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

用偏微分方程（PDE）建模的系统在科学和工程中无处不在。它们被用于建模问题，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，医疗和经济学等领域。偏微分方程（PDE）是一个用于预测系统响应的正向模型，也是求解逆问题的关键组成部分，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的输入下重复多次。它涉及基础方程的选择，合适的数值求解器的选择，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一任务。但是，要使这些库适应特定的模型，并将各种组件组合到一个低级的高性能编程语言中，需要进行大量的开发工作。随着异构混合CPU/GPU设备的出现，这种所需的工作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，以实现良好的性能。因此，大规模开发新的模拟已成为一项成本更高、时间更密集的任务。在本项目中，我们提出了一种不同的模拟范式，基于使用Python等高生产力语言来描述问题，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就绪代码。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技术，在非结构化网格上构建一个工具链，用于复杂的exascale PDE模拟。该研究将包括数学和算法基础，具体的软件开发，用于低级别CPU/GPU内核的自动代码生成，高生产力语言接口，以及应用于电池存储系统，净零飞行和高频波传播等领域的21世纪世纪艾级挑战问题。

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.