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We propose a machine learning (ML) non-Markovian closure modelling framework for accurate predictions of statistical responses of turbulent dynamical systems subjected to external forcings. One of the difficulties in this statistical closure problem is the lack of training data, which is a configuration that is not desirable in supervised learning with neural network models. In this study with the 40-dimensional Lorenz-96 model, the shortage of data is due to the stationarity of the statistics beyond the decorrelation time. Thus, the only informative content in the training data is from the short-time transient statistics. We adopt a unified closure framework on various truncation regimes, including and excluding the detailed dynamical equations for the variances. The closure framework employs a Long-Short-Term-Memory architecture to represent the higher-order unresolved statistical feedbacks with a choice of ansatz that accounts for the intrinsic instability yet produces stable long-time predictions. We found that this unified agnostic ML approach performs well under various truncation scenarios. Numerically, it is shown that the ML closure model can accurately predict the long-time statistical responses subjected to various time-dependent external forces that have larger maximum forcing amplitudes and are not in the training dataset. This article is part of the theme issue ‘Data-driven prediction in dynamical systems’.
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Predicting glass structure by physics-informed machine learning
Abstract Machine learning (ML) is emerging as a powerful tool to predict the properties of materials, including glasses. Informing ML models with knowledge of how glass composition affects short-range atomic structure has the potential to enhance the ability of composition-property models to extrapolate accurately outside of their training sets. Here, we introduce an approach wherein statistical mechanics informs a ML model that can predict the non-linear composition-structure relations in oxide glasses. This combined model offers an improved prediction compared to models relying solely on statistical physics or machine learning individually. Specifically, we show that the combined model accurately both interpolates and extrapolates the structure of Na2O–SiO2glasses. Importantly, the model is able to extrapolate predictions outside its training set, which is evidenced by the fact that it is able to predict the structure of a glass series that was kept fully hidden from the model during its training.
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- PAR ID:
- 10370667
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- npj Computational Materials
- Volume:
- 8
- Issue:
- 1
- ISSN:
- 2057-3960
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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