Dear all,
I’m trying to the solve the following problem. Consider some volume V \in \mathbb{R}^3 with an almost everywhere smooth function f(x) \in \mathbb{R} \leq 0 with x \in V . For symmetry reasons, all zero manifolds f(x) = 0 of that function are onedimensional.

How can I find them numerically? Do you know julia packages fitting to that problem? Right now I’m just calculating a large grid over all of the volume, and make it finer within some threshold of f(x). However, that is very inefficient. I wonder if there is a way to follow the lines? Could I parametrize these lines by splines (instead of saving millions of trajectory levels)?

I wondered if there was maybe a very julian way to solve this problem. Particularly, I wondered if I could use AD to follow the zerolevel sets.
Disclaimer: I do not have an optimization background. That is why maybe this question might sound knowledgeable and/or badlyposed to you.
Thanks,
v.