发表机构
Indian Institute of Technology Bombay; IBM Research（印度理工学院孟买分校; IBM研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
COSMOS提出软机制混合神经算子，通过连续混合四个过程偏置专家实现长时程PDE预测，在组合基准上相比硬路由显著降低误差，但路由标签与机制不对齐。
AI 中文摘要
神经算子为经典PDE求解器提供了一种高效替代方案，但大多数神经算子针对每个方程族和离散化学习一个单一映射。真实系统是组合性的：输运、扩散、波动和反应过程可以同时发生。现有的专家混合算子通常采用稀疏的top-K路由，尽管并发物理过程本质上是混合而非离散选择。我们提出COSMOS（具有机制级算子软路由的协作式算子专家），一种软机制混合神经算子。四个过程偏置专家在每一步都保持活跃，并由一个学习到的门控连续混合，其特征通过一个小型网络融合。专家共享一个粗潜空间网格，而一个零初始化的全分辨率残差恢复通过瓶颈丢失的细节。我们还引入了一个具有已知每轨迹混合权重w*的算子分裂组合基准。在与针对族调优的FNO进行20步展开的对比中，初始3种子评估表明在扩散-反应问题上有所提升，在Navier-Stokes问题上持平，而在浅水问题上表现较弱。一次11种子审计显示扩散-反应的增益不稳定，这提醒我们在小种子展开比较中需谨慎，并排除了在这些族上可靠地宣称精度提升的可能性。消融研究表明，均匀路由或移除专家混合会显著降低稳定状态下的展开性能。在标注基准上，密集软路由在相同融合下比硬top-1路由误差低2.2倍；在推理时使用生成器权重w*进一步将展开误差降低至0.034，诊断了学习门控的局限性。然而，路由标签与专家的预期机制并不对齐：COSMOS支持组合精度，而非机制同一性。
英文摘要
Neural operators offer an efficient alternative to classical PDE solvers, but most learn a monolithic map per equation family and discretization. Real systems are compositional: transport, diffusion, wave, and reaction processes can act simultaneously. Existing mixture-of-experts operators typically use sparse top-$K$ routing, although concurrent physics is naturally a blend rather than a discrete choice. We propose COSMOS (Cooperative Operator Specialists with Mechanism-level Operator Soft-routing), a soft mechanism-mixture neural operator. Four process-biased specialists remain active at every step and are continuously mixed by a learned gate, with their features fused by a small network. Specialists share a coarse latent grid, while a zero-initialized full-resolution residual restores detail lost through the bottleneck. We also introduce an operator-splitting compositional benchmark with known mixture weights $w^\star$ per trajectory. Against family-tuned FNO under 20-step rollouts, an initial 3-seed evaluation suggested gains on diffusion--reaction, parity on Navier--Stokes, and weaker shallow-water performance. An 11-seed audit showed that the diffusion--reaction gain was unstable, motivating caution in small-seed rollout comparisons and precluding a reliable accuracy-win claim on these families. Ablations show that uniform routing or removing the specialist mixture substantially degrades stable-regime rollouts. On the labeled benchmark, dense soft routing yields $2.2\times$ lower error than hard top-1 routing at identical fusion; using generator weights $w^\star$ at inference further lowers rollout error to $0.034$, diagnosing limitations of the learned gate. However, routing labels do not align with the specialists' intended mechanisms: COSMOS supports compositional accuracy, not mechanism identity.
