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Discussion papers
https://doi.org/10.5194/npg-2019-23
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-2019-23
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 14 Jun 2019

Research article | 14 Jun 2019

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Nonlinear Processes in Geophysics (NPG).

Generalization properties of neural networks trained on Lorenzsystems

Sebastian Scher1 and Gabriele Messori1,2 Sebastian Scher and Gabriele Messori
  • 1Department of Meteorology and Bolin Centre for Climate Research, Stockholm University, Stockholm, Sweden
  • 2Department of Earth Sciences, Uppsala University, Uppsala, Sweden

Abstract. Neural networks are able to approximate chaotic dynamical systems when provided with training data that covers all relevant regions of the system's phase space. However, many practical applications diverge from this idealised scenario. Here, we investigate the ability of neural networks to: 1) learn the behaviour of dynamical systems from incomplete training data, and 2) learn the influence of an external forcing on the dynamics. Our analysis is performed on the Lorenz63 and Lorenz95 models. We show that neural networks trained on data covering only part of the system's phase space struggle to make skillful short-term forecasts in the regions missed during the training. Additionally, when making long series of consecutive forecasts, the networks mostly do not reproduce trajectories exploring regions beyond those seen in the training data. We also find that it is challenging for the standard network architectures to learn the influence of a slowly changing external forcing, highlighting the limitations of a network trained on a specific forcing regime for generalising a system's behaviour. These results outline challenges for a variety of machine-learning applications. An example is climate science, which is concerned with a non-stationary chaotic system whose behaviour is known only through comparatively short data series.

Sebastian Scher and Gabriele Messori
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Sebastian Scher and Gabriele Messori
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Code for "Generalization properties of neural networks trained on Lorenz systems" S. Scher https://doi.org/10.5281/zenodo.2649879

Sebastian Scher and Gabriele Messori
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Latest update: 22 Jul 2019
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Short summary
Neural networks are a technique that is widely used to predict the time-evolution of physical systems. For this the neural network is shown past evolution of the system – it is "trained" – and then can be used to predict the evolution in the future. We show some limitations in this approach for certain systems that are important to consider when using neural networks for climate and weather-related applications.
Neural networks are a technique that is widely used to predict the time-evolution of physical...
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