论文标题
超越具有快速环境的系统的绝热限制：$τ$ leaping算法
Beyond the adiabatic limit in systems with fast environments: a $τ$-leaping algorithm
论文作者
论文摘要
我们建议使用快速环境变化的随机系统提出$τ$的模拟算法。类似于传统的$τ$ - 在离散的时间步骤中进行的算法进行，但作为主要添加，它捕获了超出绝热限制的环境噪声。关键的想法是将$τ$的输入率视为（剪裁）高斯随机变量，并用环境过程构建的第一和第二次矩。这样，该算法的每个步骤都将环境随机性保留到系统和环境之间的时间尺度分离中。我们在几个具有离散和连续环境状态的玩具示例上测试了算法，并在快速环境动态的制度中找到了良好的性能。同时，与组合系统和环境的完整模拟相比，该算法所需的计算时间要少得多。在这种情况下，我们还讨论了在具有连续状态的时变环境中模拟随机种群动态的几种方法。
We propose a $τ$-leaping simulation algorithm for stochastic systems subject to fast environmental changes. Similar to conventional $τ$-leaping the algorithm proceeds in discrete time steps, but as a principal addition it captures environmental noise beyond the adiabatic limit. The key idea is to treat the input rates for the $τ$-leaping as (clipped) Gaussian random variables with first and second moments constructed from the environmental process. In this way, each step of the algorithm retains environmental stochasticity to sub-leading order in the time scale separation between system and environment. We test the algorithm on several toy examples with discrete and continuous environmental states, and find good performance in the regime of fast environmental dynamics. At the same time, the algorithm requires significantly less computing time than full simulations of the combined system and environment. In this context we also discuss several methods for the simulation of stochastic population dynamics in time-varying environments with continuous states.
