I Neural Networks vs Traditional Numerical Methods

[BWV]

As neural networks are 'universal approximators' for nonlinear functions, in general how do they perform in comparison to traditional numerical methods for nonlinear PDEs? Just googling, I can find papers on applications to Navier Stokes and other problems, but I don't really have the background to judge how potentially useful they are. For example, can NNs perform better (i.e. comparable accuracy but less computationally intensive) than current numerical methods for modelling the NS equations?

(this may be better in the Computer Science forum)

https://en.wikipedia.org/wiki/Universal_approximation_theorem

 

[FactChecker]

The question is a little confusing to me. I am not an expert in neural networks. Neural networks does have the ability to fit a model through data points and in the examples I have seen they did a better job than other curve fitting or statistical regression algorithms. That agrees with how I would interpret the term "universal estimator". I'm not sure that finding the solution of a PDE is the same thing. But maybe I am missing something.

PS. It only took a quick Google search to find articles on solving PDEs using neural networks, so I will leave this to others with more expertise.