We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics, and high-dimensional, large fast modes. Given only access to a black box simulator from which short bursts of simulation can be obtained, we design an algorithm that outputs an estimate of the invariant manifold, a process of the effective stochastic dynamics on it, which has averaged out the fast modes, and a simulator thereof. This simulator is efficient in that it exploits of the low dimension of the invariant manifold, and takes time steps of size dependent on the regularity of the effective process, and therefore typically much larger than that of the original simulator, which had to resolve the fast modes. The algorithm and the estimation can be performed on-the-fly, leading to efficient exploration of the effective state space, without losing consistency with the underlying dynamics. This construction enables fast and efficient simulation of paths of the effective dynamics, together with estimation of crucial features and observables of such dynamics, including the stationary distribution, identification of metastable states, and residence times and transition rates between them.

翻译：本文针对高维随机动力系统提出一种非线性随机模型降阶技术，此类系统具有低维不变有效流形（慢动力学）及高维大振幅快模态。仅通过访问黑箱模拟器（可获取短时爆发模拟数据）的条件下，我们设计了一种算法，可输出不变流形的估计、其上已平均快模态的有效随机动力学过程及其模拟器。该模拟器利用不变流形的低维特性，其时间步长取决于有效过程的规则性，通常远大于原模拟器为解析快模态所需的时间步长。算法与估计可即时执行，从而在保持与底层动力学一致性的前提下高效探索有效状态空间。本方法不仅能够快速高效模拟有效动力学路径，还可估计该动力学的关键特征与可观测量，包括稳态分布、亚稳态辨识、驻留时间及状态间转移速率。