发表机构
AE Studio（AE工作室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究针对不同状态空间区域动态不同时EDMD效率低的问题，提出聚类加权EDMD，通过期望最大化目标联合学习相空间划分与聚类EDMD算子，在多个系统预测中显著提升效果，降低误差。
AI 中文摘要
扩展动态模态分解（EDMD）从数据中逼近柯普曼算子，但当不同状态空间区域呈现不同局部动态时，单个全局算子效率低下。我们引入聚类加权EDMD（CW-EDMD），它联合学习软相空间划分和每个聚类的EDMD算子。其期望最大化（EM）目标基于几何接近度和预测残差分配每个转移，使聚类在局部柯普曼模型准确的地方而非数据密集的地方进行专门化。在洛伦兹、阻尼摆和杜芬系统上，跨越36种配置和10个种子，CW-EDMD在一步和5秒滚动预测中改进了匹配度EDMD。在288次配对比较中，258例显著降低误差，4例增加，26例无差异。在摆、杜芬和洛伦兹系统上，一步误差中位数分别降低57倍、2.7倍和12倍。
英文摘要
Extended Dynamic Mode Decomposition (EDMD) approximates Koopman operators from data, but a single global operator is inefficient when different state-space regions exhibit distinct local dynamics. We introduce Cluster-Weighted EDMD (CW-EDMD), which jointly learns a soft phase-space partition and a per-cluster EDMD operator. Its Expectation-Maximization (EM) objective assigns each transition based on both geometric proximity and prediction residuals, so clusters specialize where local Koopman models are accurate rather than where the data are dense. On Lorenz, damped pendulum, and Duffing systems, across 36 configurations and 10 seeds, CW-EDMD improves matched-degree EDMD in one-step and 5s-rollout prediction. Across 288 paired comparisons, there are significant error reductions in 258 cases, increases in 4, and no differences in 26. Median one-step error reductions are 57x, 2.7x, and 12x on pendulum, Duffing, and Lorenz, respectively.
CommentsAccepted at the International Conference on Scientific Computing and Machine Learning 2026 (SCML2026)
