AI 中文总结
该研究针对非定常流动稳定预测需求，提出CoKo-UNO模型，结合U形谱主干与Koopman潜在传播，经四组基准测试，其平均推进误差最低，训练时间仅为RNO的约41.40%。
AI 中文摘要
非定常流动的稳定预测需要精确的多尺度空间表示和鲁棒的时间传播。我们提出了补偿Koopman U形神经算子（CoKo-UNO），它将U形谱主干与以Koopman为主的潜在传播相结合。有限维Koopman截断会产生状态相关残差，该残差在自回归推进过程中被重复注入。CoKo-UNO用选择性状态空间模型（SSM，一种基于输入的原则性补偿机制）对该残差进行建模，同时采用分辨率自适应补偿跳跃连接和重叠预热推进策略。在四个基准问题上，CoKo-UNO在所有对比方法中实现了最低的平均推进误差，其最大增益是相对于最强基线降低76.76%，而所需训练时间约为RNO的41.40%。这些结果表明，显式残差补偿可改进非定常流动的稳定自回归预测。
英文摘要
Stable prediction of unsteady flows requires accurate multiscale spatial representation and robust temporal propagation. We introduce the Compensated Koopman U-shaped Neural Operator (CoKo-UNO), which combines a U-shaped spectral backbone with Koopman-dominated latent propagation. Finite-dimensional Koopman truncation produces a state-dependent residual that is repeatedly reinjected during autoregressive rollout. CoKo-UNO models this residual with a selective state-space model (SSM), a principled input-dependent compensation mechanism, together with resolution-adaptive compensatory skip connections and an overlapping-warmup rollout strategy. \NEW{Across four benchmark problems, CoKo-UNO achieves the lowest mean rollout error among all compared methods. Its largest gain is a $76.76\%$ reduction relative to the strongest baseline, while requiring about $41.40\%$ of RNO's training time.} These results show that explicit residual compensation improves stable autoregressive prediction of unsteady flows.
Comments43 Pages, 12 Figures
