Cluster-Weighted EDMD
Not on the map. Why?
Abstract (arXiv)
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.
Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 6 of its 15 references that are in the map. First posted on arXiv 14 Jul 2026.
Builds on
6 of 15 references.
References · 6
- 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 491
- 2021Modern Koopman Theory for Dynamical Systemscited by 269
- 2017Learning Koopman Invariant Subspaces for Dynamic Mode Decompositioncited by 156
- 2017Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systemscited by 125
- 2017Koopman operator-based model reduction for switched-system control of PDEscited by 31
- 2021Data-Driven Operator Theoretic Methods for Phase Space Learning and Analysiscited by 5
Built on by
Not cited yet.