Related papers: A low memory, highly concurrent multigrid algorith…
In this work, we present a framework for the matrix-free solution to a monolithic quasi-static phase-field fracture model with geometric multigrid methods. Using a standard matrix based approach within the Finite Element Method requires…
Reduction multigrids have recently shown good performance in hyperbolic problems without the need for Gauss-Seidel smoothers. When applied to the hyperbolic limit of the Boltzmann Transport Equation (BTE), these methods result in very close…
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…
Efficient and suitably preconditioned iterative solvers for elliptic partial differential equations (PDEs) of the convection-diffusion type are used in all fields of science and engineering. To achieve optimal performance, solvers have to…
Neural operators (NOs) struggle with high-contrast multiscale partial differential equations (PDEs), where fine-scale heterogeneities cause large errors. To address this, we use the Generalized Multiscale Finite Element Method (GMsFEM) that…
Algebraic multigrid (AMG) solvers and preconditioners are some of the fastest numerical methods to solve linear systems, particularly in a parallel environment, scaling to hundreds of thousands of cores. Most AMG methods and theory assume a…
Balanced hypergraph partitioning is an NP-hard problem with many applications, e.g., optimizing communication in distributed data placement problems. The goal is to place all nodes across $k$ different blocks of bounded size, such that…
The evolution of parallel I/O library as well as new concepts such as 'in transit' and 'in situ' visualization and analysis have been identified as key technologies to circumvent I/O bottleneck in pre-exascale applications. Nevertheless,…
Dispersion-free ultra-high order FFT-based Maxwell solvers have recently proven to be paramount to a large range of applications, including the high-fidelity modeling of high-intensity laser-matter interactions with Particle-In-Cell (PIC)…
Multi-exit network is a promising architecture for efficient model inference by sharing backbone networks and weights among multiple exits. However, the gradient conflict of the shared weights results in sub-optimal accuracy. This paper…
Semi-Lagrangian (SL) schemes are highly efficient for simulating transport equations and are widely used across various applications. Despite their success, designing genuinely multi-dimensional and conservative SL schemes remains a…
The aggressive application of scalar replacement to array references substantially reduces the number of memory operations at the expense of a possibly very large number of registers. In this paper we describe a register allocation…
Graph Spectral Sparsification (GSS) identifies an ultra-sparse subgraph, or sparsifier, whose Laplacian matrix closely approximates the spectral properties of the original graph, enabling substantial reductions in computational complexity…
In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…
Matrix Factorization (MF) on large scale data takes substantial time on a Central Processing Unit (CPU). While Graphical Processing Unit (GPU)s could expedite the computation of MF, the available memory on a GPU is finite. Leveraging GPUs…
Neural networks that map between low dimensional spaces are ubiquitous in computer graphics and scientific computing; however, in their naive implementation, they are unable to learn high frequency information. We present a comprehensive…
Reducing the memory footprint of neural networks is a crucial prerequisite for deploying them in small and low-cost embedded devices. Network parameters can often be reduced significantly through pruning. We discuss how to best represent…
In recent years, the increasing size of deep learning models and their growing demand for computational resources have drawn significant attention to the practice of pruning neural networks, while aiming to preserve their accuracy. In…
This report provides an introduction to algorithms for fundamental linear algebra problems on various parallel computer architectures, with the emphasis on distributed-memory MIMD machines. To illustrate the basic concepts and key issues,…
Operator splitting schemes are a class of powerful algorithms that solve complicated monotone inclusion and convex optimization problems that are built from many simpler pieces. They give rise to algorithms in which all simple pieces of the…