Roy Mousumi, Senapati Abhishek, Poria Swarup, Mishra Arindam, Hens Chittaranjan
Department of Applied Mathematics, University of Calcutta, 92, A.P.C. Road, Kolkata 700009, India.
Center for Advanced Systems Understanding (CASUS), 02826 Görlitz, Germany.
Phys Rev E. 2022 Jun;105(6-1):064205. doi: 10.1103/PhysRevE.105.064205.
In this study, we use a reservoir computing based echo state network (ESN) to predict the collective burst synchronization of neurons. Specifically, we investigate the ability of ESN in predicting the burst synchronization of an ensemble of Rulkov neurons placed on a scale-free network. We have shown that a limited number of nodal dynamics used as input in the machine can capture the real trend of burst synchronization in this network. Further, we investigate the proper selection of nodal inputs of degree-degree (positive and negative) correlated networks. We show that for a disassortative network, selection of different input nodes based on degree has no significant role in the machine's prediction. However, in the case of assortative network, training the machine with the information (i.e., time series) of low degree nodes gives better results in predicting the burst synchronization. The results are found to be consistent with the investigation carried out with a continuous time Hindmarsh-Rose neuron model. Furthermore, the role of hyperparameters like spectral radius and leaking parameter of ESN on the prediction process has been examined. Finally, we explain the underlying mechanism responsible for observing these differences in the prediction in a degree correlated network.
在本研究中，我们使用基于储层计算的回声状态网络（ESN）来预测神经元的集体爆发同步。具体而言，我们研究了ESN预测放置在无标度网络上的一组鲁尔科夫神经元爆发同步的能力。我们已经表明，在机器中用作输入的有限数量的节点动态可以捕捉该网络中爆发同步的真实趋势。此外，我们研究了度-度（正相关和负相关）相关网络的节点输入的适当选择。我们表明，对于一个异配网络，基于度选择不同的输入节点对机器的预测没有显著作用。然而，在同配网络的情况下，用低度节点的信息（即时间序列）训练机器在预测爆发同步方面会得到更好的结果。结果发现与使用连续时间 Hindmarsh-Rose 神经元模型进行的研究一致。此外，还研究了ESN的超参数如谱半径和泄漏参数在预测过程中的作用。最后，我们解释了在度相关网络中观察到这些预测差异的潜在机制。
