Related papers: Reduced-order modelling based on Koopman operator …
The Koopman operator is an useful analytical tool for studying dynamical systems -- both controlled and uncontrolled. For example, Koopman eigenfunctions can provide non-local stability information about the underlying dynamical system.…
Recent advances in diffusion-based robot policies have demonstrated significant potential in imitating multi-modal behaviors. However, these approaches typically require large quantities of demonstration data paired with corresponding robot…
The Koopman Mode Decomposition (KMD) is a data-analysis technique which is often used to extract the spatio-temporal patterns of complex flows. In this paper, we use KMD to study the dynamics of the lid-driven flow in a two-dimensional…
This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…
The Dynamic Mode Decomposition (DMD) is a tool of trade in computational data driven analysis of fluid flows. More generally, it is a computational device for Koopman spectral analysis of nonlinear dynamical systems, with a plethora of…
Autonomous Underwater Vehicles (AUVs) play an essential role in modern ocean exploration, and their speed control systems are fundamental to their efficient operation. Like many other robotic systems, AUVs exhibit multivariable nonlinear…
Koopman analysis of a general dynamics system provides a linear Koopman operator and an embedded eigenfunction space, enabling the application of standard techniques from linear analysis. However, in practice, deriving exact operators and…
This paper proposes a robust nonlinear observer synthesis method for a population of systems modelled using the Koopman operator. The Koopman operator allows nonlinear systems to be rewritten as infinite-dimensional linear systems. A…
Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This framework enables the use of linear operator theory for…
Reduced order modeling (ROM) provides an efficient framework to compute solutions of parametric problems. Basically, it exploits a set of precomputed high-fidelity solutions --- computed for properly chosen parameters, using a full-order…
We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…
The Koopman operator enables the analysis of nonlinear dynamical systems through a linear perspective by describing time evolution in the infinite-dimensional space of observables. Here this formalism is applied to shear flows, specifically…
Piecewise-linear nonlinear systems appear in many engineering disciplines. Prediction of the dynamic behavior of such systems is of great importance from practical and theoretical viewpoint. In this paper, a data-driven model order…
In this work we perform full-state LQR feedback control of fluid flows using non-intrusive data-driven reduced-order models. We propose a model reduction method called low-rank Dynamic Mode Decomposition (lrDMD) that solves for a…
Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…
This paper proposes a new method to propagate uncertainties undergoing nonlinear dynamics using the Koopman Operator (KO). Probability density functions are propagated directly using the Koopman approximation of the solution flow of the…
Data-driven approximations of the Koopman operator are promising for predicting the time evolution of systems characterized by complex dynamics. Among these methods, the approach known as extended dynamic mode decomposition with dictionary…
Mode-based model-reduction is used to reduce the degrees of freedom of high dimensional systems, often by describing the system state by a linear combination of spatial modes. Transport dominated phenomena, ubiquitous in technical and…
A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing accuracy much, which…
We propose a neural network-based model for nonlinear dynamics in continuous time that can impose inductive biases on decay rates and/or frequencies. Inductive biases are helpful for training neural networks especially when training data…