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STENCIL-NET for equation-free forecasting from data.

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Maddu,  Suryanarayana
Max Planck Institute for Molecular Cell Biology and Genetics, Max Planck Society;

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Sturm,  Dominik
Max Planck Institute for Molecular Cell Biology and Genetics, Max Planck Society;

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Cheeseman,  Bevan
Max Planck Institute for Molecular Cell Biology and Genetics, Max Planck Society;

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Sbalzarini,  Ivo F.
Max Planck Institute for Molecular Cell Biology and Genetics, Max Planck Society;

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Citation

Maddu, S., Sturm, D., Cheeseman, B., Müller, C. L., & Sbalzarini, I. F. (2023). STENCIL-NET for equation-free forecasting from data. Scientific reports, 13(1): 12787. doi:10.1038/s41598-023-39418-6.


Cite as: https://hdl.handle.net/21.11116/0000-000E-AB4E-B
Abstract
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.