Hamiltonian Neural Networks from a Differential Geometry Perspective [D]

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. I've been meaning to put everything in writing for a while now.

I just feel like Noether's Theorem - which shows conservations can be mapped to symmetries (and in the 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 it as easy as it is to follow. Hopefully, I did a good job.

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