Statistical prediction of extreme events from small datasets

TL;DR

This paper demonstrates that Echo State Networks can predict the statistics of extreme events in turbulent flows using small, imperfect datasets, effectively extrapolating to heavy-tail event distributions.

Contribution

The study introduces the use of ESNs for predicting extreme event statistics from limited data, showing successful extrapolation and improved statistical predictions.

Findings

ESNs accurately predict extreme event statistics

Networks improve system statistics beyond training data

Effective extrapolation from small datasets

Abstract

We propose Echo State Networks (ESNs) to predict the statistics of extreme events in a turbulent flow. We train the ESNs on small datasets that lack information about the extreme events. We asses whether the networks are able to extrapolate from the small imperfect datasets and predict the heavy-tail statistics that describe the events. We find that the networks correctly predict the events and improve the statistics of the system with respect to the training data in almost all cases analysed. This opens up new possibilities for the statistical prediction of extreme events in turbulence.