Related papers: A Three-Level Parallelisation Scheme and Applicati…
The multilevel Schwarz preconditioner is one of the most popular parallel preconditioners for enhancing convergence and improving parallel efficiency. However, its parallel implementation on arbitrary unstructured triangular/tetrahedral…
The K-Means clustering using LLoyd's algorithm is an iterative approach to partition the given dataset into K different clusters. The algorithm assigns each point to the cluster based on the following objective function \[\ \min…
An algorithm is proposed to solve robust control problems constrained by partial differential equations with uncertain coefficients, based on the so-called MG/OPT framework. The levels in this MG/OPT hierarchy correspond to discretization…
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,…
Multilevel methods are among the most efficient numerical methods for solving large-scale systems of equations that arise from discretized partial differential equations. Two-level convergence theory plays a fundamental role in the analysis…
We propose two novel techniques for overcoming load-imbalance encountered when implementing so-called look-ahead mechanisms in relevant dense matrix factorizations for the solution of linear systems. Both techniques target the scenario…
In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature range around the critical point. By combining the parallel tempering algorithm with cluster updates and an…
We study the problem of complexity estimation in the context of parallelizing an advanced Branch and Bound-type algorithm over graphical models. The algorithm's pruning power makes load balancing, one crucial element of every distributed…
In this two-part paper, we propose a general algorithmic framework for the minimization of a nonconvex smooth function subject to nonconvex smooth constraints. The algorithm solves a sequence of (separable) strongly convex problems and…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…
This paper proposes a scheme to efficiently execute distributed learning tasks in an asynchronous manner while minimizing the gradient staleness on wireless edge nodes with heterogeneous computing and communication capacities. The approach…
A new method for solving Laplacian linear systems proposed by Kelner et al. involves the random sampling and update of fundamental cycles in a graph. Kelner et al. proved asymptotic bounds on the complexity of this method but did not report…
A multilevel correction scheme is proposed to solve defective and nodefective of nonsymmetric partial differential operators by the finite element method. The method includes multi correction steps in a sequence of finite element spaces. In…
Stochastic Gradient Descent is used for large datasets to train models to reduce the training time. On top of that data parallelism is widely used as a method to efficiently train neural networks using multiple worker nodes in parallel.…
We describe a parallel approximation algorithm for maximizing monotone submodular functions subject to hereditary constraints on distributed memory multiprocessors. Our work is motivated by the need to solve submodular optimization problems…
In parallel computing, a problem is divided into a set of smaller tasks that are distributed across multiple processing elements. Balancing the load of the processing elements is key to achieving good performance and scalability. If the…
Gradient-based optimization has been critical to the success of machine learning, updating a single set of parameters to minimize a single loss. A growing number of applications rely on a generalization of this, where we have a bilevel or…
We propose a new family of multilevel methods for unconstrained minimization. The resulting strategies are multilevel extensions of high-order optimization methods based on q-order Taylor models (with q >= 1) that have been recently…
As compute power increases with time, more involved and larger simulations become possible. However, it gets increasingly difficult to efficiently use the provided computational resources. Especially in particle-based simulations with a…