Related papers: Improving Efficiency of Parallel Across the Method…
Implicit Runge--Kutta (IRK) methods are highly effective for solving stiff ordinary differential equations (ODEs) but can be computationally expensive for large-scale problems due to the need of solving coupled algebraic equations at each…
Massively parallel hardware (GPUs) and long sequence data have made parallel algorithms essential for machine learning at scale. Yet dynamical systems, like recurrent neural networks and Markov chain Monte Carlo, were thought to suffer from…
Contraction Hierarchies (CH) (Geisberger et al., 2008) is one of the most widely used algorithms for shortest-path queries on road networks. Compared to Dijkstra's algorithm, CH enables orders of magnitude faster query performance through a…
We present a fourth-order finite-volume algorithm in space and time for low Mach number reacting flow with detailed kinetics and transport. Our temporal integration scheme is based on a multi-implicit spectral deferred correction (MISDC)…
Round Robin (RR) Algorithm is considered as optimal in time shared environment because the static time is equally shared among the processes. If the time quantum taken is static then it undergoes degradation of the CPU performance and leads…
Sparse Tucker Decomposition (STD) algorithms learn a core tensor and a group of factor matrices to obtain an optimal low-rank representation feature for the \underline{H}igh-\underline{O}rder, \underline{H}igh-\underline{D}imension, and…
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…
In this paper, we design a novel algorithm based on Least-Squares Monte Carlo (LSMC) in order to approximate the solution of discrete time Backward Stochastic Differential Equations (BSDEs). Our algorithm allows massive parallelization of…
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…
Many HPC applications that solve differential equations rely on the Runge-Kutta family of methods for time integration. Among these methods, the fourth-order accurate RK4 scheme is especially popular. This time integration scheme requires…
The need for scalable numerical solutions has motivated the development of asynchronous parallel algorithms, where a set of nodes run in parallel with little or no synchronization, thus computing with delayed information. This paper studies…
Parallel thinking has emerged as a promising paradigm for reasoning, yet it imposes significant computational burdens. Existing efficiency methods primarily rely on local, per-trajectory signals and lack principled mechanisms to exploit…
With the increase in the amount of data and the expansion of model scale, distributed parallel training becomes an important and successful technique to address the optimization challenges. Nevertheless, although distributed stochastic…
Semidefinite programming (SDP) is a fundamental class of convex optimization problems with diverse applications in mathematics, engineering, machine learning, and related disciplines. This paper investigates the application of the…
Dense pixel matching is important for many computer vision tasks such as disparity and flow estimation. We present a robust, unified descriptor network that considers a large context region with high spatial variance. Our network has a very…
This work proposes and analyzes a generalized acceleration technique for decreasing the computational complexity of using stochastic collocation (SC) methods to solve partial differential equations (PDEs) with random input data. The SC…
Despite the numerous uses of semidefinite programming (SDP) and its universal solvability via interior point methods (IPMs), it is rarely applied to practical large-scale problems. This mainly owes to the computational cost of IPMs that…
Stencil computations consume a major part of runtime in many scientific simulation codes. As prototypes for this class of algorithms we consider the iterative Jacobi and Gauss-Seidel smoothers and aim at highly efficient parallel…
The stable principal component pursuit (SPCP) is a non-smooth convex optimization problem, the solution of which enables one to reliably recover the low rank and sparse components of a data matrix which is corrupted by a dense noise matrix,…
Reduction operations are extensively employed in many computational problems. A reduction consists of, given a finite set of numeric elements, combining into a single value all elements in that set, using for this a combiner function. A…