Low latency abstractions for extreme scale simulation.

用于极端规模模拟的低延迟抽象。

• 批准号: 2478907
• 金额: --
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2024
• 资助国家: 英国
• 起止时间: 2024 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2478907
• 关键词: Low; latency; abstractions; extreme; scale

High-fidelity numerical simulations bridge the gap between theory and experiment and are essential in many areas of science. This is particularly the case when studying complex systems such as the ocean or atmosphere where the theory cannot be solved exactly and experiments are hard, or even impossible, to perform. Historically, high-performance numerical codes have been written exclusively in low-level, compiled languages such as C and Fortran. While such codes can be highly efficient and performant, they are difficult to write and maintain as the coder is required to understand all aspects of the problem from the abstract mathematical description to the specific parallel implementation. Any changes to the mathematics and/or platform are also likely to require significant amount of re-coding. Runtime code generation (RTCG) is a solution to these problems. Rather than starting with the low-level code, the performance critical sections are generated during the program runtime and then compiled with a just-in-time (JIT) compiler before they are used. This approach permits abstractions to be introduced between the mathematics and computer science, allowing specialists from either domain, but not necessarily both, to contribute to the code. The code can also be much more flexible regarding both the mathematical constructs allowed and the platforms that it can run on. Strong scaling In the current computing landscape, by far the easiest way to make your code run faster is to run it on a more powerful computer. It is therefore essential that the problem can be broken apart and distributed across the machine for solving in parallel. One would naively assume that running your problem on a machine with twice the computing power would lead to a halving of the time-to-solution but unfortunately this is rarely the case. In all pieces of software there are elements of the program that cannot be run in parallel. As the number of processors increases, this serial overhead ends up taking up an increasingly large fraction of the total runtime until no more speedup is possible. This effect is known as strong-scaling and is formalised in Amdahl's Law. Firedrake This thesis focuses on the Firedrake project, a library for numerically solving PDEs using the finite-element method (FEM). Firedrake uses RTCG to create a high-performance kernel that is used to assemble matrices. Unfortunately, compared with other FEM packages, Firedrake scales poorly in the small-problem limit (analogous to the strong-scaling limit for a fixed number of processors) during both matrix assembly and when solving the linear system. As the problem size decreases, the time-to-solution plateaus at a much greater value than is desirable. Aims and objectives Aims Improve the scaling behaviour of Firedrake in the small problem limit Objectives Profile Firedrake to identify performance bottlenecks Possibly rewrite the parallel scheduling layer of Firedrake (PyOP2) to expand the JIT-compiled kernel and reduce the time spent executing Python Novelty of the research methodology Code generation is an emerging technique in simulation science. By enabling the composition of sophisticated numerics and advanced parallel implementation for any differential equation the scientist can imagine, this technology combines productivity and performance in a combination which enables more scientists to conduct more sophisticated simulation science than ever before. Alignment to EPSRC's strategic theme and research area. This project spans the Engineering, ICT, LWEC, Manufacturing the Future, Mathematical Sciences, and Physical sciences themes. It sits in the Continuum Mechanics Research area. Collaborators: Dr Lawrence Mitchell, Durham University

高保真数值模拟弥合了理论与实验之间的差距，在许多科学领域至关重要。在研究海洋或大气等复杂系统时尤其如此，因为理论无法精确求解，实验也很难甚至不可能进行。从历史上看，高性能数字代码都是用低级编译语言（例如 C 和 Fortran）编写的。虽然此类代码非常高效且高性能，但它们难以编写和维护，因为编码人员需要理解问题的所有方面，从抽象数学描述到具体并行实现。对数学和/或平台的任何更改也可能需要大量的重新编码。运行时代码生成（RTCG）是这些问题的解决方案。性能关键部分不是从低级代码开始，而是在程序运行时生成，然后在使用之前使用即时 (JIT) 编译器进行编译。这种方法允许在数学和计算机科学之间引入抽象，允许来自任一领域（但不一定是两个领域）的专家为代码做出贡献。就允许的数学结构和可以运行的平台而言，代码也可以更加灵活。强大的扩展能力 在当前的计算环境中，迄今为止，让代码运行得更快的最简单方法就是在更强大的计算机上运行它。因此，必须将问题分解并分布到机器上以并行解决。人们会天真地认为，在具有两倍计算能力的机器上运行问题会导致解决时间减半，但不幸的是，这种情况很少发生。在所有软件中，都有一些程序元素无法并行运行。随着处理器数量的增加，这种串行开销最终会占据总运行时间的越来越大的一部分，直到无法再进行加速。这种效应被称为强缩放效应，并在阿姆达尔定律中得到了形式化。 Firedrake 本论文重点介绍 Firedrake 项目，这是一个使用有限元方法 (FEM) 数值求解偏微分方程的库。 Firedrake 使用 RTCG 创建一个用于组装矩阵的高性能内核。不幸的是，与其他 FEM 包相比，Firedrake 在矩阵组装和求解线性系统期间在小问题限制（类似于固定数量处理器的强扩展限制）方面的扩展性很差。随着问题规模的减小，解决问题的时间稳定在比期望值大得多的值上。目的和目标 目的 改善 Firedrake 在小问题限制下的扩展行为 目标 分析 Firedrake 以识别性能瓶颈 可能重写 Firedrake 的并行调度层 (PyOP2) 以扩展 JIT 编译的内核并减少执行 Python 所花费的时间研究方法 代码生成是模拟科学中的一项新兴技术。通过对科学家可以想象的任何微分方程进行复杂的数字组合和高级并行实现，该技术将生产力和性能结合在一起，使更多的科学家能够进行比以往更复杂的模拟科学。与 EPSRC 的战略主题和研究领域保持一致。该项目涵盖工程、ICT、LWEC、未来制造、数学科学和物理科学主题。它位于连续体力学研究区。合作者：杜伦大学劳伦斯·米切尔博士