Today Soledad Villar (JHU) and I tried to write down a zeroth-order problem statement for looking at the applicability of graph neural networks for solving cosmological large-scale-structure problems. The idea is that the universe has graph symmetries: The physics is not sensitive to the order in which we label our particles. This, the machine learners call “graph equivariance”. The universe also has many other symmetries like rotation, translation, boost and so on. These we are calling (for now) “gauge equivariances”. The mathematical language is different from the physical language, as usual!
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