Advectra: Asymmetric Latent Transport for Non-Stationary Physics

Many latent neural operators represent input and output fields in a stationary latent chart. In particular, common latent routing mechanisms use fixed or shared assignment weights for feature projection and reconstruction, limiting their ability to model transport-dominated systems where coherent structures move relative to fixed coordinate frames. We propose Advectra, a transport-aware latent operator that introduces a regularized kinematic coordinate map to decouple source and target coordinate systems. This yields an approximately co-moving latent reference frame and enables asymmetric feature aggregation and reconstruction. Combined with a geometry-aware ordering mechanism for state-space models, Advectra captures advective dynamics while maintaining stable global interactions. Advectra achieves the best performance among evaluated geometry-constrained and form-free baselines on advection-dominated benchmarks, including passive scalar transport in Navier--Stokes flows and Rayleigh--Taylor instability, while demonstrating strong generalization on real-world engineering tasks. These results highlight the benefit of explicit moving-frame structure in neural operators for non-stationary physics.