Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to investigating the effective dynamics for slow-fast stochastic dynamical systems. Given observation data on a short-term period satisfying some unknown slow-fast stochastic systems, we propose a novel algorithm including a neural network called Auto-SDE to learn invariant slow manifold. Our approach captures the evolutionary nature of a series of time-dependent autoencoder neural networks with the loss constructed from a discretized stochastic differential equation. Our algorithm is also validated to be accurate, stable and effective through numerical experiments under various evaluation metrics.

翻译：多尺度随机动力系统因其描述现实世界中复杂现象的能力，已被广泛应用于科学和工程问题。本文致力于研究慢-快随机动力系统的有效动力学。给定满足未知慢-快随机系统的短期观测数据，我们提出了一种包含名为Auto-SDE的神经网络的新型算法来学习不变慢流形。我们的方法捕捉了一系列随时间变化的自编码器神经网络的演化特性，其损失函数基于离散化的随机微分方程构建。通过多种评估指标下的数值实验，我们的算法被验证具有准确性、稳定性和有效性。