STENCIL-NET for equation-free forecasting from data.

Autor: Maddu S; Faculty of Computer Science, Technische Universität Dresden, Dresden, Germany.; Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany.; Center for Systems Biology Dresden, Dresden, Germany.; Center for Scalable Data Analytics and Artificial Intelligence ScaDS.AI Dresden/Leipzig, Dresden, Germany.; Center for Computational Biology, Flatiron Institute, New York City, USA., Sturm D; Helmholtz-Zentrum Dresden-Rossendorf (HZDR), Dresden, Germany.; Center for Advanced Systems Understanding (CASUS), Görlitz, Germany., Cheeseman BL; Faculty of Computer Science, Technische Universität Dresden, Dresden, Germany.; Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany.; Center for Systems Biology Dresden, Dresden, Germany.; ONI, Inc., Linacre House, Banbury Road, Oxford, OX2 8TA, UK., Müller CL; Department of Statistics, LMU München, Munich, Germany.; Institute of Computational Biology, Helmholtz Zentrum München, Munich, Germany.; Center for Computational Mathematics, Flatiron Institute, New York City, USA., Sbalzarini IF; Faculty of Computer Science, Technische Universität Dresden, Dresden, Germany. ivo.sbalzarini@tu-dresden.de.; Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany. ivo.sbalzarini@tu-dresden.de.; Center for Systems Biology Dresden, Dresden, Germany. ivo.sbalzarini@tu-dresden.de.; Center for Scalable Data Analytics and Artificial Intelligence ScaDS.AI Dresden/Leipzig, Dresden, Germany. ivo.sbalzarini@tu-dresden.de.
Jazyk: angličtina
Zdroj: Scientific reports [Sci Rep] 2023 Aug 07; Vol. 13 (1), pp. 12787. Date of Electronic Publication: 2023 Aug 07.
DOI: 10.1038/s41598-023-39418-6
Abstrakt: 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.
(© 2023. Springer Nature Limited.)
Databáze: MEDLINE
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