Related papers: Dynamic mode decomposition with control
Dynamic Mode Decomposition (DMD) is a data-driven method for approximating the spatiotemporal modes of a system. The eigenvectors and eigenvalues of the system are approximated from a series of time-snapshots of the state variables. The…
We revisit the setting and the assumptions that underlie the methodology of Dynamic Mode Decomposition (DMD) in order to highlight caveats as well as potential measures of when the applicability is warranted.
Aero-optical beam control relies on the development of low-latency forecasting techniques to quickly predict wavefronts aberrated by the Turbulent Boundary Layer (TBL) around an airborne optical system, and its study applies to a…
Dynamic mode decomposition (DMD) is a data-driven method for estimating the dynamics of a discrete dynamical system. This paper proposes a tensor-based approach to DMD for applications in which the states can be viewed as tensors.…
The Dynamic Mode Decomposition (DMD)---a popular method for performing data-driven Koopman spectral analysis---has gained increased adoption as a technique for extracting dynamically meaningful spatio-temporal descriptions of fluid flows…
This paper introduces a fast algorithm for randomized computation of a low-rank Dynamic Mode Decomposition (DMD) of a matrix. Here we consider this matrix to represent the development of a spatial grid through time e.g. data from a static…
We introduce the dynamics mode decomposition for monitoring wide-area power grid networks from sparse measurement data. The mathematical framework fuses data from multiple sensors based on multivariate statistics, providing accurate full…
Dimensionality reduction represents the process of generating a low dimensional representation of high dimensional data. Motivated by the formation control of mobile agents, we propose a nonlinear dynamical system for dimensionality…
This paper presents unifying results for subspace identification (SID) and dynamic mode decomposition (DMD) for autonomous dynamical systems. We observe that SID seeks to solve an optimization problem to estimate an extended observability…
Dynamic mode decomposition (DMD) is a widely used data-driven algorithm for predicting the future states of dynamical systems. However, its standard formulation often struggles with poor long-term predictive accuracy. To address this…
Decomposing multivariate time series with certain basic dynamics is crucial for understanding, predicting and controlling nonlinear spatiotemporally dynamic systems such as the brain. Dynamic mode decomposition (DMD) is a method for…
We introduce Variational Latent Mode Decomposition (VLMD), a new algorithm for extracting oscillatory modes and associated connectivity structures from multivariate signals. VLMD addresses key limitations of existing Multivariate Mode…
Temporal or spatial structures are readily extracted from complex data by modal decompositions like Proper Orthogonal Decomposition (POD) or Dynamic Mode Decomposition (DMD). Subspaces of such decompositions serve as reduced order models…
This work recasts time-dependent optimal control problems governed by partial differential equations in a Dynamic Mode Decomposition with control framework. Indeed, since the numerical solution of such problems requires a lot of…
We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally,…
Detecting changes in data streams is a vital task in many applications. There is increasing interest in changepoint detection in the online setting, to enable real-time monitoring and support prompt responses and informed decision-making.…
Designing faster optimization algorithms is of ever-growing interest. In recent years, learning to learn methods that learn how to optimize demonstrated very encouraging results. Current approaches usually do not effectively include the…
Accurate and efficient aeroelastic models are critically important for enabling the optimization and control of highly flexible aerospace structures, which are expected to become pervasive in future transportation and energy systems.…
Modelling biological or engineering swarms is challenging due to the inherently high dimension of the system, despite the often low-dimensional emergent dynamics. Most existing swarm modelling approaches are based on first principles and…
We present a low-rank Koopman operator formulation for accelerating deformable subspace simulation. Using a Dynamic Mode Decomposition (DMD) parameterization of the Koopman operator, our method learns the temporal evolution of deformable…