Weak-form Extended Dynamic Mode Decomposition

Christopher W. Curtis; David M. Bortz

Weak-form Extended Dynamic Mode Decomposition

Dynamical Systems 2026-07-28 v1

Authors: Christopher W. Curtis , David M. Bortz

Abstract

In this work, we develop a weak-form version of Extended Dynamic Mode Decomposition that we call WEDMD. We establish a number of analytic results about the method and show explicitly how the weak form is able to mitigate the impacts of noise in linear stochastic differential equations. In nonlinear systems, we likewise show how the method is able to generate excellent approximations to Koopman modes without making recourse to sparsity promoting approaches. This excellent approximation property allows for meaningful forecasting even in the presence of noisy data.

Cite

@article{arxiv.2607.25950,
  title  = {Weak-form Extended Dynamic Mode Decomposition},
  author = {Christopher W. Curtis and David M. Bortz},
  journal= {arXiv preprint arXiv:2607.25950},
  year   = {2026}
}