arXiv Machine Learning
Spatially Aware Dictionary-Free Koopman Eigenfunction Identification for Modeling and Control
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it 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.
arXiv Machine Learning
Sep 22
Stability and Bifurcation Analysis of Nonlinear PDEs via Random Projection-based PINNs: A Krylov-Arnoldi Approach
arXiv:2603.21568v2 Announce Type: replace-cross Abstract: We present a numerical framework for the stability and bifurcation analysis of nonlinear partial differential equations (PDEs) in which the s...
arXiv Machine Learning
Aug 6
Koopman-Based Nonlinear Identification and Model Predictive Control of a Turbofan Engine
arXiv:2604. 01730v2 Announce Type: replace Abstract: This paper investigates Koopman operator-based approaches for multivariable control of a two-spool turbofan engine.
arXiv Machine Learning
Jul 3
Koopman operator theory: fundamentals, control, and applications
arXiv:2607. 01819v1 Announce Type: cross Abstract: The Koopman operator has gained considerable attention due to its ability to provide a global linear representation of highly complex dynamical systems.
arXiv Machine Learning
Jun 30
Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation
arXiv:2606. 29083v1 Announce Type: cross Abstract: Koopman theory promises linear structure in nonlinear dynamics, but numerical Koopman spectra are easy to compute and hard to trust.
arXiv Machine Learning
Aug 3
Dynamics-aware identification of governing equations from sparse and noisy data
arXiv:2607. 29036v1 Announce Type: new Abstract: Sparse identification of nonlinear dynamics (SINDy) and PDE functional identification (PDE-FIND) recover parsimonious ordinary and partial differential equations (ODEs and PDEs) from data.