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，并为我们提供了关于潜在宜居行星在我们银河系中有多常见的线索。行星系统的动力学结构对我们回答基本问题的能力起着重要的作用。这种动态状态不仅是我们在许多系统中可以准确测量的为数不多的可观测到的观测数据之一，而且它也是了解行星形成阶段的唯一窗口。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)对行星之间微妙的动力相互作用进行建模所需的高精度，以及2)行星的轨道周期(通常是几天到几年)和行星系统的年龄(长达数十亿年)之间的巨大时间尺度间隔。在这份提案中，我概述了我的计划，即进一步改进求解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的动力系统的理解。我计划通过以下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)来加速数值模拟；以及3)我将使研究人员更容易在不同的计算资源上设置、运行和分析大量这样的模拟。这包括开发一种新的工具，利用机器学习来预测行星系统的长期演化。我的整个研究计划非常强调广泛传播我的研究小组开发的所有工具和算法。我的团队的算法不仅是世界上最准确、最快的算法之一，而且也是最常用的算法之一。

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.