We introduce a recent symplectic integration scheme derived for solving
physically motivated systems with non-separable Hamiltonians. We show its
relevance to Riemannian manifold Hamiltonian Monte Carlo (RMHMC) and provide an
alternative to the currently used generalised leapfrog symplectic integrator,
which relies on solving multiple fixed point iterations to convergence. Via
this approach, we are able to reduce the number of higher-order derivative
calculations per leapfrog step. We explore the implications of this integrator
and demonstrate its efficacy in reducing the computational burden of RMHMC. Our
code is provided in a new open-source Python package, hamiltorch.

介绍了最近为解决具有非可分离哈密顿量的物理动机系统导出的辛积分方案，并展示了它与 Riemann 流形哈密顿蒙特卡罗 (RMHMC) 的相关性，并提供了目前使用的广义跳跃辛积分器的替代方案，通过这种方法，我们能够减少每个跳跃步的高阶导数计算的数量。探讨了该积分器的影响，并展示了其在减少 RMHMC 的计算负担方面的效果。我们的代码提供在一个新的开源 Python 包 hamiltorch 中。