← Back to all news
arXiv Machine Learning By Stefan Klus, Eirini Ioannou

Functional dynamic mode decomposition: Learning infinite-dimensional systems from data

Read the original on arXiv Machine Learning →

The paper introduces Functional Dynamic Mode Decomposition (fDMD), extending traditional DMD to infinite-dimensional systems by learning finite-rank operators from functional data such as observables, densities, or wavefunctions. It demonstrates that conventional DMD algorithms are special cases of fDMD and illustrates the approach with examples involving Koopman, Perron‑Frobenius, and Koopman‑von Neumann operators for graphons, ODEs, and SDEs.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

Related stories

arXiv Machine Learning
Aug 28

Data-driven Koopman mode approximation: A neural power iteration algorithm

This paper introduces a data‑driven neural power‑iteration algorithm for approximating the dominant eigenfunctions (modes) of the Koopman operator in nonlinear dynamical systems. By avoiding explicit construction of the operator’s projection, the method sidesteps the curse of dimensionality that plagues expressive neural templates. The authors provide theoretical convergence guarantees tied to sample size and network width, and demonstrate through numerical experiments that the approach yields accurate, smooth mode approximations without the drawbacks of traditional techniques such as extended dynamic mode decomposition.

By Guillaume O. Berger, Rapha\"el M. Jungers
More like this →