Neural Differential Equations for Hudgkin-Huxley Model

Hudgkin-Huxley Model are important tool in neuronal modelling, it captures the detailed gating properties of the ion channel in the cell membrane. It describes how action potential initiated and propagated through neurons, the neuronal unit of communication. Neuronal Modelling can be computationally expensive, specially when modelling with the high resolution level models. It becomes even more challenging when considering tuning many parameters that changes with the biological properties of each sample, making the large-scale modelling big challenge in the field. Neural differential equations can propose a promising direction as data-driven differential solvers, these models can combine the current advance of machine learning with the domain knowledge of the systems. In this project, neural differential equation models are represented to solve Hodgkin-Huxley equations by combination of neural networks Approximators for gating variables of ion channels and the differential equation of how voltage is changing cross cell membrane.