Speaker
Description
One of the most appealing characteristics of neural networks is their ability for data generalization and the extraction of data features that may initially appear obscure. In the context of dynamical systems reconstruction, this aptitude could facilitate 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 parameters, when only a single scalar time series of this system is available. Created neural network models are a family of dynamical systems parameterized by a control parameter. This family exhibits behavior consistent with that of the original system. 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. 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. This approach was applied to the experimental time series of transmembrane potential of a cell culture.
The work was supported by the project “International academic cooperation” of HSE University.
