Accuracy of neural networks for the simulation of chaotic dynamics: precision of training data vs precision of the algorithm
This work addresses the challenge of time-series prediction in chaotic systems for applications with limited data precision, offering incremental insights into neural network reliability.
The study investigated how the precision of training data versus algorithm precision affects neural networks' ability to simulate chaotic dynamics, finding that algorithm precision is more critical for accuracy, with ESN performing best in predicting the Lorenz system.
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.