论文标题
从数据驱动的随机系统中学习有效的动态
Learning effective dynamics from data-driven stochastic systems
论文作者
论文摘要
由于在许多现实世界应用中描述复杂现象的能力，多尺度随机动力系统已被广泛采用了各种科学和工程问题。这项工作致力于研究慢速随机动力学系统的有效动力学。鉴于在满足某些未知慢速随机系统的短期时期的观察数据，我们提出了一种新型算法，其中包括一个名为Auto-SDE的神经网络，以学习不变的慢速歧管。我们的方法捕获了一系列时间依赖性自动编码器神经网络的进化性质，其损失是由离散的随机微分方程构成的。通过在各种评估指标下的数值实验中，我们的算法也被验证为准确，稳定和有效。
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.
