One of the most appealing characteristics of neural networks is their ability for data generalization. This is achieved through the extraction of data features and dependencies that may initially appear obscure. In the context of dynamical systems reconstruction, this aptitude could facilitate significant advancements in the development of models based on experimental data. We investigate the extent to which neural networks can reproduce the dynamical regimes of a system and nonlinear effects, observed for various values of its control parameters, when only a single scalar time series of this system is available. Created neural network models a family of dynamical systems parameterized by a control parameter. This family exhibits behavior consistent with that of the original system, i.e. discovers its specific regimes and transitions. This is demonstrated by the example of a neuromorphic Hodgkin–Huxley system. The reconstruction is carried out 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.
This approache was applied to the experimental data corresponding to the electrical activity of a cell culture. Obtained dynamical system reproduce typical patterns of oscillatory activity of cells and can be interpreted as of digital twin of cell culture. In the talk we discuss some perspectives of approach for tissue engineering.
