Learning Stochastic Dynamics with Statistics-Informed Neural Network

• URL: http://arxiv.org/abs/2202.12278v1
• Date: Thu, 24 Feb 2022 18:21:01 GMT
• Title: Learning Stochastic Dynamics with Statistics-Informed Neural Network
• Authors: Yuanran Zhu, Yu-Hang Tang, Changho Kim
• Abstract summary: We introduce a machine-learning framework named statistics-informed neural network (SINN) for learning dynamics from data. We devise mechanisms for training the neural network model to reproduce the correct emphstatistical behavior of a target process. 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.
• Score: 0.4297070083645049
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 introduced 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 model 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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