neural networks. However, many of…

AI accelerator processing capabilities and memory constraints largely dictate the scale in which machine learning workloads (e.g., training and inference) can be executed within a desirable time frame. Training a state of the art,…

Deep neural networks (DNNs) are currently predominantly trained using first-order methods. Some of these methods (e.g., Adam, AdaGrad, and RMSprop, and their variants) incorporate a small amount of curvature information by using a diagonal…

The multigroup neutron transport criticality calculations using modern supercomputers have been widely employed in a nuclear reactor analysis for studying whether or not a system is self-sustaining. However, the design and development of…

Recurrent Neural Networks (RNNs) can be seriously impacted by the initial parameters assignment, which may result in poor generalization performances on new unseen data. With the objective to tackle this crucial issue, in the context of RNN…

Link prediction in multilayer networks is a key challenge in applications such as recommendation systems and protein-protein interaction prediction. While many techniques have been developed, most rely on assumptions about shared structures…

In urban computing, precise and swift forecasting of multivariate time series data from traffic networks is crucial. This data incorporates additional spatial contexts such as sensor placements and road network layouts, and exhibits complex…

In this work, restricted additive Schwarz (RAS) and optimized restricted additive Schwarz (ORAS) preconditioners from the Trilinos package FROSch (Fast and Robust Overlapping Schwarz) are employed to solve model problems implemented using…

In this paper we are concerned with restricted additive Schwarz with local impedance transformation conditions for a family of Helmholtz problems in two dimensions. These problems are discretized by the finite element method with conforming…

It is tested whether machine learning methods can be used for preconditioning to increase the performance of the linear solver -- the backbone of the semi-implicit, grid-point model approach for weather and climate models. Embedding the…

Segmentation-based, two-stage neural network has shown excellent results in the surface defect detection, enabling the network to learn from a relatively small number of samples. In this work, we introduce end-to-end training of the…

Deep Neural Network (DNN) models are usually trained sequentially from one layer to another, which causes forward, backward and update locking's problems, leading to poor performance in terms of training time. The existing parallel…

We present a deep learning-based iterative approach to solve the discrete heterogeneous Helmholtz equation for high wavenumbers. Combining classical iterative multigrid solvers and convolutional neural networks (CNNs) via preconditioning,…

Deep neural networks are capable of modelling highly non-linear functions by capturing different levels of abstraction of data hierarchically. While training deep networks, first the system is initialized near a good optimum by greedy…

When the obstacle problem of clamped Kirchhoff plates is discretized by a partition of unity method, the resulting discrete variational inequalities can be solved by a primal-dual active set algorithm. In this paper we develop and analyze…

In the current work we present a spectral analysis of the additive and multiplicative Schwarz methods within the framework of domain decomposition techniques, by investigating the spectral properties of these classical Schwarz…