标题： 底盘 - 松弛动力系统的逆向建模 显示英文标题

标题： CHASSIS - Inverse Modelling of Relaxed Dynamical Systems

摘要： 一个非相对论性引力动力系统的状态在任何时间$t$都已知，如果可以求解动力学规则，即牛顿运动方程；这需要指定引力势。一组相空间坐标${\bf w}$的演化是确定性的，尽管通常是非线性的。我们讨论了新颖的贝叶斯非参数算法 CHASSIS，它能够给出平衡引力系统的相空间$pdf$ $f({\bf w})$ 和势能$\Phi({\bf x})$。CHASSIS 在输入要求方面不太苛刻，因为它在给定系统成员的不完整、单组分速度信息的情况下仍可行。 这里 ${\bf x}$ 是三维空间坐标， ${\bf w}={\bf x+v}$ 其中 ${\bf v}$ 是三维速度向量。CHASSIS 使用一个二积分 $f=f(E, L)$ 其中能量 $E=\Phi + v^2/2, \: v^2 = \sum_{i=1}^{3}{v_i^2}$ 和角动量是 $L = |{\bf r}\times{\bf v}|$，其中 ${\bf r}$ 是球面空间向量。 同时，我们假设球面对称。 CHASSIS从$f(\cdot)$获取数据，这些数据最可能是从$\Phi(\cdot)$中选择的最佳结果，使用MCMC优化器（Metropolis-Hastings）。似然函数${\cal{L}}$是根据$f(\cdot)$在可观测空间中的投影来定义的，优化器寻找${\cal{L}}$中的最大值。 显示英文摘要

摘要： The state of a non-relativistic gravitational dynamical system is known at any time $t$ if the dynamical rule, i.e. Newton's equations of motion, can be solved; this requires specification of the gravitational potential. The evolution of a bunch of phase space coordinates ${\bf w}$ is deterministic, though generally non-linear. We discuss the novel Bayesian non-parametric algorithm CHASSIS that gives phase space $pdf$ $f({\bf w})$ and potential $\Phi({\bf x})$ of a relaxed gravitational system. CHASSIS is undemanding in terms of input requirements in that it is viable given incomplete, single-component velocity information of system members. Here ${\bf x}$ is the 3-D spatial coordinate and ${\bf w}={\bf x+v}$ where ${\bf v}$ is the 3-D velocity vector. CHASSIS works with a 2-integral $f=f(E, L)$ where energy $E=\Phi + v^2/2, \: v^2 = \sum_{i=1}^{3}{v_i^2}$ and the angular momentum is $L = |{\bf r}\times{\bf v}|$, where ${\bf r}$ is the spherical spatial vector. Also, we assume spherical symmetry. CHASSIS obtains the $f(\cdot)$ from which the kinematic data is most likely to have been drawn, in the best choice for $\Phi(\cdot)$, using an MCMC optimiser (Metropolis-Hastings). The likelihood function ${\cal{L}}$ is defined in terms of the projections of $f(\cdot)$ into the space of observables and the maximum in ${\cal{L}}$ is sought by the optimiser.