U-HNO: A U-shaped Hybrid Neural Operator with Sparse-Point Adaptive Routing for Non-stationary PDE Dynamics
Solutions to many partial differential equations (PDEs) display coexisting smooth global transport and localized sharp features within a single trajectory: shock fronts, thin interfaces, and concentrated high-frequency content sit on top of slowly varying backgrounds. This poses a challenge for neural operators: Fourier-based architectures mix nonlocal interactions efficiently but tend to under-resolve localized non-smooth features, whereas spatially local architectures recover fine detail at the cost of long-range propagation and rollout stability. Existing hybrid operators paper over this tension with a fixed, spatially uniform fusion that forces the same trade-off everywhere. We propos...
| Authors | Yingzhe Ma, Xiao Yang, Yuxin Xie et al. |
|---|---|
| Primary category | cs.LG |
| Published | 13 May 2026 |
| Last updated at source | 13 May 2026 |
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