Generalization properties of neural networks trained on Lorenzsystems

Abstract

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.