# Statistical prediction of extreme events from small datasets

arXiv: https://arxiv.org/abs/2201.08294 · HTML: https://mlsanity.com/paper/2201.08294/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 13 references that are in the map.
- First posted on arXiv 20 Jan 2022.

## Builds on (most cited first, 3 of 3)

- [Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamics](https://mlsanity.com/paper/1910.05266/) (2019)
- [Robust Optimization and Validation of Echo State Networks for learning chaotic dynamics](https://mlsanity.com/paper/2103.03174/) (2021)
- [Auto-Encoded Reservoir Computing for Turbulence Learning](https://mlsanity.com/paper/2012.10968/) (2020)

## Built on by (most cited first, 2 of 2)

- [Robust quantum reservoir computers for forecasting chaotic dynamics: generalized synchronization and stability](https://mlsanity.com/paper/2506.22335/) (2025)
- [Modelling spatiotemporal turbulent dynamics with the convolutional autoencoder echo state network](https://mlsanity.com/paper/2211.11379/) (2022)

## Abstract (arXiv)

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.