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
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...
By Gianluca Fabiani, Michail E. Kavousanakis, Constantinos Siettos, Ioannis G. Kevrekidis
arXiv:2604. 01730v2 Announce Type: replace Abstract: This paper investigates Koopman operator-based approaches for multivariable control of a two-spool turbofan engine.
By David Grasev
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.
By Igor Mezi\'c, Jorge Cort\'es, Karl Worthmann, Mircea Lazar, Armin Lederer
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.
By George Coote, Matthew J. Colbrook
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.
By Pongpisit Thanasutives, Yoshinobu Kawahara
arXiv:2604. 03086v2 Announce Type: replace-cross Abstract: This work establishes a rigorous bridge between infinite-dimensional delay dynamics and finite-dimensional Koopman learning, with explicit and interpretable error guarantees.
By Santosh Mohan Rajkumar, Dibyasri Barman, Kumar Vikram Singh, Debdipta Goswami
arXiv:2405. 07312v5 Announce Type: replace-cross Abstract: This paper presents a novel Koopman composition operator representation framework for control systems in reproducing kernel Hilbert spaces (RKHSs) that is free of explicit dictionary or input parametrizations.
By Petar Bevanda, Bas Driessen, Lucian Cristian Iacob, Stefan Sosnowski, Roland T\'oth, Sandra Hirche
arXiv:2605. 01835v2 Announce Type: replace Abstract: Nonlinear coupled systems are ubiquitous in science and engineering.
By Tatsuya Naoi, Jun Ohkubo
arXiv:2607. 19628v1 Announce Type: new Abstract: In this work we investigate reinforcement learning (RL) as a framework for the robust control of parametrized dynamical systems in presence of measurements and model uncertainties.
By Nicol\`o Botteghi, Gabriele Pascali, Urban Fasel, Andrea Manzoni
The paper introduces a Bayesian method for jointly estimating Linear Parameter-Varying (LPV) state-space models and their scheduling maps from input-output data, while explicitly quantifying both aleatoric and epistemic uncertainties. This approach preserves the LPV structure necessary for controller synthesis and provides confidence bounds on predicted responses, enabling efficient simulation and uncertainty propagation. The method is illustrated on a surrogate model of a two-dimensional nonlinear mass‑spring‑damper system.
By E. Javier Olucha, Amritam Das, Roland T\'oth
arXiv:2607. 15077v1 Announce Type: new Abstract: Many engineering problems involve phenomena whose governing equations are poorly characterized or only partially known.
By Yao Cheng Li, Ana Larra\~naga, Steven L. Brunton, Urban Fasel