Discovery of mechanistic terms from UODE vs using the UODE

Hi everyone,

Going through the missing physics example, there is a section on symbolic regression via sparse regression. I understand that this has the advantage of more clearly exposing the relationship between the system variables. My question is the following: does this offer any other benefit in terms of inference speed if such a model were to be used in a setting where given the state of the system, its future is to be predicted? Is there a compromise on prediction quality as the symbolic regression form is derived from the UODE?

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Yes, inference speed increases because you get a simpler calculation.

We generally see that sparsification improves extrapolation.


Could you elaborate a bit more on this please? I was of the impression that the forward pass through the neural network part of the UDE would be fairly quick.

Interesting. This sounds to me somewhat similar to the effect that regularization methods like drop-out and L1 achieve.

Neural networks are slow. They do a matrix multiplication. That’s O(n^3) flops. Writing down a polynomial or trig function etc. is a lot faster. I’m not sure there’s much more too it than that. NNs are slow, that’s why they are taking up so much GPU compute these days. Other things are faster running in serial on one core.

Yes it’s similar.

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