DESSNO: Enhancing Neural Operators for Multiscale PDE Systems with DCT-based Explicit Scale Separation

Neural operators have emerged as efficient surrogates for partial differential equation (PDE) simulations, yet accurately resolving multiscale spatial dynamics remains challenging. Existing methods often represent different scales within a shared latent space, potentially entangling smooth large-scale structures with localized fine-scale dynamics and making the latter difficult to capture. To address this limitation, we propose DESSNO, which explicitly separates latent fields into macroscopic and microscopic components using the discrete cosine transform (DCT) and evolves them through asymmetric spatial pathways. The macroscopic pathway captures broad spatial dependencies, while the microscopic pathway models localized structures using a dedicated transient evolution module. The two components are then recoupled through a content-adaptive spatial gate before global temporal propagation. This decompose-evolve-couple design turns explicit scale separation into structured dynamical routing, enabling scale-dependent evolution while preserving cross-scale interactions. Experiments on six challenging PDE benchmarks demonstrate that DESSNO consistently improves prediction accuracy and parameter efficiency, better preserves fine-scale structures, and remains stable over long-horizon autoregressive rollouts.