Worth noting that this paper is from 2009.

For anyone interested they released the code about a decade later: https://arepo-code.org/getting-started

> about a decade later

Practically the blink of an eye to a cosmologist!

> is based on a mov- ing unstructured mesh defined by the Voronoi tessellation of a set of discrete points. The mesh is used to solve the hyperbolic conservation laws of ideal hydrodynamics with a finite volume approach, based on a second-order unsplit Godunov scheme with an exact Riemann solver. The mesh-generating points can in principle be moved ar- bitrarily.

The visual examples at the bottom feel very impressive. I haven't diced fully in, but it feels like there's points where they need to be, that represent the simulation well.

Where-as the previous grids couldn't adapt to the problem.

Neat to see!

This is really nice work that solves a lot of practical problems related to fixed gridding.

I wonder if this could be applied to electromagnetic simulations. Common systems in that field have even more serious problems with gridding.

Do this in time and not only in space, using energy-momentum as the metric and you get Gravity and General Relativity. They are so close and yet they don’t seem to see it.

(HN never fails to give me titles that I can use for my own random music projects :P)

Is classical HPC still alive and well in the current neural network craze?

Definitely. There are techniques that purport to replace traditional PDE solvers (FNOs, LNOs, all sorts of PINNs, ...), but I have yet to see something that can give reasonable predictions of even a second-year grad student level fluid dynamics problem without extensive fine-tuning on an extremely similar problem.