Ion current models and differential equations in Machine Learning

Does It exist? Why or why not? What are the advantages and disadvantages?

I'd presume a disadvantage is the computational cost of the numerical simulations.

Not sure of the advantages. The underlying currents can do a lot to modulate the excitability of individual neurons and of course chaotic systems can have infinite input/output relationships, so I could imagine how some optimization problems could benefit, but I have no experience in machine learning, only pure theoretical neuroscience.