Reduced-order modelling based on Koopman operator theory
CoRRThe present study focuses on a subject of significant interest in fluid dynamics: the identification of a model with decreased computational complexity from numerical code output using Koopman operator theory.
D. Bistrian +2 more
semanticscholar +4 more sources
Dynamical systems and complex networks: a Koopman operator perspective [PDF]
Journal of Physics: ComplexityThe Koopman operator has entered and transformed many research areas over the last years. Although the underlying concept—representing highly nonlinear dynamical systems by infinite-dimensional linear operators—has been known for a long time, the ...
Stefan Klus, Nataša Djurdjevac Conrad
doaj +3 more sources
Robot formation control in nonlinear manifold using Koopman operator theory [PDF]
Nonlinear Theory and Its Applications, IEICE, 2022 Formation control of multi-agent systems has been a prominent research topic, spanning both theoretical and practical domains over the past two decades.
Yanran Wang, Tatsuya Baba, T. Hikihara
semanticscholar +3 more sources
Adversarial dynamical systems characterize when data-driven learning succeeds or fails [PDF]
Nature CommunicationsMany systems resist analytical modeling, making data-driven inference of dynamics important. Yet data-driven methods can fail to converge or generalize, leaving open a central question: When can system behavior be learned reliably from data, and when is ...
Matthew J. Colbrook +2 more
doaj +2 more sources
Nonlinear System Identification of Soft Robot Dynamics Using Koopman Operator Theory [PDF]
2019 International Conference on Robotics and Automation (ICRA), 2018 Soft robots are challenging to model due in large part to the nonlinear properties of soft materials. Fortunately, this softness makes it possible to safely observe their behavior under random control inputs, making them amenable to large-scale data ...
Daniel Bruder, C. Remy, Ram Vasudevan
semanticscholar +4 more sources
Ergodic Theory, Dynamic Mode Decomposition, and Computation of Spectral Properties of the Koopman Operator [PDF]
SIAM Journal on Applied Dynamical Systems, 2017 We establish the convergence of a class of numerical algorithms, known as Dynamic Mode Decomposition (DMD), for computation of the eigenvalues and eigenfunctions of the infinite-dimensional Koopman operator. The algorithms act on data coming from observables on a state space, arranged in Hankel-type matrices.
Igor Mezic, Hassan Arbabi
exaly +4 more sources
Two Roads to Koopman Operator Theory for Control: Infinite Input Sequences and Operator Families
CoRRThe Koopman operator, originally defined for dynamical systems without input, has inspired many applications in control. Yet, the theoretical foundations underpinning this progress in control remain underdeveloped. This paper investigates the theoretical
Masih Haseli, Igor Mezic, Jorge Cortés
semanticscholar +4 more sources
Representing Neural Network Layers as Linear Operations via Koopman Operator Theory
CoRRThe strong performance of simple neural networks is often attributed to their nonlinear activations. However, a linear view of neural networks makes understanding and controlling networks much more approachable.
Nishant Aswani +2 more
semanticscholar +4 more sources
Koopman operator theory: fundamentals, control, and applications
arXiv.orgThe Koopman operator has gained considerable attention due to its ability to provide a global linear representation of highly complex dynamical systems. The operator describes nonlinear dynamics in a linear way through the lens of real- or complex-valued
Igor Mezić +4 more
semanticscholar +3 more sources
Temporally consistent Koopman autoencoders for forecasting dynamical systems [PDF]
Scientific ReportsAbsence of sufficiently high-quality data often poses a key challenge in data-driven modeling of high-dimensional spatio-temporal dynamical systems.
Indranil Nayak +4 more
doaj +2 more sources