发表机构
ETH Zürich; Swiss Data Science Center（苏黎世联邦理工学院; 瑞士数据科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
Advectra通过引入正则化运动学坐标映射解耦源/目标坐标系，实现不对称潜空间聚合与重构，在平流主导基准（如Navier-Stokes被动标量输运、Rayleigh-Taylor不稳定性）上取得最优性能，并展现良好泛化能力。
AI 中文摘要
许多潜空间神经算子将输入和输出场表示在固定的潜空间坐标系中。特别是，常见的潜空间路由机制使用固定或共享的分配权重进行特征投影和重构，这限制了它们对以输运为主导的系统的建模能力，在这些系统中，相干结构相对于固定坐标系移动。我们提出了Advectra，一种具有输运感知能力的潜空间算子，它引入了一个正则化的运动学坐标映射来解耦源坐标系和目标坐标系。这产生了一个近似共动的潜空间参考系，并实现了不对称的特征聚合和重构。结合状态空间模型的几何感知排序机制，Advectra在保持稳定的全局交互的同时捕捉平流动力学。Advectra在平流主导的基准测试中，包括Navier-Stokes流中的被动标量输运和Rayleigh-Taylor不稳定性，取得了优于所有评估的几何约束和形式自由基线的性能，同时在真实世界的工程任务中展现出强大的泛化能力。这些结果凸显了神经算子中显式移动框架结构对非平稳物理的益处。
英文摘要
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.
