Advectra improves modeling of moving physics in fluid flows
Advectra: Asymmetric Latent Transport for Non-Stationary Physics
Machine Learning
Summary
Modeling how things like smoke or fluids move and change over time is hard because their shapes and positions keep changing. This paper presents Advectra, a new approach that follows moving parts instead of assuming everything stays in one place. By doing this, Advectra better captures the flow and movement patterns, making it more accurate in predicting complex fluid behaviors. The authors tested it on common physics problems and real engineering tasks, showing it works well even when things move a lot.
What this means in practice
- •For fluid dynamics engineers: Use Advectra to improve simulation accuracy for fluid flows where features move across space, such as in aerodynamics or weather prediction.
- •For computational physicists: Employ Advectra's transport-aware framework to better model non-stationary phenomena involving moving coherent structures in complex systems.
Authors
Nodens Koren, Thomas Hofmann, Georgios Kissas
Abstract
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.