Identificação esparsa de modelos da eletrofisiologia celular com o uso do método SINDy e autoenconders

Abstract

Data-driven sparse identification of dynamical systems consists of finding a reduced set of important variables to describe the behavior of complex systems. This approach is crucial for analyzing and modeling complex systems in various scientific and engineering areas. In the field of cellular electrophysiology, this technique can be applied to identify models described by ordinary differential equations that explain the generation of action potential in the heart. Computational models of cardiac electrical activity are essential for understanding diseases and developing new therapies, however, some of these detailed mathematical models contain hundreds of variables, a context that can be favored by the use of sparse identification of dynamic systems. In this study, the SINDy (Sparse Identification of Nonlinear Dynamics) method was used to find the differential equations associated with cellular electrophysiology. Preliminary experiments with simulated data from the classical FitzHugh-Nagumo and Hodgkin-Huxley models show promising results when employing the SINDy method. Autoencoder neural networks coupled to the SINDy method can be used to identify complex dynamical systems from observed data. In this configuration, an autoencoder is used to learn a latent representation of the input data, while the SINDy method is employed to identify the differential equations that govern the system dynamics from this latent representation. In this study, identifications were made without dimension reduction of classical models, for the purpose of validating the SINDy-Autoencoder method. A second section of results shows that it is possible to identify a two-variable model from a model with four, in this case, the Hodgkin-Huxley model. This integration allows for the efficient discovery of mathematical models that describe the temporal evolution of the system while capturing non-linear and complex relationships between variables.