Hodgkin Huxley

The Hodgkin-Huxley model is a foundational mathematical description of neuronal action potential generation, aiming to accurately represent the complex interplay of ion channels and membrane potential. Current research focuses on improving parameter estimation using techniques like probabilistic integrators with diffusion tempering and operator learning methods such as DeepONets and neural operators, enhancing model fitting and predictive accuracy. These advancements are facilitating more efficient and robust simulations, enabling applications in deep brain stimulation control strategies and providing new insights into neuronal dynamics through hybrid models combining Hodgkin-Huxley equations with artificial neural networks. This refined understanding of neuronal behavior has significant implications for neuroscience research and the development of novel therapeutic interventions.