  We design the helicity-conservative physics-informed neural network model for
the Navier-Stokes equation in the ideal case. The key is to provide an
appropriate PDE model as loss function so that its neural network solutions
produce helicity conservation. Physics-informed neural network model is based
on the strong form of PDE. We compare the proposed Physics-informed neural
network model and a relevant helicity-conservative finite element method. We
arrive at the conclusion that the strong form PDE is better suited for
conservation issues. We also present theoretical justifications for helicity
conservation as well as supporting numerical calculations.

Computational Physics;Numerical Analysis;Numerical Analysis