论文标题
通过统计信息的神经网络学习随机动力学
Learning Stochastic Dynamics with Statistics-Informed Neural Network
论文作者
论文摘要
我们介绍了一个名为统计信息的神经网络（SINN）的机器学习框架，用于从数据中学习随机动力学。从理论上讲，这种新结构的灵感来自于随机系统的通用近似定理，我们在本文中介绍了它，以及用于随机建模的投影手术形式。我们设计了训练神经网络模型的机制，以重现目标随机过程的正确\ emph {统计}行为。数值模拟结果表明，受过良好训练的Sinn可以可靠地近似马尔可夫和非马克维亚随机动力学。我们证明了SINN对粗粒问题的适用性和过渡动力学的建模。此外，我们表明，所获得的减少阶模型可以在时间粗粒的数据上进行训练，因此非常适合稀有事实模拟。
We introduce a machine-learning framework named statistics-informed neural network (SINN) for learning stochastic dynamics from data. This new architecture was theoretically inspired by a universal approximation theorem for stochastic systems, which we introduce in this paper, and the projection-operator formalism for stochastic modeling. We devise mechanisms for training the neural network model to reproduce the correct \emph{statistical} behavior of a target stochastic process. Numerical simulation results demonstrate that a well-trained SINN can reliably approximate both Markovian and non-Markovian stochastic dynamics. We demonstrate the applicability of SINN to coarse-graining problems and the modeling of transition dynamics. Furthermore, we show that the obtained reduced-order model can be trained on temporally coarse-grained data and hence is well suited for rare-event simulations.
