Learning Stochastic Dynamics with Statistics-Informed Neural Network
Learning Stochastic Dynamics with Statistics-Informed Neural Network
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DOI：
10.1016/j.jcp.2022.111819
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发表时间：
2022-02
期刊：
影响因子：
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通讯作者：
Yuanran Zhu;Yunhao Tang;Changho Kim
中科院分区：
文献类型：
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作者：
Yuanran Zhu;Yunhao Tang;Changho Kim
我们介绍了一个机器学习框架，称为随机通知神经网络（SINN）从数据中学习随机动态。这种新的架构理论上的灵感来自于随机系统的普遍逼近定理，我们在本文中介绍，和随机建模的投影算子形式主义。我们设计了训练神经网络模型的机制，以再现目标随机过程的正确行为。数值仿真结果表明，训练好的SINN可以可靠地逼近马尔可夫和非马尔可夫随机动力学。我们证明了SINN对粗粒化问题和转变动力学建模的适用性。此外，我们表明，所获得的降阶模型可以在时间粗粒度数据上训练，因此非常适合于稀有事件模拟。
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 correctstatisticalbehavior 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.