Numerical tools to study the dynamical evolution of planetary systems

在过去的25年里，我们在太阳系外发现了4000多颗行星。这些所谓的系外行星彻底改变了我们对行星系统如何形成和演化的理解，并为我们提供了线索，让我们了解银河系中潜在的宜居行星有多普遍。行星系统的动力结构在我们回答基本问题的能力中起着重要作用。动力学状态不仅是我们在许多系统中可以精确测量的少数几个可观测值之一，它也是观察行星形成阶段的独特窗口。 我的研究小组开发了最先进的数值工具来模拟行星系统的动力学。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学相互作用所需的高精度，以及2）行星轨道周期（通常是几天到几年）和行星系统年龄（高达数十亿年）之间的时间尺度巨大分离。 在这个建议中，我概述了我的计划，以进一步改善算法，解决行星系统中行星的运动。这些改进将帮助我们审查和描述观测到的系外行星，限制它们的演化，并促进我们对这些复杂动力系统的理解。我计划通过瞄准三个可以取得重大进展的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，以便它们可以用于行星系统的动力学模拟; 2）我将探索使用新型高性能计算硬件（现场可编程门阵列，FPGA），以加速数值模拟;和3）我将使研究人员更容易设置，运行和分析大量的这种模拟在一组不同的计算资源。这包括开发一种新工具，利用机器学习来预测行星系统的长期演变。我的整个研究计划非常重视我的研究小组开发的所有工具和算法的广泛传播。我的团队的算法不仅是世界上最准确和最快的，而且也是最常用的。

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.