标题： 从数据驱动的随机系统学习有效动力学 显示英文标题

标题： Learning effective dynamics from data-driven stochastic systems

摘要： 多尺度随机动力系统因其能够描述许多实际应用中的复杂现象，在众多科学和工程问题中得到了广泛应用。 本文致力于研究慢快随机动力系统的有效动力学。 给定一个满足某些未知慢快随机系统的短期观测数据，我们提出了一种新的算法，其中包括一种称为Auto-SDE的神经网络，用于学习不变的慢流形。 我们的方法通过从离散化的随机微分方程构建的损失函数，捕捉了一系列时间相关的自编码器神经网络的演化特性。 我们的算法还通过各种评估指标下的数值实验验证了其准确性、稳定性和有效性。 显示英文摘要

摘要： 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.