Related papers: Model free data assimilation with Takens embedding

For nonlinear (control) systems, extended dynamic mode decomposition (EDMD) is a popular method to obtain data-driven surrogate models. Its theoretical foundation is the Koopman framework, in which one propagates observable functions of the…

We present a general framework for classifying partially observed dynamical systems based on the idea of learning in the model space. In contrast to the existing approaches using model point estimates to represent individual data items, we…

Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…

This paper presents a novel framework for stabilizing nonlinear systems represented in state-dependent form. We first reformulate the nonlinear dynamics as a state-dependent parameter-varying model and synthesize a stabilizing controller…

Sensing is one of the most fundamental tasks for the monitoring, forecasting and control of complex, spatio-temporal systems. In many applications, a limited number of sensors are mobile and move with the dynamics, with examples including…

We develop a new method which extends Dynamic Mode Decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems. DMD finds spatial-temporal coherent modes, connects local-linear…

Inferring latent dynamics from multivariate time-series defined over topological cell complexes is crucial for capturing the complex, higher-order interactions inherent in real-world systems such as in water, sensor, and transportation…

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…

We develop a new generalization of Koopman operator theory that incorporates the effects of inputs and control. Koopman spectral analysis is a theoretical tool for the analysis of nonlinear dynamical systems. Moreover, Koopman is intimately…

This paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models. The key ingredient of the approach…

This paper presents a data-driven algorithm for simultaneous system identification and parameter estimation in control-affine nonlinear systems. Parameter estimation is achieved by training a data-driven predictive model using state-action…

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…

Starting from limited measurements of a turbulent flow, data assimilation (DA) attempts to estimate all the spatio-temporal scales of motion. Success is dependent on whether the system is observable from the measurements, or how much of the…

We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…

This note explores the idea of utilising a state-space model, congruent with the underlying equations of the Kalman filter with control input, for reconstructing the state of crowdedness in a transit network. The envisaged role of the…

Accurate interpolation of seismic data is crucial for improving the quality of imaging and interpretation. In recent years, deep learning models such as U-Net and generative adversarial networks have been widely applied to seismic data…

A Bayesian data assimilation scheme is formulated for advection-dominated or hyperbolic evolutionary problems, and observations. The method is referred to as the dynamic likelihood filter because it exploits the model physics to dynamically…

Data assimilation (DA) methods use priors arising from differential equations to robustly interpolate and extrapolate data. Popular techniques such as ensemble methods that handle high-dimensional, nonlinear PDE priors focus mostly on state…

A seismic wavefield reconstruction framework based on compressed sensing using the data-driven reduced-order model (ROM) is proposed and its characteristics are investigated through numerical experiments. The data-driven ROM is generated…

This paper introduces a novel distributed consensus-based observer design that enables a group of agents in an undirected communication network to solve the problem of target tracking, where the target is modelled as a chain of integrators…