Learning the Hodgkin-Huxley Model with Operator Learning Techniques
This work addresses the challenge of modeling complex biological neural dynamics for computational neuroscience, but it is incremental as it applies existing operator learning methods to a known model.
The paper tackled the problem of learning the operator mapping applied current to transmembrane potential in the Hodgkin-Huxley model using operator learning techniques, achieving a relative L2 error as low as 1.4%.
We construct and compare three operator learning architectures, DeepONet, Fourier Neural Operator, and Wavelet Neural Operator, in order to learn the operator mapping a time-dependent applied current to the transmembrane potential of the Hodgkin- Huxley ionic model. The underlying non-linearity of the Hodgkin-Huxley dynamical system, the stiffness of its solutions, and the threshold dynamics depending on the intensity of the applied current, are some of the challenges to address when exploiting artificial neural networks to learn this class of complex operators. By properly designing these operator learning techniques, we demonstrate their ability to effectively address these challenges, achieving a relative L2 error as low as 1.4% in learning the solutions of the Hodgkin-Huxley ionic model.