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形成和演化的理解，并为我们提供了银河系中潜在宜居行星有多普遍的线索。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可以在许多系统中精确测量的少数可观测到的状态之一，而且它还作为一个独特的窗口，可以观察到行星的形成阶段，否则就无法观测到。

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.