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STENCIL-NET for equation-free forecasting from data.
Sci. Rep. 13:12787 (2023)
We present an artificial neural network architecture, termed STENCIL-NET, for equation-free forecasting of spatiotemporal dynamics from data. STENCIL-NET works by learning a discrete propagator that is able to reproduce the spatiotemporal dynamics of the training data. This data-driven propagator can then be used to forecast or extrapolate dynamics without needing to know a governing equation. STENCIL-NET does not learn a governing equation, nor an approximation to the data themselves. It instead learns a discrete propagator that reproduces the data. It therefore generalizes well to different dynamics and different grid resolutions. By analogy with classic numerical methods, we show that the discrete forecasting operators learned by STENCIL-NET are numerically stable and accurate for data represented on regular Cartesian grids. A once-trained STENCIL-NET model can be used for equation-free forecasting on larger spatial domains and for longer times than it was trained for, as an autonomous predictor of chaotic dynamics, as a coarse-graining method, and as a data-adaptive de-noising method, as we illustrate in numerical experiments. In all tests, STENCIL-NET generalizes better and is computationally more efficient, both in training and inference, than neural network architectures based on local (CNN) or global (FNO) nonlinear convolutions.
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Publication type
Article: Journal article
Document type
Scientific Article
ISSN (print) / ISBN
2045-2322
e-ISSN
2045-2322
Journal
Scientific Reports
Quellenangaben
Volume: 13,
Issue: 1,
Article Number: 12787
Publisher
Nature Publishing Group
Publishing Place
London
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Computational Biology (ICB)
Grants
Projekt DEAL
Saxon Ministry for Science, Culture and Tourism (SMWK)
Germany's Federal Ministry of Education and Research (BMBF)
German Federal Ministry of Education and Research (Bundesministerium fuer Bildung und Forschung, BMBF) as part of the Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI) Dresden/Leipzig
German Research Foundation (Deutsche Forschungsgemeinschaft, DFG)
Saxon Ministry for Science, Culture and Tourism (SMWK)
Germany's Federal Ministry of Education and Research (BMBF)
German Federal Ministry of Education and Research (Bundesministerium fuer Bildung und Forschung, BMBF) as part of the Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI) Dresden/Leipzig
German Research Foundation (Deutsche Forschungsgemeinschaft, DFG)