Related papers: Data-driven modelling of autonomous and forced dyn…

Similar to static systems, periodically driven systems can host a variety of topologically non-trivial phases. Unlike the case of static Hamiltonians, the topological indices of bulk Floquet bands may fail to describe the presence and…

This work presents a purely data-driven, wavelet-based framework for modal identification and reduced-order modeling of mechanical systems with assumed linear dynamics characterized by closely spaced modes with classical or non-classical…

We introduce a data-driven approach to the modelling and analysis of viscous fluid mechanics. Instead of including constitutive laws for the fluid's viscosity in the mathematical model, we suggest to directly use experimental data. Only a…

Dynamic mode decomposition (DMD) has emerged as a popular data-driven modeling approach to identifying spatio-temporal coherent structures in dynamical systems, owing to its strong relation with the Koopman operator. For dynamical systems…

In solid mechanics, Data-driven approaches are widely considered as the new paradigm that can overcome the classic problems of constitutive models such as limiting hypothesis, complexity, and high dependence on training data. However,…

Input-affine dynamical systems often arise in control and modeling scenarios, such as the data-driven case when state-derivative observations are recorded under bounded noise. Common tasks in system analysis and control include optimal…

Aeroelastic structures, from insect wings to wind turbine blades, experience transient unsteady aerodynamic loads that are coupled to their motion. Effective real-time control of flexible structures relies on accurate and efficient…

In this work, we demonstrate how physical principles -- such as symmetries, invariances, and conservation laws -- can be integrated into the dynamic mode decomposition (DMD). DMD is a widely-used data analysis technique that extracts…

Finite-time Lyapunov exponents (FTLEs) provide a powerful approach to compute time-varying analogs of invariant manifolds in unsteady fluid flow fields. These manifolds are useful to visualize the transport mechanisms of passive tracers…

This paper presents a data-driven optimal control policy for a micro flapping wing unmanned aerial vehicle. First, a set of optimal trajectories are computed off-line based on a geometric formulation of dynamics that captures the nonlinear…

Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…

This paper investigates model-order reduction methods for geometrically nonlinear structures. The parametrisation method of invariant manifolds is used and adapted to the case of mechanical systems expressed in the physical basis, so that…

We consider the problem of reconstructing missing data on a smooth manifold from incomplete and nonuniform samples. While classical methods for manifold approximation typically assume quasi-uniform data, their performance deteriorates…

This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical…

We introduce a data-driven dynamic factor framework for modeling the joint evolution of high-dimensional covariates and responses without parametric assumptions. Standard factor models applied to covariates alone often lose explanatory…

Invariant manifolds of unstable periodic orbits organize the dynamics of chaotic orbits in phase space. They provide insight into the mechanisms of transport and chaotic advection and have important applications in physical situations…

Data-driven machine learning models often require extensive datasets, which can be costly or inaccessible, and their predictions may fail to comply with established physical laws. Current approaches for incorporating physical priors…

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.…

The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…

The reliability of machine learning in multiscale physical systems depends on how physical structure is embedded into the learning process. We investigate this in the context of turbulent multiphase flows, focusing on the prediction of…