Cluster-Weighted EDMD
Mirrored from arXiv — Machine Learning for archival readability. Support the source by reading on the original site.
Computer Science > Machine Learning
Title:Cluster-Weighted EDMD
Abstract: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.
| Comments: | Accepted at the International Conference on Scientific Computing and Machine Learning 2026 (SCML2026) |
| Subjects: | Machine Learning (cs.LG); Machine Learning (stat.ML) |
| Cite as: | arXiv:2607.12243 [cs.LG] |
| (or arXiv:2607.12243v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2607.12243
arXiv-issued DOI via DataCite (pending registration)
|
Access Paper:
- View PDF
- HTML (experimental)
- TeX Source
Current browse context:
References & Citations
Bookmark
Bibliographic and Citation Tools
Code, Data and Media Associated with this Article
Demos
Recommenders and Search Tools
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
More from arXiv — Machine Learning
-
SLM-Conditioned Hierarchical Relation Routing for Labeled Property Graph Learning
Aug 28
-
NeuronFuzz: Safety Neuron Guided Fuzzing for LLM Safety Evaluation
Aug 28
-
Pruning Binarized Neural Networks: A Dedicated Framework and Globally Weighted Algorithms
Aug 28
-
Muon with Finite Newton-Schulz: The Smoothing Benefit in Nonsmooth Nonconvex Optimization
Aug 28
Discussion (0)
Sign in to join the discussion. Free account, 30 seconds — email code or GitHub.
Sign in →No comments yet. Sign in and be the first to say something.