# Data-driven prediction of a multi-scale Lorenz 96 chaotic system using deep learning methods: Reservoir computing, ANN, and RNN-LSTM

## TL;DR

This study compares deep learning methods for predicting a multi-scale Lorenz 96 chaotic system, finding reservoir computing (RC-ESN) significantly outperforms ANN and RNN-LSTM in short-term forecasting and reproducing long-term statistics.

## Contribution

It demonstrates the superior performance of reservoir computing over traditional neural networks in modeling complex chaotic systems with limited observable variables.

## Key findings

- RC-ESN accurately forecasts chaotic trajectories for hundreds of time steps.
- RNN-LSTM outperforms ANN in prediction accuracy.
- Predicted data from RC-ESN and RNN-LSTM closely match true probability distributions.

## Abstract

In this paper, the performance of three deep learning methods for predicting short-term evolution and for reproducing the long-term statistics of a multi-scale spatio-temporal Lorenz 96 system is examined. The methods are: echo state network (a type of reservoir computing, RC-ESN), deep feed-forward artificial neural network (ANN), and recurrent neural network with long short-term memory (RNN-LSTM). This Lorenz 96 system has three tiers of nonlinearly interacting variables representing slow/large-scale ($X$), intermediate ($Y$), and fast/small-scale ($Z$) processes. For training or testing, only $X$ is available; $Y$ and $Z$ are never known or used. We show that RC-ESN substantially outperforms ANN and RNN-LSTM for short-term prediction, e.g., accurately forecasting the chaotic trajectories for hundreds of numerical solver's time steps, equivalent to several Lyapunov timescales. The RNN-LSTM and ANN show some prediction skills as well; RNN-LSTM bests ANN. Furthermore, even after losing the trajectory, data predicted by RC-ESN and RNN-LSTM have probability density functions (PDFs) that closely match the true PDF, even at the tails. The PDF of the data predicted using ANN, however, deviates from the true PDF. Implications, caveats, and applications to data-driven and data-assisted surrogate modeling of complex nonlinear dynamical systems such as weather/climate are discussed.