  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.
