论文标题
神经网络模拟混乱动力学的准确性：训练数据的精度与算法的精度
Accuracy of neural networks for the simulation of chaotic dynamics: precision of training data vs precision of the algorithm
论文作者
论文摘要
我们探讨了通过神经网络技术模拟数据精度和算法的影响。为此，我们使用适合时间序列的三种不同的神经网络技术，即储层计算（使用ESN），LSTM和TCN，以不同的时间序列模拟Lorenz系统，以进行短期和长时间的预测，并评估其效率和准确性。我们的结果表明，ESN网络更擅长准确预测系统的动力学，并且在所有情况下，算法的精度比训练数据的精度更为重要，以确保预测的准确性。该结果支持了这样一个观念，即神经网络可以在许多实际应用中执行时间序列预测，这些应用程序必须与最近的结果相符，这些应用程序必然具有有限的精度。它还表明，对于给定的数据集，通过使用比其中一个数据更高的网络，可以通过更高的精度来显着提高预测的可靠性。
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.
