Rossi Riccardo, Murari Andrea, Gaudio Pasquale
Department of Industrial Engineering, University of Rome "Tor Vergata", via del Politecnico 1, 00100 Roma, Italy.
Consorzio RFX (CNR, ENEA, INFN, Universita di Padova, Acciaierie Venete SpA), Corso Stati Uniti 4, 35127 Padova, Italy.
Entropy (Basel). 2020 May 21;22(5):584. doi: 10.3390/e22050584.
Determining the coupling between systems remains a topic of active research in the field of complex science. Identifying the proper causal influences in time series can already be very challenging in the trivariate case, particularly when the interactions are non-linear. In this paper, the coupling between three Lorenz systems is investigated with the help of specifically designed artificial neural networks, called time delay neural networks (TDNNs). TDNNs can learn from their previous inputs and are therefore well suited to extract the causal relationship between time series. The performances of the TDNNs tested have always been very positive, showing an excellent capability to identify the correct causal relationships in absence of significant noise. The first tests on the time localization of the mutual influences and the effects of Gaussian noise have also provided very encouraging results. Even if further assessments are necessary, the networks of the proposed architecture have the potential to be a good complement to the other techniques available in the market for the investigation of mutual influences between time series.
确定系统之间的耦合仍然是复杂科学领域一个活跃的研究课题。在三变量情况下，识别时间序列中适当的因果影响已经极具挑战性，尤其是当相互作用是非线性的时候。在本文中，借助专门设计的人工神经网络，即时延神经网络（TDNN），研究了三个洛伦兹系统之间的耦合。TDNN可以从其先前的输入中学习，因此非常适合提取时间序列之间的因果关系。所测试的TDNN的性能一直非常出色，显示出在无显著噪声情况下识别正确因果关系的卓越能力。关于相互影响的时间定位和高斯噪声影响的首次测试也给出了非常令人鼓舞的结果。即使需要进一步评估，所提出架构的网络有潜力成为市场上用于研究时间序列之间相互影响的其他现有技术的良好补充。
