Data-driven reduction of action-potential models using SINDy

Mathematical models of excitable cells, such as neurons and cardiac myocytes, are fundamental tools for understanding electrical activity and action-potential generation. However, biophysically detailed models often involve numerous state variables, making their simulation computationally demanding in the context of tissue or whole-organ level. In this work, we explore a data-driven alternative for model discovery and reduction based on the Sparse Identification of Nonlinear Dynamics (SINDy) framework. Using the classical Hodgkin-Huxley model as the reference system, we introduce an ionic current-based approach in which reduced variables are constructed directly from membrane current measurements and fitted using physically structured sparse libraries, enabling compact surrogate models of the ionic dynamics. The method can reproduce the essential dynamics of action-potential generation with compact representations. For the Hodgkin-Huxley model, we further combine principal component analysis with SINDy to reduce the dimensionality of the system equations prior to identification, yielding low-dimensional models that accurately reproduce excitable dynamics. These results highlight the potential of a data-driven approach to derive models of excitable membranes, paving the way for the reduction of electrophysiological models based on ionic current data and for large-scale or real-time neuronal and cardiac simulations.