Related papers: Mixed-precision finite element kernels and assembl…

Mixture proportion estimation (MPE) is the problem of estimating the weight of a component distribution in a mixture, given samples from the mixture and component. This problem constitutes a key part in many "weakly supervised learning"…

Many recent computational accelerators provide non-standard (e.g., reduced precision) arithmetic operations to enhance performance for floating-point matrix multiplication. Unfortunately, the properties of these accelerators are not widely…

Kernel functions are vital ingredients of several machine learning algorithms, but often incur significant memory and computational costs. We introduce an approach to kernel approximation in machine learning algorithms suitable for…

We implement and benchmark the frozen core approximation, a technique commonly adopted in electronic structure theory to reduce the computational cost by means of mathematically fixing the chemically inactive core electron states. The…

Using the standard finite element method (FEM) to solve general partial differential equations, the round-off error is found to be proportional to $N^{\beta_{\rm R}}$, with $N$ the number of degrees of freedom (DoFs) and $\beta_{\rm R}$ a…

This chapter provides an overview of state-of-the-art adaptive finite element methods (AFEMs) for the numerical solution of second-order elliptic partial differential equations (PDEs), where the primary focus is on the optimal interplay of…

Matrix multiplication is the bedrock in Deep Learning inference application. When it comes to hardware acceleration on edge computing devices, matrix multiplication often takes up a great majority of the time. To achieve better performance…

In this paper we propose a mixed precision algorithm in the context of the semi-Lagrangian discontinuous Galerkin method. The performance of this approach is evaluated on a traditional dual socket workstation as well as on a Xeon Phi and an…

This work studies three multigrid variants for matrix-free finite-element computations on locally refined meshes: geometric local smoothing, geometric global coarsening, and polynomial global coarsening. We have integrated the algorithms…

Federated Learning (FL) has become a viable technique for realizing privacy-enhancing distributed deep learning on the network edge. Heterogeneous hardware, unreliable client devices, and energy constraints often characterize edge computing…

Machine-learned interatomic potentials can offer near first-principles accuracy but are computationally expensive, limiting their application to large-scale molecular dynamics simulations. Inspired by quantum mechanics/molecular mechanics…

We present an FPGA-based study of matrix-element acceleration for Monte Carlo event generation, using MadGraph5_aMC@NLO as a benchmark framework. Two complementary scenarios are considered. First, we implement the full matrix-element…

To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve…

Mixed-precision computing has the potential to significantly reduce the cost of exascale computations, but determining when and how to implement it in programs can be challenging. In this article, we propose a methodology for enabling…

The devices designed for the Internet-of-Things encompass a large variety of distinct processor architectures, forming a highly heterogeneous zoo. In order to tackle this, we employ a simulator to estimate the performance of the…

In recent years, high performance scientific computing on graphics processing units (GPUs) have gained widespread acceptance. These devices are designed to offer massively parallel threads for running code with general purpose. There are…

The acceleration of deep-learning kernels in hardware relies on matrix multiplications that are executed efficiently on Systolic Arrays (SA). To effectively trade off deep-learning training/inference quality with hardware cost, SA…

In finite element methods (FEMs), the accuracy of the solution cannot increase indefinitely because the round-off error increases when the number of degrees of freedom (DoFs) is large enough. This means that the accuracy that can be reached…

The advent of foundation models have revolutionized various fields, enabling unprecedented task accuracy and flexibility in computational linguistics, computer vision and other domains. Attention mechanism has become an essential component…

In the present work, we investigate the computational efficiency afforded by higher-order finite-element discretization of the saddle-point formulation of orbital-free density functional theory. We first investigate the robustness of viable…