Learning the Hodgkin-Huxley Model with Operator Learning Techniques

TL;DR

This paper compares three operator learning architectures—DeepONet, Fourier Neural Operator, and Wavelet Neural Operator—in modeling the Hodgkin-Huxley system, achieving high accuracy despite its non-linearity and stiffness.

Contribution

It introduces and evaluates the effectiveness of different operator learning methods for complex biological dynamical systems like Hodgkin-Huxley.

Findings

Achieved a relative L2 error as low as 1.4% in modeling Hodgkin-Huxley.

Demonstrated the ability of operator learning techniques to handle non-linearity and stiffness.

Compared the performance of three different neural operator architectures.

Abstract

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.