Precursor-driven machine learning prediction of chaotic extreme pulses in Kerr resonators

TL;DR

This paper presents a novel machine learning approach using transfer entropy and LSTM networks to predict extreme chaotic pulses in Kerr resonators, achieving high accuracy and early detection in complex high-dimensional systems.

Contribution

It introduces a precursor-driven, model-free prediction method for chaotic extreme events based on transfer entropy and deep learning, extending prediction horizons beyond traditional limits.

Findings

Achieved 92% true positive prediction rate.

Predicted extreme events up to 9 round trips ahead.

Demonstrated effectiveness on experimental Kerr resonator data.

Abstract

Machine learning algorithms have opened a breach in the fortress of the prediction of high-dimensional chaotic systems. Their ability to find hidden correlations in data can be exploited to perform model-free forecasting of spatiotemporal chaos and extreme events. However, the extensive feature of these evolutions constitutes a critical limitation for full-size forecasting processes. Hence, the main challenge for forecasting relevant events is to establish the set of pertinent information. Here, we identify precursors from the transfer entropy of the system and a deep Long Short-Term Memory network to forecast the complex dynamics of a system evolving in a high-dimensional spatiotemporal chaotic regime. Performances of this triggerable model-free prediction protocol based on the information flowing map are tested from experimental data originating from a passive resonator operating in such a complex nonlinear regime. We have been able to predict the occurrence of extreme events up to 9 round trips after the detection of precursor, i.e., 3 times the horizon provided by Lyapunov exponents, with 92 % of true positive predictions leading to 60 % of accuracy.