Getting Started with Torch-Harmonics (opens in new tab)

Basically to model anything on a sphere (usually the Earth). Spherical harmonics are orthogonal functions on the sphere, just like Fourier modes are orthogonal functions in normal space. They solve Laplace's equation on the sphere.

Gravity, geomagnetism, and many other things are often given in terms of spherical harmonics.

Any 3D shape/distribution can be expressed as some infinite mixture of Cartesian x-y-z (plane) waves, but if your object is closer to being radially symmetric then it might be more appropriate to express it as a mixture of azimuth-declination & radius waves instead. Technically you can choose any esoteric shape to split of your three degrees-of-freedom and your description will be mathematically identical as long as your DoF basis don’t have redundant parts, but usually we tend to use either Cartesian or spherical descriptions, and the frequency-domain (reciprocal space) description of those choice of symmetry corresponds to [xyz plane waves] or [spherical harmonics (angular part) + Spherical Hankel functions (radius part)]

I'm guessing it's for global temperature modeling

Disclaimer, this is out of my field.

Essentially: Spherical harmonics are one of the classic methods to solve PDEs on spheres, modeling complex processes like climate change, or black hole physics, etc. The spherical harmonic transform is part of this process. torch-harmonics implements the transform in way that it's differentiable with the standard automatic processes, allowing you to play the traditional tricks (optimizing over it, sensitivity analysis, etc.) The first paper linked on the repo uses it to learn the dynamics of a set of shallow water equations first and then over a larger timescale from the ERA5 climate dataset. These types approaches are beginning to gain traction for solving actual climate-scale problems (speaking from inside a national lab context). Which is not to say the problem is solved, this is a nice proof of concept that may accelerate others wanting to solve this type of problem.

TLDR: To enable data-driven deep learning methods based off of physics on a sphere (read: Earth), torch-harmonics is an important middle step.