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Learning stochastic dynamics with statistics-informed neural network
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DOI：10.1016/j.jcp.2022.111819.png)
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摘要
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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 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.(c) 2022 Elsevier Inc. All rights reserved.
Keyword:
Scientific machine learning
Recurrent neural network
Reduced-order stochastic modeling
Rare events
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3.8
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1.6W
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