The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
A kernel-based method for data-driven koopman spectral analysis
Open accessAbstract
A data-driven, kernel-based method for approximating the leading Koopmaneigenvalues, eigenfunctions, and modes in problems with high-dimensional statespaces is presented.This approach uses a set of scalar observables (functions that map a state to a scalar value) that are defined implicitly by the feature map associated with a user-defined kernel function.This circumvents the computational issues that arise due to the number offunctions required to span a ``sufficiently rich'' subspace of all possible scalar observables in such applications.We illustrate this method on two examples: the first is the FitzHugh-Nagumo PDE, a prototypical one-dimensional reaction-diffusionsystem, and the second is a set of vorticity data computed from experimentally obtainedvelocity data from flow past a cylinder at Reynolds number 413.In both examples, we use the output of Dynamic Mode Decomposition, which has a similar computational cost, as the benchmark for our approach.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Gaussian Processes for Machine Learning
Rasmussen, C. E., & Williams, C. K. I. (2005) · doi:10.7551/mitpress/3206.001.0001 · Cited by 11,705
Cited by
Machine Learning for Fluid Mechanics
Brunton, S. L., Noack, B. R., & Koumoutsakos, P. (2020) · Annual Review of Fluid Mechanics · doi:10.1146/annurev-fluid-010719-060214 · Cited by 3,063
Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control
Korda, M., & Mezić, I. (2018) · Automatica · doi:10.1016/j.automatica.2018.03.046 · Cited by 1,157
Data-driven discovery of coordinates and governing equations
Champion, K., Lusch, B., Kutz, J. N., & Brunton, S. L. (2019) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1906995116 · Cited by 909
Dynamic Mode Decomposition and Its Variants
Schmid, P. J. (2022) · Annual Review of Fluid Mechanics · doi:10.1146/annurev-fluid-030121-015835 · Cited by 640
Higher Order Dynamic Mode Decomposition
Le Clainche, S., & Vega, J. M. (2017) · SIAM Journal on Applied Dynamical Systems · doi:10.1137/15m1054924 · Cited by 417
Metadata
- Authors
- Williams, M. O., Rowley, C. W., & Kevrekidis, I. G.
- Venue
- Journal of Computational Dynamics
- Published
- 2015
- Volume
- 2
- Issue
- 2
- Pages
- 247-265
- ISSN
- 2158-2491 (ISSN-L)
- 2158-2505
- OpenAlex
- W2395962256
- Cited by
- 324
- References
- 1
- FWCI
- 4.49
- Type
- journal article
- Language
- en
- Open access
- diamond
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: A kernel-based method for data-driven koopman spectral analysis. https://app.cochat.ai/papers/10.3934/jcd.2015005
- The paper
- Williams, M. O., Rowley, C. W., & Kevrekidis, I. G. (2015). A kernel-based method for data-driven koopman spectral analysis. Journal of Computational Dynamics. https://doi.org/10.3934/jcd.2015005
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
