Determining hidden shared patterns behind dynamic phenomena can be a game-changer in multiple areas of research. Here we present the principles and show a method to identify hidden shared dynamics from time series by a two-module, feedforward neural network architecture: the Mapper-Coach network. We reconstruct unobserved, continuous latent variable input, the time series generated by a chaotic logistic map, from the observed values of two simultaneously forced chaotic logistic maps. The network has been trained to predict one of the observed time series based on its own past and conditioned on the other observed time series by error-back propagation. It was shown, that after this prediction have been learned successfully, the activity of the bottleneck neuron, connecting the mapper and the coach module, correlated strongly with the latent shared input variable. The method has the potential to reveal hidden components of dynamical systems, where experimental intervention is not possible.

翻译：确定动态现象背后隐藏的共享模式，可能成为多个研究领域的突破性进展。本文提出了一种通过双模块前馈神经网络架构——Mapper-Coach网络——从时间序列中识别隐藏共享动力学的原理与方法。我们通过两个受同步强迫的混沌逻辑斯蒂映射的观测值，重构了未被观测的连续潜变量输入，即由混沌逻辑斯蒂映射生成的时间序列。该网络通过误差反向传播进行训练，以基于自身过去值并在另一观测时间序列的条件下预测其中一个观测时间序列。结果表明，在成功学习此预测任务后，连接映射器模块与教练模块的瓶颈神经元活动与隐藏的共享输入变量呈现强相关性。该方法具备揭示动力学系统隐藏成分的潜力，尤其适用于无法进行实验干预的研究场景。