[vutekst]

Also ML non-expert here. I think this is about a different kind of neuron(your 2nd suggestion). The paper another commenter linked says:

Hamiltonian neural network (HNN) intakes position and momenta {q,p}, outputs the scalar function H, takes its gradient to find its position and momentum rates of change, and minimizes the loss

<latex equation for a modified loss function that differs from traditional NN>

which enforces Hamilton's equations of motion.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.101.0...

[zone411]

I haven't used HNNs in practice but it seems that the main difference from common NNs is that the loss function incorporates gradients. It's not a new type of a neuron.