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arXiv · 2202.12278

Learning Stochastic Dynamics with Statistics-Informed Neural Network

Yuanran Zhu·Yu-Hang Tang·Changho Kim
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Abstract

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.

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BibTeXRIS

Yuanran Zhu, Yu-Hang Tang, Changho Kim. 2022-02-24. Learning Stochastic Dynamics with Statistics-Informed Neural Network. https://doi.org/10.1016/j.jcp.2022.111819

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