Advectra: Asymmetric Latent Transport for Non-Stationary Physics

2026-10-04

AI Summary

This study addresses the challenge of modeling advection-dominated non-stationary physical systems using fixed latent variables by proposing the Advectra framework. This method introduces a regularized motion coordinate mapping to decouple source and target coordinate systems, thereby constructing a co-moving reference frame. Furthermore, it integrates neural operators, geometry-aware sorting, and state space models to achieve asymmetric feature aggregation and reconstruction. By explicitly incorporating a moving frame structure, Advectra overcomes the limitations of conventional fixed-coordinate paradigms. Experimental results demonstrate that the proposed framework achieves state-of-the-art performance on advection benchmarks while exhibiting strong generalization capabilities in real-world engineering tasks.

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.

Problem

• latent neural operators
• non-stationary physics
• advection-dominated systems
• transport dynamics
• moving coordinate frames

Innovation

• Latent Neural Operator
• Asymmetric Latent Transport
• Co-moving Reference Frame
• State-Space Models
• Advection-dominated Dynamics