Accuracy of neural networks for the simulation of chaotic dynamics: precision of training data vs precision of the algorithm

TL;DR

This study compares neural network techniques for simulating chaotic dynamics, finding that algorithm precision outweighs data precision in prediction accuracy, with reservoir computing outperforming LSTM and TCN.

Contribution

It demonstrates that neural network prediction accuracy for chaotic systems depends more on algorithm precision than data precision, highlighting the effectiveness of reservoir computing.

Findings

ESN predicts chaotic dynamics more accurately

Algorithm precision impacts prediction more than data precision

Higher network precision improves reliability of predictions

Abstract

We explore the influence of precision of the data and the algorithm for the simulation of chaotic dynamics by neural networks techniques. For this purpose, we simulate the Lorenz system with different precisions using three different neural network techniques adapted to time series, namely reservoir computing (using ESN), LSTM and TCN, for both short and long time predictions, and assess their efficiency and accuracy. Our results show that the ESN network is better at predicting accurately the dynamics of the system, and that in all cases the precision of the algorithm is more important than the precision of the training data for the accuracy of the predictions. This result gives support to the idea that neural networks can perform time-series predictions in many practical applications for which data are necessarily of limited precision, in line with recent results. It also suggests that for a given set of data the reliability of the predictions can be significantly improved by using a network with higher precision than the one of the data.