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We discuss several strategies to implement Dykstra's projection algorithm on NVIDIA's compute unified device architecture (CUDA). Dykstra's algorithm is the central step in and the computationally most expensive part of statistical…
The rising computational and energy demands of deep learning, particularly in large-scale architectures such as foundation models and large language models (LLMs), pose significant challenges to sustainability. Traditional gradient-based…
Modern HPC systems are increasingly relying on greater core counts and wider vector registers. Thus, applications need to be adapted to fully utilize these hardware capabilities. One class of applications that can benefit from this increase…
High-Level Synthesis (HLS) enables rapid prototyping of complex hardware designs by translating C or C++ code to low-level RTL code. However, the testing and evaluation of HLS designs still typically rely on slow RTL-level simulators that…
Modern computer architectures support low-precision arithmetic, which present opportunities for the adoption of mixed-precision algorithms to achieve high computational throughput and reduce energy consumption. As a growing number of…
Sparse linear system solvers ($Ax=b$) are critical computational kernels in Electronic Design Automation (EDA), underpinning vital simulations for modern IC and system design. Applications like power integrity verification and…
Consecutive matrix multiplications are commonly used in graph neural networks and sparse linear solvers. These operations frequently access the same matrices for both reading and writing. While reusing these matrices improves data locality,…
We introduce microJAX, the first fully differentiable implementation of the image-centered ray-shooting (ICRS) algorithm for gravitational microlensing. Built on JAX and its XLA just-in-time compiler, microJAX exploits GPU parallelism while…
In recent years, convolutional networks have demonstrated unprecedented performance in the image restoration task of super-resolution (SR). SR entails the upscaling of a single low-resolution image in order to meet application-specific…
We present a fast direct solver for boundary integral equations on complex surfaces in three dimensions using an extension of the recently introduced recursive strong skeletonization scheme. For problems that are not highly oscillatory, our…
The accurate assembly of the system matrix is an important step in any code that solves partial differential equations on a mesh. We either explicitly set up a matrix, or we work in a matrix-free environment where we have to be able to…
Sparse matrix-sparse matrix multiplication (SpGEMM) is a key kernel in many scientific applications and graph workloads. Unfortunately, SpGEMM is bottlenecked by data movement due to its irregular memory access patterns. Significant work…
Large language models have high compute, latency, and memory requirements. While specialized accelerators such as GPUs and TPUs typically run these workloads, CPUs are more widely available and consume less energy. Accelerating LLMs with…
In this article, we introduce a fast and memory efficient solver for sparse matrices arising from the finite element discretization of elliptic partial differential equations (PDEs). We use a fast direct (but approximate) multifrontal…
The design of heterogeneous systems that include domain specific accelerators is a challenging and time-consuming process. While taking into account area constraints, designers must decide which parts of an application to accelerate in…
The aim of this work is to develop a fast algorithm for approximating the matrix function $f(A)$ of a square matrix $A$ that is symmetric and has hierarchically semiseparable (HSS) structure. Appearing in a wide variety of applications,…
Applications with low data reuse and frequent irregular memory accesses, such as graph or sparse linear algebra workloads, fail to scale well due to memory bottlenecks and poor core utilization. While prior work with prefetching,…
We introduce synax, a novel library for automatically differentiable simulation of Galactic synchrotron emission. Built on the JAX framework, synax leverages JAX's capabilities, including batch acceleration, just-in-time compilation, and…
Exascale systems, expected to emerge by the end of the next decade, will require the exploitation of billion-way parallelism at multiple hierarchical levels in order to achieve the desired sustained performance. The task of assessing future…
One of the most computationally challenging problems expected for the High-Luminosity Large Hadron Collider (HL-LHC) is determining the trajectory of charged particles during event reconstruction. Algorithms used at the LHC today rely on…