Related papers: Weighted Relaxation for Multigrid Reduction in Tim…
In this manuscript, we present a collective multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty, and develop a novel convergence…
We study gradient compression methods to alleviate the communication bottleneck in data-parallel distributed optimization. Despite the significant attention received, current compression schemes either do not scale well or fail to achieve…
Two of the most popular parallel-in-time methods are Parareal and multigrid-reduction-in-time (MGRIT). Recently, a general convergence theory was developed in Southworth (2019) for linear two-level MGRIT/Parareal that provides necessary and…
This paper presents a new algorithm for the parallel in time (PiT) numerical simulation of time dependent partial/ordinary differential equations. We propose a reliable alternative to the well know parareal in time algorithm, by formulating…
Non-stationary parametric bandits have attracted much attention recently. There are three principled ways to deal with non-stationarity, including sliding-window, weighted, and restart strategies. As many non-stationary environments exhibit…
In multiobjective optimization, inertial gradient systems accelerate convergence toward weakly Pareto optimal solutions. To achieve even faster convergence, we introduce a multiobjective inertial gradient system with time scaling (MITS),…
In this paper, we present an advanced high-order compact gas-kinetic scheme (CGKS) for 3D unstructured mixed-element meshes, augmented with a geometric multigrid technique to accelerate steady-state convergence. The scheme evolves…
We develop a parallel-in-time multigrid preconditioner for augmented systems. These saddle-point systems are foundational to numerical optimization. Our preconditioner, when paired with a suitable optimization method, accelerates the…
Group Relative Policy Optimization (GRPO) has become a standard approach for training mathematical reasoning models; however, its reliance on multiple completions per prompt makes training computationally expensive. Although recent work has…
This paper is concerned with developing an efficient numerical algorithm for fast implementation of the sparse grid method for computing the $d$-dimensional integral of a given function. The new algorithm, called the MDI-SG ({\em multilevel…
The Scheduled Relaxation Jacobi (SRJ) method is a linear solver algorithm which greatly improves the convergence of the Jacobi iteration through the use of judiciously chosen relaxation factors (an SRJ scheme) which attenuate the solution…
Implicit methods and GPU parallelization are two distinct yet powerful strategies for accelerating high-order CFD algorithms. However, few studies have successfully integrated both approaches within high-speed flow solvers. The core…
Parallel multigrid is widely used as preconditioners in solving large-scale sparse linear systems. However, the current multigrid library still needs more satisfactory performance for structured grid problems regarding speed and…
We present GRIP, a graph neural network accelerator architecture designed for low-latency inference. AcceleratingGNNs is challenging because they combine two distinct types of computation: arithmetic-intensive vertex-centric operations and…
Multigrid methods have proven to be an invaluable tool to efficiently solve large sparse linear systems arising in the discretization of partial differential equations (PDEs). Algebraic multigrid methods and in particular adaptive algebraic…
We present a first step towards a multigrid method for solving the min-cost flow problem. Specifically, we present a strategy that takes advantage of existing black-box fast iterative linear solvers, i.e. algebraic multigrid methods. We…
This work focuses on the construction of a new class of fourth-order accurate methods for multirate time evolution of systems of ordinary differential equations. We base our work on the Recursive Flux Splitting Multirate (RFSMR) version of…
Parallel imaging is widely used in magnetic resonance imaging as an acceleration technology. Traditional linear reconstruction methods in parallel imaging often suffer from noise amplification. Recently, a non-linear robust…
A multigrid scheme is proposed for the pressure equation of the incompressible unsteady fluid flow equations, allowing efficient implementation on clusters of modern CPUs, many integrated core devices (MICs), and graphics processing units…
Improving both accuracy and computational performance of numerical tools is a major challenge for seismic imaging and generally requires specialized implementations to make full use of modern parallel architectures. We present a…