论文标题
幻想：具有自动差异的任意指标的用户友好符合符号的大地测量积分器
FANTASY: User-Friendly Symplectic Geodesic Integrator for Arbitrary Metrics with Automatic Differentiation
论文作者
论文摘要
我们提出幻想（最后是一种直接和符号的数字轨迹算法），这是一种用户友好的开源符号符号符号测量集成符。 Fantasy旨在工作“开箱即用”，除了指标和测量学的初始条件外，用户不需要任何东西。幻想有效地将衍生物计算为使用自动差异化的机器精度，从而可以在任意空间（时代）中集成地理素，而无需用户手动输入ChristOffel符号或任何其他度量导数。此外，Fantasy利用了将相位空间加倍的哈密顿集成方案，其中粒子相空间的两个副本一起进化在一起。该技术允许一个既明确又具有符号性的集成方案，即使在哈密顿不可分离的情况下也是如此。 Fantasy带有第二和第四阶方案，并且很容易扩展到高级方案。 Fantasy还包括一个自动的Jacobian计算器，该计算器允许自动进行坐标转换。
We present FANTASY (Finally A Numerical Trajectory Algorithm both Straightforward and sYmplectic), a user-friendly, open-source symplectic geodesic integrator written in Python. FANTASY is designed to work "out-of-the-box" and does not require anything from the user aside from the metric and the initial conditions for the geodesics. FANTASY efficiently computes derivatives up to machine precision using automatic differentiation, allowing the integration of geodesics in arbitrary space(times) without the need for the user to manually input Christoffel symbols or any other metric derivatives. Further, FANTASY utilizes a Hamiltonian integration scheme that doubles the phase space, where two copies of the particle phase space are evolved together. This technique allows for an integration scheme that is both explicit and symplectic, even when the Hamiltonian is not separable. FANTASY comes prebuilt with second and fourth order schemes, and is easily extendible to higher order schemes. FANTASY also includes an automatic Jacobian calculator that allows for coordinate transformations to be done automatically.
