Using polars and rust might be the best option right now, offering high level operations such as SQL like joins as well as performance. Although im not a rust programmer and i only use tbe python library polars, so please correct me as necessary.
》 if, for instance, you don’t care how fast the particle is moving but only which way it’s facing at any moment in time — you could describe its motion using a three-dimensional state space.
This is assuming we are on a curve across 2D space like the equator and face east or west. This sentence was puzzling me at first glance. In usual 3D space, direction/orientation is represented as a 3 dimensonal vector with length one, so on top of the position dimensions, that makes six dimensions, even if we dont care about magnitude of direction a.k.a. speed. Using angle coordinates changes the support domain, but still three dimensions are needed for direction.
That's the point. A particle moving in 3D space can instead be considered as a curve on a 2D manifold (a surface) embedded in 3D space. So then you only need two dimensions for position and one for orientation.
What you wrote is naive. I dont think AI will ever be able to guess what correct output for arbitrary inputs should look like, just based on examples. You need to specify an algorithm that produces the correct output for all inputs. AI could be able to optimize that, but not fill in gaps in the definition of the goal.
