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Maddu, S.* ; Sturm, D.* ; Cheeseman, B.L.* ; Müller, C.L. ; Sbalzarini, I.F.*

STENCIL-NET for equation-free forecasting from data.

Sci. Rep. 13:12787 (2023)
Verlagsversion DOI PMC
Open Access Gold
Creative Commons Lizenzvertrag
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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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Korrespondenzautor
ISSN (print) / ISBN 2045-2322
e-ISSN 2045-2322
Zeitschrift Scientific Reports
Quellenangaben Band: 13, Heft: 1, Seiten: , Artikelnummer: 12787 Supplement: ,
Verlag Nature Publishing Group
Verlagsort London
Nichtpatentliteratur Publikationen
Begutachtungsstatus Peer reviewed
Institut(e) Institute of Computational Biology (ICB)
Förderungen 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)