SysGenX: Composable software generation for system-level simulation at exascale

由偏微分方程（PDEs）建模的系统在科学和工程中无处不在。它们被用来模拟问题，包括结构、流体、材料、电磁学、波传播和生物系统，以及航空航天、图像处理、医学治疗和经济学等领域。偏微分方程包括预测系统响应的正演模型，但也是反问题解决方案的关键组成部分，用于设计优化，不确定性量化和数据科学应用，其中正向计算在不同输入下重复多次。用偏微分方程建模的复杂系统的数值模拟是一个具有挑战性的课题。它涉及到基础方程的选择，合适的数值解算器的选择，以及在特定硬件上的实现。几十年来，已经开发了许多软件库来支持这项任务。但是使这些库适应特定的模型，并在低级高性能编程语言中组合各种组件需要大量的开发工作。随着异构混合CPU/GPU设备在通往百亿亿级系统的道路上的出现，这种需要的努力变得更加具有挑战性。实现需要针对每个单独的设备类型进行调整，以获得良好的性能。因此，大规模开发新的模拟已经成为一项更加昂贵和耗时的任务。在这个项目中，我们提出了一个不同的模拟范例，基于使用高生产率语言（如Python）来描述问题，以及自动代码生成和即时编译，将高级公式转换为高性能的exascale代码。基于组件软件库Firedrake、FEniCS和Bempp的经验，研究人员将使用最先进的有限元和边界元素技术，为非结构化网格上的pde的复杂百亿亿次模拟建立一个工具链。该研究将包括数学和算法基础，用于低级CPU/GPU内核自动代码生成的具体软件开发，高生产率语言接口，以及在电池存储系统，净零飞行和高频波传播领域的21世纪百亿亿次挑战问题的应用。

Systems modelled by partial differential equations (PDEs) are ubiquitous in science and engineering. They are used to model problems including structures, fluids, materials, electromagnetics, wave propagation and biological systems, and in areas as varied as aerospace, image processing, medical therapeutics and economics. PDEs comprise a forward model for predicting the response of a system, but are also a key component in the solution of inverse problems, for design optimisation, uncertainty quantification and data science applications, where the forward computation is repeated many times with different inputs.The numerical simulation of complex systems modeled by PDEs is a challenging topic. It involves the choice of underlying equations, the selection of suitable numerical solvers, and implementation on specific hardware. Over the decades numerous software libraries have been developed to support this task. But adapting these libraries to the specific model and combining the various components in a low-level high-performance programming language requires a major development effort. This required effort has become significantly more challenging with the advent of heterogeneous mixed CPU/GPU devices on the path to exascale systems. Implementations need to be adapted for each individual device type in order to achieve good performance. As a consequence, developing new simulations at scale has become an ever more costly and time-intensive task.In this project we propose a different simulation paradigm, based on the use of high-productivity languages such as Python to describe the problem, and automatic code generation and just-in-time compilation to translate the high-level formulations into high-performance exascale-ready code. Based on the experience with the component software libraries Firedrake, FEniCS and Bempp, the investigators will build a toolchain for complex exascale simulations of PDEs on unstructured grids, using state of the art finite element and boundary element technologies. The research will include mathematical and algorithmic underpinnings, concrete software development for automatic code generation of low-level CPU/GPU kernels, high-productivity language interfaces, and the application to 21st century exascale challenge problems in the areas of battery storage systems, net-zero flight, and high-frequency wave propagation.