Koopman Generative Operator 概率时序预测：单步生成提速 25 倍
Koopman Generative Operators for Efficient Probabilistic Time-Series Forecasting
一篇时序预测论文，用 Koopman 算子把扩散模型的多步采样换成一步闭式计算，快 25 倍还拿了 ProbTS 上 13/17 的 CRPS 第一，做预测的可以看看。
arXiv 论文提出 Koopman Generative Operator（KGO），将概率时序预测建模为结构化不确定性的演化。方法包含 Koopman Patch Embedding、Koopman Flow Matching 和 Adaptive Uncertainty Gate 三个组件，其中 KoFM 通过 Koopman 潜空间中的闭式矩阵指数实现单步生成，省去扩散模型的迭代采样。KGO 在 ProbTS 基准的 17 项中拿下 13 项 CRPS 最优和 16 项 NMAE 最优，推理时间至少比迭代生成模型快 25 倍。
Koopman Generative Operators for Efficient Probabilistic Time-Series Forecasting
Probabilistic time-series forecasting requires models that simultaneously capture structured temporal dynamics, expressive uncertainty, and efficient inference, yet existing approaches fall short of this goal: latent dynamical models impose structure but rely on restrictive generation mechanisms, while modern generative methods such as diffusion and flow matching achieve flexibility at the cost of iterative and computationally expensive sampling. We introduce the Koopman Generative Operator (KGO), a probabilistic forecasting method that conceptualizes prediction as the evolution of structured uncertainty. KGO integrates three core components: (1) Koopman Patch Embedding (KoPE) for temporally consistent latent trajectory extrapolation; (2) Koopman Flow Matching (KoFM), which enables fast, single-step generation through a closed-form matrix exponential in a Koopman latent space, bypassing iterative sampling; and (3) an Adaptive Uncertainty Gate (AUG), which provides probabilistic forecasts by adapting uncertainty per-variable and per-horizon, corresponding to a learned decomposition of aleatoric uncertainty without manual tuning. By unifying these components, KGO achieves state-of-the-art accuracy on 13/17 ProbTS benchmarks in CRPS and 16/17 in NMAE. Further, by eliminating iterative sampling, KGO delivers at least a 25$\times$ reduction in inference time compared to iterative generative models. These results position KGO as a practical and principled framework that advances the accuracy-efficiency trade-off in probabilistic time-series forecasting, combining leading accuracy on the evaluated benchmarks with fast, single-step generation.