仅用一个变量时间序列，重建神经形态系统动态行为
Reconstruction of neuromorphic dynamics from a single scalar time series using variational autoencoder and neural network map
- 用变分自编码器压缩单变量时间序列，恢复状态空间
- 训练神经网络映射，实现与原系统一致的动态响应
- 无需显式标注，适合神经动力学建模研究者
本文研究仅通过单一标量时间序列重构具有神经形态特性的动力系统。以基于霍奇金-赫胥黎模型的生理神经元为例，证明其某一变量的单个时间序列足以训练出一个具有单个控制参数的离散时间动力系统神经网络。该网络构建分两步：首先利用延迟坐标嵌入构造向量，并通过变分自编码器降维，获得重构的状态空间向量；适当降维可通过分析自编码器训练过程确定。其次，将连续时间步的重构向量对与恒定控制参数组合，用于训练另一神经网络，使其作为递归映射运行。当调节该网络控制参数时，所观察到的动力学行为与原始系统高度一致，尽管这些行为在训练中未被显式提供。
原文摘要 · Abstract (English)
This paper examines the reconstruction of a family of dynamical systems with neuromorphic behavior using a single scalar time series. A model of a physiological neuron based on the Hodgkin-Huxley formalism is considered. Single time series of one of its variables is shown to be enough to train a neural network that can operate as a discrete time dynamical system with one control parameter. The neural network system is created in two steps. First, the delay-coordinate embedding vectors are constructed form the original time series and their dimension is reduced with by means of a variational autoencoder to obtain the recovered state-space vectors. It is shown that an appropriate reduced dimension can be determined by analyzing the autoencoder training process. Second, pairs of the recovered state-space vectors at consecutive time steps supplied with a constant value playing the role of a control parameter are used to train another neural network to make it operate as a recurrent map. The regimes of thus created neural network system observed when its control parameter is varied are in very good accordance with those of the original system, though they were not explicitly presented during training.
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