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Due to the sequential nature of the successive-cancellation (SC) algorithm, the decoding of polar codes suffers from significant decoding latencies. Fast SC decoding is able to speed up the SC decoding process, by implementing parallel…

Information Theory · Computer Science 2022-11-21 Yang Lu , Ming-Min Zhao , Ming Lei , Min-Jian Zhao

The implementation of a vast majority of machine learning (ML) algorithms boils down to solving a numerical optimization problem. In this context, Stochastic Gradient Descent (SGD) methods have long proven to provide good results, both in…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-10-06 Janis Keuper , Franz-Josef Pfreundt

In this paper, we demonstrate that the explicit ADER approach as it is used inter alia in [1] can be seen as a special interpretation of the deferred correction (DeC) method as introduced in [2]. By using this fact, we are able to embed…

Numerical Analysis · Mathematics 2022-11-17 Maria Han Veiga , Philipp Öffner , Davide Torlo

Semi-Lagrangian schemes with various splitting methods, and with different reconstruction/interpolation strategies have been applied to kinetic simulations. For example, the order of spatial accuracy of the algorithms proposed in {[Qiu and…

Numerical Analysis · Mathematics 2015-06-17 Andrew Christlieb , Wei Guo , Maureen Morton , Jing-Mei Qiu

We construct a space-time parallel method for solving parabolic partial differential equations by coupling the Parareal algorithm in time with overlapping domain decomposition in space. The goal is to obtain a discretization consisting of…

Numerical Analysis · Mathematics 2022-01-17 Jehanzeb Chaudhry , Donald Estep , Simon Tavener

This paper proposes a control algorithm for stable implementation of asynchronous parallel quadratic programming (PQP) through dual decomposition technique. In general, distributed and parallel optimization requires synchronization of data…

Systems and Control · Electrical Eng. & Systems 2019-11-26 Kooktae Lee

Model predictive control (MPC) is a powerful framework for optimal control of dynamical systems. However, MPC solvers suffer from a high computational burden that restricts their application to systems with low sampling frequency. This…

Optimization and Control · Mathematics 2025-03-12 Casian Iacob , Hany Abdulsamad , Simo Särkkä

We proposed a parallel-in-time method based on preconditioner for Biot's consolidation model in poroelasticity. In order to achieve a fast and stable convergence for the matrix system of the Biot's model, we design two preconditioners with…

Numerical Analysis · Mathematics 2023-10-17 Zeyuan Zhou , Huipeng Gu , Guoliang Ju , Wei Xing

In diffusion models, samples are generated through an iterative refinement process, requiring hundreds of sequential model evaluations. Several recent methods have introduced approximations (fewer discretization steps or distillation) to…

Machine Learning · Computer Science 2024-12-12 Nikil Roashan Selvam , Amil Merchant , Stefano Ermon

We develop a multi-dimensional, parallelized domain decomposition strategy (DDC) for mass-transfer particle tracking (MTPT) methods. These methods are a type of Lagrangian algorithm for simulating reactive transport and are able to be…

In the realm of big data and machine learning, data-parallel, distributed stochastic algorithms have drawn significant attention in the present days.~While the synchronous versions of these algorithms are well understood in terms of their…

Optimization and Control · Mathematics 2020-04-07 Atal Narayan Sahu , Aritra Dutta , Aashutosh Tiwari , Peter Richtárik

Most machine learning and deep neural network algorithms rely on certain iterative algorithms to optimise their utility/cost functions, e.g. Stochastic Gradient Descent. In distributed learning, the networked nodes have to work…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-10-06 Liang Wang , Ben Catterall , Richard Mortier

Time-parallel methods can reduce the wall clock time required for the accurate numerical solution of differential equations by parallelizing across the time-dimension. In this paper, we present and test the convergence behavior of a…

Numerical Analysis · Mathematics 2025-02-03 Ignace Bossuyt , Giovanni Samaey , Stefan Vandewalle

Large graphs commonly appear in social networks, knowledge graphs, recommender systems, life sciences, and decision making problems. Summarizing large graphs by their high level properties is helpful in solving problems in these settings.…

Machine Learning · Statistics 2022-08-01 Elise van der Pol , Ian Gemp , Yoram Bachrach , Richard Everett

We study preconditioned gradient-based optimization methods where the preconditioning matrix has block-diagonal form. Such a structural constraint comes with the advantage that the update computation is block-separable and can be…

Machine Learning · Computer Science 2020-12-08 Celestine Mendler-Dünner , Aurelien Lucchi

We present a parallel version of the well-known Split-Step Fourier method (SSF) for solving the Nonlinear Schr\"odinger equation, a mathematical model describing wave packet propagation in fiber optic lines. The algorithm is implemented…

Computational Physics · Physics 2007-05-23 S. M. Zoldi , V. Ruban , A. Zenchuk , S. Burtsev

This paper proposes a parallel in time (called also time parareal) method to solve Volterra integral equations of the second kind. The parallel in time approach follows the same spirit as the domain decomposition that consists of breaking…

Numerical Analysis · Mathematics 2016-11-26 Xianjuan Li , Tao Tang , Chuanju Xu

We explore a scaled spectral preconditioner for the efficient solution of sequences of symmetric and positive-definite linear systems. We design the scaled preconditioner not only as an approximation of the inverse of the linear system but…

Numerical Analysis · Mathematics 2024-10-04 Youssef Diouane , Selime Gürol , Oussama Mouhtal , Dominique Orban

In this paper we propose a novel parallel stochastic coordinate descent (SCD) algorithm with convergence guarantees that exhibits strong scalability. We start by studying a state-of-the-art parallel implementation of SCD and identify…

Machine Learning · Computer Science 2019-11-19 Nikolas Ioannou , Celestine Mendler-Dünner , Thomas Parnell

Motivated by the idea of imposing paralleling computing on solving stochastic differential equations (SDEs), we introduce a new Domain Decomposition Scheme to solve forward-backward stochastic differential equations (FBSDEs) parallely. We…

Numerical Analysis · Mathematics 2010-08-03 Minh-Binh Tran