Viewing a single comment thread. View all comments

danja t1_j8tes8q wrote

Reply to comment by crimson1206 in Physics-Informed Neural Networks by vadhavaniyafaijan

I don't quite see how approximation theorems aren't relevant to approximation problems. I'm not criticising the post, I just thought your response was a bit wide of the mark, not much fun.

1

crimson1206 t1_j8ts496 wrote

Well how is it relevant then? Im happy to be corrected but I dont see how its relevant to this post

It just tells you that there is a well approximating NN for any given function. It doesn't tell you how to find such a NN and it doesnt tell you about extrapolation capabilities of a NN which is well approximating on just a subdomain (which is what this post here is mainly about) either.

The universal approximation theorem in practice just gives a justification for why using NNs as function approximators could be a reasonable thing to do. That's already pretty much the extent of their relevancy to practical issues though

1