MAthematics for Competitive ADvantage (MACAD)

该项目解决了现代大规模计算系统在性能和能源效率方面的主要挑战。随着行业转向加速器技术，以继续提供海量数据处理应用程序所需的性能提升，关注这些应用程序中的优化算法行为变得越来越重要。该项目将为应用程序的数值特性提供新的分析和建模技术。这将使我们能够利用加速器技术的灵活性，通过专门的数字格式和根据应用程序的独特要求定制的算法离散化步骤。建议的方法的效率将在两个具有高度学术和工业影响的应用领域得到证明：线性代数的蒙特卡罗混合方法是具有线性复杂性的随机方法，其线性复杂度与矩阵的大小成正比。在算法上，这些方法实现了高度的并行性：马尔可夫链的生成可以独立完成，从而使用流水线以最少的通信提供高效的计算。蒙特卡罗矩阵逆可以计算并用作GMRES、BICGSTAB或任何其他高效迭代方法的预条件，从而提供了一种高效的混合方法。机器学习成为一种几乎无处不在的技术，支撑着多个经济部门。此外，机器学习应用程序以其数值灵活性而臭名昭著，其中许多核心矩阵运算可以以降低(一半)或混合精度执行。这使其成为Maxeler硬件和软件优化的理想选择。这个项目将探索和优化多个机器学习应用程序的核心关键线性代数运算：用于卡尔曼过滤器的矩阵求逆，用于训练神经网络的共轭梯度法，以及用于主成分分析的大型稠密矩阵的对角化。部署的新优化技术有可能在处理速度和能源效率方面比传统数字格式的实现提高10倍。此外，我们希望有一种通用的方法来在数据流类型的体系结构上有效地映射这些类型的问题。

This project addresses the major challenges of performance and energy efficiency in modern large-scale computing systems. As the industry shifts towards accelerator technology in order to continue delivering the performance gains needed in massive data processing applications, focusing on optimised algorithmic behaviour inside these applications is becoming increasingly important. This project will deliver new analysis and modelling techniques for the numerical properties of applications. This will allow us to harness the flexibility of accelerator technology through specialised number formats and algorithm discretisation steps that are tailored to the unique requirements of the application.The efficiency of the proposed approach will be demonstrated in two application areas with high academic and industrial impact:Monte Carlo hybrid methods for linear algebra, are stochastic methods which have linear complexity proportional to the size of the matrix. Algorithmically these methods enable high levels of parallelism: Markov chains generation can be done independently to provide efficient computation with minimal communication using pipelining. The Monte Carlo matrix inverse can be calculated and used as a preconditioner with GMRES, BICGSTAB or any other efficient iterative method thus delivering a highly efficient hybrid method.Machine Learning became an almost ubiquitous technology underpinning multiple economic sectors. Besides Machine Learning applications are notorious for their numerical flexibility, where many core matrix operations can be performed in reduced (half) or mixed precision. This makes it an ideal candidate for optimisation with Maxeler hardware and software. This project will explore and optimise key linear algebra operations at the heart of multiple Machine Learning applications: matrix inversion for Kahlman filters, Conjugate Gradient Method for training neural networks and diagonalisation of large dense matrices for principal components analysis.The new optimisation techniques deployed have the potential to deliver a 10x improvement in terms of processing speed and energy efficiency over implementations in traditional numeric formats. In addition, we expect to have a generalised methodology of mapping these type of problems efficiently on dataflow type architectures.