Verify that the domains of all the GT4Py programs are as minimal as possible using an LLM

TL;DR Let an LLM check the whole icon4py frontend code to figure out if there are opportunities to restrict the domain of GT4Py field operators/programs

Problem / motivation

In icon4py PR#1378 Jacopo figured out that by restricting the domain computation of field it fixed not only the correctness but it also helped the GT4Py-DaCe passes to split and fuse more beneficially the Maps/GPU kernels. We are wondering if there are more cases like that in icon4py.

Proposal

The idea is to feed the icon4py frontend code for dycore, diffusion and tracer_advection to an LLM and explain to it or let it figure out the concepts of computation domains in the frontend. Then we can ask it to figure out if there are domains in GT4Py programs of icon4py that can be restricted without any influence at the generated results. For that purpose we have to give it a good test to check its changes with. Doing this in a completely agentic mode is useful because compiling all the GT4Py programs is time consuming.

Alternatives considered

Go program by program by hand I guess.

Open questions / conflicts

How can the domain restriction be done with the help of the GT4Py domain inference. My guess is that the necessary information to make the GT4Py domain inference as good as possible are missing from the frontend code and that’s why we ended up in the case of PR#1378.