Related papers: Mixed-precision finite element kernels and assembl…
Recent hardware acceleration advances have enabled powerful specialized accelerators for finite element computations, spiking neural network inference, and sparse tensor operations. However, existing approaches face fundamental limitations:…
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…
The paper presents investigations on the implementation and performance of the finite element numerical integration algorithm for first order approximations and three processor architectures, popular in scientific computing, classical CPU,…
Emerging deep learning workloads urgently need fast general matrix multiplication (GEMM). To meet such demand, one of the critical features of machine-learning-specific accelerators such as NVIDIA Tensor Cores, AMD Matrix Cores, and Google…
Motivated by the increasing availability of low- and mixed-precision arithmetic on modern hardware, we develop mixed-precision variants of Lloyd's algorithm for k-means clustering. The main ingredient is a family of mixed-precision kernels…
Recent hardware-aware matrix-free algorithms for higher-order finite-element (FE) discretized matrix-vector multiplications reduce floating point operations and data access costs compared to traditional sparse matrix approaches. This work…
The rapid adoption of low-precision arithmetic in artificial intelligence and edge computing has created a strong demand for energy-efficient and flexible floating-point multiply-accumulate (MAC) units. This paper presents a dual-precision…
The rapid updates in error-resilient applications along with their quest for high throughput have motivated designing fast approximate functional units for Field-Programmable Gate Arrays (FPGAs). Studies that proposed imprecise functional…
Support for lower precision computation is becoming more common in accelerator hardware due to lower power usage, reduced data movement and increased computational performance. However, computational science and engineering (CSE) problems…
Finite element method (FEM) is one of the most important numerical methods in modern engineering design and analysis. Since traditional serial FEM is difficult to solve large FE problems efficiently and accurately, high-performance parallel…
Pixel- and voxel-based representations of microstructures obtained from tomographic imaging methods is an established standard in computational materials science. The corresponding highly resolved, uniform discretitization in numerical…
The rapid adaptation of data driven AI models, such as deep learning inference, training, Vision Transformers (ViTs), and other HPC applications, drives a strong need for runtime precision configurable different non linear activation…
This work proposes a mathematically founded mixed precision accumulation strategy for the inference of neural networks. Our strategy is based on a new componentwise forward error analysis that explains the propagation of errors in the…
Finite mixture models have been widely used for the modelling and analysis of data from heterogeneous populations. Maximum likelihood estimation of the parameters is typically carried out via the Expectation-Maximization (EM) algorithm. The…
Low precision arithmetic, in particular half precision floating point arithmetic, is now available in commercial hardware. Using lower precision can offer significant savings in computation and communication costs with proportional savings…
Although mixed precision arithmetic has recently garnered interest for training dense neural networks, many other applications could benefit from the speed-ups and lower storage cost if applied appropriately. The growing interest in…
Finite-element (FE) discretisations have emerged as a powerful real-space alternative to large-scale Kohn-Sham density functional theory (DFT) calculations, offering systematic convergence, excellent parallel scalability, while…
On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and…
Numerical methods such as the Finite Element Method (FEM) have been successfully adapted to utilize the computational power of GPU accelerators. However, much of the effort around applying FEM to GPU's has been focused on high-order FEM due…
In this paper, we propose a mixed-precision convolution unit architecture which supports different integer and floating point (FP) precisions. The proposed architecture is based on low-bit inner product units and realizes higher precision…