Hamiltonian Neural Networks from a Differential Geometry Perspective [D]

This is a write-up on our company blog that I wrote, sharing our perspective into Hamiltonian Neural Networks (Greydanus et al., 2019) from a differential-geometry angle rather than the usual "here's the loss function" treatment. I've been working on HNN and LNN adjacent topics for years now and I found this particular lens made the *why* click in a way the standard framing never did for me, and I've been meaning to put everything in writing for a while now.

I just feel like the Noether's Theorem which shows conservations can be mapped to symmetries (and in ML context, generalization) is not getting the attention that it deserves around physics informed neural networks. Also, it's a really beautiful architecture and I just love talking about it at every opportunity.

It's math-heavy, but I did my best to sprinkle some tension relievers and interactive visuals here and there and make is as easy as it is to follow. Hopefully, I did a good job.

I'd genuinely love to see your thoughts and your feedback