group theory and the laws of physics

I was very fortunate to be part of a meeting today between Soledad Villar (JHU) and Benjamin Blum-Smith (NYU) in which we spoke about the possible forms of universally approximating functions that are equivariant under rotations and reflections (the orthogonal group O(d)). From my perspective, this is a physics question: What are all the possible physical laws in classical physics? From Villar's perspective, this is a machine-learning question: How can we build universal or expressive machine-learning methods for the natural sciences? From Blum-Smith's perspective, this is a group-theory question: What are the properties of the orthogonal group and its neighbors? We discussed the possibility that we might be able to write an interdisciplinary paper on this subject.