  Systems biology and systems neurophysiology in particular have recently
emerged as powerful tools for a number of key applications in the biomedical
sciences. Nevertheless, such models are often based on complex combinations of
multiscale (and possibly multiphysics) strategies that require ad hoc
computational strategies and pose extremely high computational demands. Recent
developments in the field of deep neural networks have demonstrated the
possibility of formulating nonlinear, universal approximators to estimate
solutions to highly nonlinear and complex problems with significant speed and
accuracy advantages in comparison with traditional models. After synthetic data
validation, we use so-called physically constrained neural networks (PINN) to
simultaneously solve the biologically plausible Hodgkin-Huxley model and infer
its parameters and hidden time-courses from real data under both variable and
constant current stimulation, demonstrating extremely low variability across
spikes and faithful signal reconstruction. The parameter ranges we obtain are
also compatible with prior knowledge. We demonstrate that detailed biological
knowledge can be provided to a neural network, making it able to fit complex
dynamics over both simulated and real data.
