Deep Learning of the Evolution Operator Enables Forecasting of Out-of-Training Dynamics in Chaotic Systems

TL;DR

This paper shows that deep learning models can predict complex chaotic system behaviors, including rare events and dynamics outside training data, by learning underlying mathematical rules rather than just observed patterns.

Contribution

It introduces a deep learning emulator capable of forecasting out-of-training dynamics in chaotic systems, demonstrating emergent behaviors and rare events prediction.

Findings

Successfully forecasted spontaneous relaminarisation.

Predicted initialisation of arbitrary chaotic states.

Achieved zero-shot prediction for unseen parameter values.

Abstract

We demonstrate that a deep learning emulator for chaotic systems can forecast phenomena absent from training data. Using the Kuramoto-Sivashinsky and beta-plane turbulence models, we evaluate the emulator through scenarios probing the fundamental phenomena of both systems: forecasting spontaneous relaminarisation, capturing initialisation of arbitrary chaotic states, zero-shot prediction of dynamics with parameter values outside of the training range, and characterisation of dynamical statistics from artificially restricted training datasets. Our results show that deep learning emulators can uncover emergent behaviours and rare events in complex systems by learning underlying mathematical rules, rather than merely mimicking observed patterns.