Numerical tools to study the dynamical evolution of planetary systems

研究行星系统动力学演化的数值工具

• 批准号: RGPIN-2020-04513
• 负责人: Rein, Hanno
• 金额: $ 2.99万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=740007
• 关键词: Numerical; tools; study; dynamical; evolution

In the last 25 years, more than 4000 planets have been discovered outside our Solar System. These so called exoplanets have revolutionized our understanding of how planetary systems form and evolve, and given us clues as to how common potentially habitable planets are in our galaxy. The dynamical architecture of planetary systems plays an important role in our ability to answer fundamental questions. Not only is the dynamical state one of the few observables that we can measure accurately in many systems, it also acts as a unique window into the otherwise unobservable formation phase of planets. My research group develops state-of-the-art numerical tools to model the dynamics of planetary systems. This is a challenging task because of 1) the high accuracy required to model subtle dynamical interactions between planets, and 2) the vast separation of timescales between the orbital period of planets (typically days to years) and the age of planetary systems (up to billions of years). In this proposal, I outline my plan to further improve algorithms that solve the motion of planets in planetary systems. These improvements will help us to vet and characterize observed exoplanets, constrain their evolution, and advance our understanding of these complex dynamical systems. I plan to achieve this goal by targeting three main areas where significant progress can be made: 1) I will adopt new mathematical methods for calculating highly oscillatory integrals and differential equations such that they can be used in dynamical simulations of planetary systems; 2) I will explore the use of novel high performance computing hardware (Field Programmable Gate Arrays, FPGA) to accelerate numerical simulations; and 3) I will make it easier for researchers to setup, run, and analyze large numbers of such simulations on a diverse set of computing resources. This includes the development of a new tool to predict the long-term evolution of planetary systems using machine learning. My entire research program puts a strong emphasis on the wide dissemination of all tools and algorithms that my research group develops. Not only are my group's algorithms among the worlds' most accurate and fastest, they are also among the most frequently used.

在过去的25年中，在我们的太阳系以外发现了4000多个行星。这些所谓的系外行星已经彻底改变了我们对行星系统如何形成和发展的理解，并给了我们有关我们银河系中潜在可居住的行星如何共同的线索。行星系统的动态架构在我们回答基本问题的能力中起着重要作用。动态状态不仅是我们可以在许多系统中准确测量的少数观察结果之一，而且还充当了行星本来是不可观察的地层阶段的独特窗口。我的研究小组开发了最先进的数值工具来对行星系统的动态进行建模。这是一项具有挑战性的任务，因为1）模拟行星之间微妙的动力相互作用所需的高精度，以及2）行星轨道时期（通常是几天到几年）和行星系统的年龄（多达数十亿年）之间的时间尺度分离。 在此提案中，我概述了我的计划，以进一步改善解决行星系统中行星运动的算法。这些改进将有助于我们审查和表征观察到的系外行星，限制它们的演变，并提高我们对这些复杂动力学系统的理解。我计划通过针对可以取得重大进展的三个主要领域来实现这一目标：1）我将采用新的数学方法来计算高度振荡的积分和微分方程，从而可以将它们用于行星系统的动态模拟； 2）我将探讨新型高性能计算硬件（现场可编程门阵列，FPGA）的使用来加速数值模拟； 3）我将使研究人员更容易在各种计算资源上进行设置，运行和分析大量此类仿真。这包括开发一种新工具，可以使用机器学习预测行星系统的长期演变。我的整个研究计划非常重视我研究小组开发的所有工具和算法的广泛传播。我小组在世界上最准确和最快的算法不仅是最常用的算法。