Differentiable programming for flows with discontinuities

具有不连续性的流动的可微分规划

• 批准号: 513718742
• 负责人: Professor Dr. Michael Herty
• 金额: --
• 依托单位: Lehrstuhl für Strömungslehre und Aerodynamisches Institut (AIA)
• 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/513718742?language=en
• 关键词: Differentiable; programming; flows; discontinuities

Differentiability is a highly desirable or even essential property of numerical programs for studying many practically relevant phenomena. Motivating examples include the design of spacecraft, e.g., rockets, shuttles, or re-entry vehicles, or in in--flight adaption of flight configurations, requiring the minimization of loads on the structure by the surrounding flow. Decision making in those complex fields typically relies on sensitivities of quantities of interest obtained through results of numerical simulations. Consequently, derivatives are crucial ingredients of a wide range of state of the art methods in scientific computing ranging from basic parameter sensitivity analysis, error and uncertainty quantification via nonlinear optimization under constraints given by partial differential equations to data-driven and hybrid simulation methods augmented with elements of artificial intelligence such as machine learning. Both differentiability of the models and the actual differentiation of their numerical implementations as computer programs are the subject of algorithmic differentiation (AD). AD compilers and/or run time libraries enable the (semi-)automatic differentiation of differentiable programs. The latter typically implement highly sophisticated numerical algorithms by means of hundreds of thousands of lines of source code. They typically run on massively parallel high-performance computers. Challenges in numerical software technology with a particular focus on differentiable program analysis and domain-specific program transformation need to be addressed. Hence, most real-world applications of AD require collaborative efforts by computer scientists, applied mathematicians, and engineers. This proposal brings together researchers from all three domains aiming to obtain substantial progress in differentiable programming for highly sensitive flows in extreme flow regimes where shocks appear. This proposal aims to develop a sensitivity calculus for flow regimes with discontinuities that are amendable to differential programming. To achieve this objective the expertise from all three domains has to be combined. Our results will be published as an extensible AD software solution for a range of inviscid flow simulations featuring shock structures. Corresponding program transformation techniques will be developed including suitable derivative code design patterns, which motivates the prominent, coordinating role of computer science in this project.

可不同性是数值程序的高度理想甚至基本属性，用于研究许多实际相关现象。激励的例子包括航天器的设计，例如火箭，穿梭或重新进入车辆，或在飞行配置的范围内适应，需要通过周围的流量最大程度地减少结构上的负载。在这些复杂领域的决策通常取决于通过数值模拟结果获得的一定量的敏感性。因此，在科学计算中，衍生物是从基本参数敏感性分析，误差和不确定性量化的科学计算中的各种至关重要的成分，该衍生物是通过非线性优化的基本参数敏感性分析，误差和不确定性定量，在部分差分方程给出的约束条件下，到数据驱动的和混合模拟方法，并增加了与人工智能的元素，例如人工智能的元素。模型的可不同性和其数值实现的实际差异化是计算机程序的主题（AD）。广告编译器和/或运行时间库可以实现可区分程序的（半）自动差异化。后者通常通过数十万行源代码实现高度复杂的数值算法。它们通常在大规模平行的高性能计算机上运行。数值软件技术的挑战需要特别关注可区分的程序分析和特定领域的程序转换。因此，广告的大多数实际应用都需要计算机科学家，应用数学家和工程师的合作努力。该提案汇集了来自所有三个领域的研究人员，旨在在出现冲击的极端流动方案中以高度敏感的流动方面的差异进行进展。该提案旨在为具有不连续性的流动制度开发一个灵敏度演算，这些流程是对差异编程的不连续性。为了实现这一目标，必须合并所有三个领域的专业知识。我们的结果将作为可扩展的广告软件解决方案发布，用于一系列具有冲击结构的无粘性流量模拟。将开发相应的程序转换技术，包括合适的导数代码设计模式，这激发了计算机科学在该项目中的突出，协调的作用。