Mixed and Variable Precision for an Exascale Hyperbolic PDE Engine

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允许解决各种模型（即，偏微分方程的双曲系统，因为它们通常源于守恒定律），使用固定网格和并行化基础设施和离散化方法，但允许相对于求解方程的灵活性。ExaHyPE基于高阶ADER-DG（具有任意高阶导数时间步进的不连续Galerkin）离散化，该离散化由具有不同性能特征的众多内核组成。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用于每个内核的精度。此外，我们还将扩展ExaHyPE以支持可变目标精度，例如在精度要求较高或较低的领域。对于混合精度和可变精度，我们将探索自适应选择精度的标准，从而引入“自适应”-自适应性（即，自适应可变精度）作为HPC动机的对应物的概念，自适应w.r.t.网格细化或离散化顺序（“h-“或“p-自适应”）。我们将系统地评估解决方案的总体时间的可能增益和对一系列广泛相关的双曲PDE系统的基准场景的准确性的影响，我们将展示对来自地震模拟和建模破裂传播的两个项目的场景的真实的用例的影响。一个关键的挑战将是如何通过扩展ExaHyPE的代码生成设施来管理由此产生的软件复杂性。

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.