Related papers: Mixed-precision finite element kernels and assembl…
Within the past years, hardware vendors have started designing low precision special function units in response to the demand of the Machine Learning community and their demand for high compute power in low precision formats. Also the…
Developing kernels for Processing-In-Memory (PIM) platforms poses unique challenges in data management and parallel programming on limited processing units. Although software development kits (SDKs) for PIM, such as the UPMEM SDK, provide…
This paper is devoted to GPU kernel optimization and performance analysis of three tensor-product operators arising in finite element methods. We provide a mathematical background to these operations and implementation details. Achieving…
In recent years, a new kind of accelerated hardware has gained popularity in the Artificial Intelligence (AI) and Machine Learning (ML) communities which enables extremely high-performance tensor contractions in reduced precision for deep…
In some situations, EM algorithm shows slow convergence problems. One possible reason is that standard procedures update the parameters simultaneously. In this paper we focus on finite mixture estimation. In this framework, we propose a…
Deploying mixed-precision neural networks on edge devices is friendly to hardware resources and power consumption. To support fully mixed-precision neural network inference, it is necessary to design flexible hardware accelerators for…
Efficient exploitation of exascale architectures requires rethinking of the numerical algorithms used in many large-scale applications. These architectures favor algorithms that expose ultra fine-grain parallelism and maximize the ratio of…
Approximate computing techniques have been successful in reducing computation and power costs in several domains. However, error sensitive applications in high-performance computing are unable to benefit from existing approximate computing…
While many hardware accelerators have recently been proposed to address the inefficiency problem of fully homomorphic encryption (FHE) schemes, none of them is able to deliver optimal performance when facing real-world FHE workloads…
Finite mixture models are powerful tools for modelling and analyzing heterogeneous data. Parameter estimation is typically carried out using maximum likelihood estimation via the Expectation-Maximization (EM) algorithm. Recently, the…
We introduce quantitative and robust tools to control the numerical accuracy in simulations performed using the Multiscale Finite Element Method (MsFEM). First, we propose a guaranteed and fully computable a posteriori error estimate for…
Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose…
The IEEE 754-2008 standard recommends the correct rounding of some elementary functions. This requires to solve the Table Maker's Dilemma which implies a huge amount of CPU computation time. We consider in this paper accelerating such…
This work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known that virtual part design and qualification in additive…
In this paper, we propose StruM, a novel structured mixed-precision-based deep learning inference method, co-designed with its associated hardware accelerator (DPU), to address the escalating computational and memory demands of deep…
In this paper, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning of high-order finite element problems. The methods described here allow for the construction of…
Deep learning has become a useful data analysis method, however mainstream adaption in distributed computer software and embedded devices has been low so far. Often, adding deep learning inference in mainstream applications and devices…
This paper establishes the first theoretical framework for analyzing the rounding-error effects on multigrid methods using mixed-precision iterative-refinement solvers. While motivated by the sparse symmetric positive definite (SPD) matrix…
In this paper, we present a finite element method (FEM) framework enhanced by an operator-adapted wavelet decomposition algorithm designed for the efficient analysis of multiscale electromagnetic problems. Usual adaptive FEM approaches,…
Finite-precision arithmetic computations face an inherent tradeoff between accuracy and efficiency. The points in this tradeoff space are determined, among other factors, by different data types but also evaluation orders. To put it simply,…