Related papers: Equation-Free Digital Twins for Nonlinear Structur…
This article presents the data-driven equation-free modeling of the dynamics of a hexafloat floating offshore wind turbine based on the application of dynamic mode decomposition (DMD). All the analyses are performed on experimental data…
The Koopman operator provides a principled framework for analyzing nonlinear dynamical systems through linear operator theory. Recent advances in dynamic mode decomposition (DMD) have shown that trajectory data can be used to identify…
This paper addresses the problem of nonlinear state estimation for dynamical systems whose governing equations are approximated through Koopman operator liftings. While Koopman-based predictors have demonstrated broad approximation…
We introduce a data-driven method and shows its skills for spatiotemporal prediction of high-dimensional chaotic dynamics and turbulence. The method is based on a finite-dimensional approximation of the Koopman operator where the…
We present a data-driven framework for reconstructing band structures using Koopman operator analysis and dynamic mode decomposition (Koopman-DMD). Instead of deriving spectra from an explicit Hamiltonian, the approach reconstructs band…
Digital twins for radiation-based imaging and therapy are most useful when they assimilate patient data, quantify predictive uncertainty, and support clinically constrained decisions. This paper presents a modular framework for actionable…
Koopman spectral theory has provided a new perspective in the field of dynamical systems in recent years. Modern dynamical systems are becoming increasingly non-linear and complex, and there is a need for a framework to model these systems…
Digital twins enable real-time simulation and prediction in engineering systems. This paper presents a novel framework for predictive digital twins of a headlamp heatsink, integrating physics-based reduced-order models (ROMs) from…
The Bellman equation and its continuous form, the Hamilton-Jacobi-Bellman equation, are ubiquitous in reinforcement learning and control theory. However, these equations become intractable for high-dimensional or nonlinear systems. This…
This paper presents a Koopman lifting linearization method that is applicable to nonlinear dynamical systems having both stable and unstable regions. It is known that DMD and other standard data-driven methods face a fundamental difficulty…
Deep learning is revolutionizing weather forecasting, with new data-driven models achieving accuracy on par with operational physical models for medium-term predictions. However, these models often lack interpretability, making their…
Nonlinear differential equations are encountered as models of fluid flow, spiking neurons, and many other systems of interest in the real world. Common features of these systems are that their behaviors are difficult to describe exactly and…
This note presents a unified analysis of the identification of dynamical systems with low-rank constraints under high-dimensional scaling. This identification problem for dynamic systems are challenging due to the intrinsic dependency of…
This work proposes a mathematical framework to increase the robustness to rare events of digital twins modelled with graphical models. We incorporate probabilistic model-checking and linear programming into a dynamic Bayesian network to…
Reduced order modelling relies on representing complex dynamical systems using simplified modes, which can be achieved through Koopman operator analysis. However, computing Koopman eigen pairs for high-dimensional observable data can be…
Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and…
Accurate modeling and control of autonomous vehicles remain a fundamental challenge due to the nonlinear and coupled nature of vehicle dynamics. While Koopman operator theory offers a framework for deploying powerful linear control…
Prediction of wireless channels and their statistics is a fundamental procedure for ensuring performance guarantees in wireless systems. Statistical radio maps powered by Gaussian processes (GPs) offer flexible, non-parametric frameworks,…
Linear dynamical systems are fully characterized by their eigenspectra, accessible directly from the generator of the dynamics. For nonlinear systems governed by partial differential equations, no equivalent theory exists. We introduce Lie…
The Koopman operator approach for data-driven control design of a nonlinear system is on the rise because of its capability to capture the behaviours of global dynamics. However, the measurement noises of inputs and outputs will bias the…