Schematic illustration of the problem setting considered in this paper: “Parameterizing PT profiles” means finding a way to represent PT profiles as vectors 𝔃 ∊ ℝ^d, together with a decoding mechanism f_𝓏 : P → T that converts these 𝔃-vectors back into a function that maps pressure values onto temperature values. Our goal in this work is to learn both the representations 𝔃 and the mechanism f_𝓏 from data obtained with simulations using full climate models.