# Partition Normalization (PartNorm)

Daedalus separates function-representation learning from operator learning: a functional autoencoder is pre-trained only on analytic functions synthesized on the fly, with no solver and no labels, and the latent space it induces is frozen and reused across tasks. On 28 benchmark problems spanning fluid dynamics, solid mechanics, acoustics, and the Helmholtz and Poisson equations, operators on the frozen representation have lower relative error than the end-to-end framework GAOT on 23 of them and train 2.1 times faster per problem on average; that comparison excludes the one-time backbone pre-training.

Daedalus separates function-representation learning from operator learning: a functional autoencoder is pre-trained only on analytic functions synthesized on the fly, with no solver and no labels, and the latent space it induces is frozen and reused across tasks. On 28 benchmark problems spanning fluid dynamics, solid mechanics, acoustics, and the Helmholtz and Poisson equations, operators on the frozen representation have lower relative error than the end-to-end framework GAOT on 23 of them and train 2.1 times faster per problem on average; that comparison excludes the one-time backbone pre-training.