Mixed and Variable Precision for an Exascale Hyperbolic PDE Engine

百亿亿次级双曲 PDE 引擎的混合精度和可变精度

• 批准号: 462423388
• 负责人: Professor Dr. Michael Bader
• 金额: --
• 依托单位: Lehrstuhl für Informatik V: Wissenschaftliches Rechnen
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/462423388?language=en
• 关键词: Mixed; Variable; Precision; Exascale; Hyperbolic

The goal of the project ExaHyPE-MVP is to systematically explore and exploit the use of mixed and variable floating point precision in the ExaHyPE engine.ExaHyPE allows to solve a wide range of models (i.e., hyperbolic systems of partial differential equations, as they often stem from conservation laws) on supercomputers, using a fixed mesh and parallelisation infrastructure and discretisation method, but allowing flexibility with respect to the solved equations. ExaHyPE is based on high-order ADER-DG (discontinuous Galerkin with Arbitrary High-order DERivative time stepping) discretisation, which consists of a multitude of kernels with different performance characteristics. We will extend ExaHyPE's code generation utilities to allow engine users and developers to specify the precision used for each kernel. In addition, we will extend ExaHyPE to support variable target precision, for example in areas of higher or lower accuracy demands. For both mixed and variable precision, we will explore criteria for adaptively selecting the precision, thus introducing "epsilon"-adaptivity (i.e., adaptive variable precision) as an HPC-motivated counterpart to the concepts of adaptivity w.r.t. mesh refinement or discretisation order (“h- “or “p-adaptivity”).We will systematically evaluate possible gains in overall time to solution and impact in terms of accuracy on benchmark scenarios from a range of widely relevant hyperbolic PDE systems, and we will demonstrate the impact on real use cases on scenarios that stem from two projects on earthquake simulation and modelling rupture propagation. A key challenge will be how to manage the resulting software complexity via expanding ExaHyPE's code generation facilities.

ExaHyPE-MVP 项目的目标是系统地探索和利用 ExaHyPE 引擎中混合和可变浮点精度的使用。ExaHyPE 允许求解各种模型（即偏微分方程的双曲系统，因为它们通常源自守恒定律）在超级计算机上，使用固定网格和并行化基础设施以及离散化方法，但允许基于高阶方程求解的灵活性。 ADER-DG（具有任意高阶 DERivative 时间步进的不连续 Galerkin）离散化，由具有不同性能特征的多个内核组成。我们将扩展 ExaHyPE 的代码生成实用程序，以允许引擎用户和开发人员指定每个内核使用的精度。此外，我们将扩展 ExaHyPE 以支持可变目标精度，例如在更高或更低精度要求的领域，我们将探索自适应选择目标精度的标准。精度，从而引入“epsilon”自适应（即自适应可变精度）作为 HPC 驱动的自适应网格细化或离散化阶数（“h-”或“p-自适应”）概念的对应项。我们将系统地评估从一系列广泛相关的双曲偏微分方程系统中，可能会缩短解决方案的总体时间，并对基准场景的准确性产生影响，我们将演示对源自两个项目的场景的实际用例的影响地震模拟和破裂传播建模的一个关键挑战是如何通过扩展 ExaHyPE 的代码生成设施来管理由此产生的软件复杂性。