Results 21 to 30 of about 472,452 (242)
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
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
Sharp Spectral Rates for Koopman Operator Learning [PDF]
, 2023 International audienceNonlinear dynamical systems can be handily described by the associated Koopman operator, whose action evolves every observable of the system forward in time.
Lounici, Karim +3 more
core +9 more sources
On the Koopman Operator of Algorithms [PDF]
SIAM Journal on Applied Dynamical Systems, 2020 27 pages, 11 ...
Felix Dietrich +2 more
openaire +3 more sources
Symplectic Geometry of the Koopman Operator [PDF]
Doklady Mathematics, 2021 Abstract We consider the Koopman operator generated by an invertible transformation of a space with a finite countably additive measure. If the square of this transformation is ergodic, then the orthogonal Koopman operator is a symplectic transformation on the real Hilbert space of square summable functions with
openaire +1 more source
Koopman Operators and the $3x+1$-Dynamical System [PDF]
SIAM Journal on Applied Dynamical Systems, 2021 The $3x+1$-problem (or Collatz problem) is a notorious conjecture in arithmetic. It can be viewed as iterating a map and, therefore, it is a dynamical system on the discrete space $\mathbb{N}$ of natural numbers. The emerging dynamical system is studied in the present work with methods from the theory of Koopman operators and $C^*$-algebras.
John Leventides, Costas Poulios
openaire +4 more sources
Model-Free Geometric Fault Detection and Isolation for Nonlinear Systems Using Koopman Operator
IEEE Access, 2022 This paper presents a model-free fault detection and isolation (FDI) method for nonlinear dynamical systems using Koopman operator theory and linear geometric technique.
Mohammadhosein Bakhtiaridoust +3 more
doaj +1 more source
Sparsity structures for Koopman operators
IEICE Proceeding Series, 2021 We present a decomposition of the Koopman operator based on the sparse structure of the underlying dynamical system, allowing one to consider the system as a family of subsystems interconnected by a graph. Using the intrinsic properties of the Koopman operator, we show that eigenfunctions for the subsystems induce eigenfunctions for the whole system ...
Schlosser, Corbinian, Korda, Milan
openaire +3 more sources
Measurement + Control, 2022 Omnidirectional mobile manipulators (OMMs) have been widely used due to their high mobility and operating flexibility. However, since OMMs are complex nonlinear systems with uncertainties, the dynamic modeling and control are always challenging problems.
Xuehong Zhu +3 more
doaj +1 more source
Koopman Operator for Nonlinear Flight Dynamics [PDF]
, 2022 Dynamical systems representing vehicle flight are inherently nonlinear. Currently there are no generalised frameworks for explicit characterisation and solution of such systems.
Bone, Viv, Jahn, Ingo, Lock, Andrew
core +1 more source