Reviews: Hamiltonian Neural Networks

This paper is very well written, nicely motivated and introduces a general principle to design neural network for data with conservation laws using Hamiltonian mechanics. Contrary to what the authors state, including energy conservation into neural networks and optimizing its gradients is now common procedure in this domain, for example: - Pukrittayakamee et al. For classical systems, as presented in this paper, it seems that this addition is rather counter-productive: while the change of momentum is described by the potential (see references above), the change of positions directly follows from the equations of motion and does not require an additional derivative of the network. This is both more computationally efficient and generalizes by design to all initial momenta (provided the corresponding positions stay close to the training manifold). On the other hand, I am not convinced that the proposed architecture would still work when applying a trained model to a different energy level.