This paper is solving (basically) high-school-level problems by training neural networks on the "obvious" cost function. All of those problems can be solved much cheaper by standard numerical solvers for ordinary differential equations. They don't even compare to standard methods. So what's the point? Riding the neural network hype?
This is basically all work in the physics-informed ML literature. (As another commenter points out and links to, more and more people have been increasingly frustrated with the hype of this subcommunity). What is more amazing is that they have conned their way into the funding agency priorities and have broadly affected hiring at universities.
Don't know if it's been used for anything practical yet but modeling dynamical systems which you only partially know by making use of data sounds useful.