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

This work is concerned with the dynamics of a slow-fast stochastic evolutionary system quantified with a scale parameter. An invariant foliation decomposes the state space into geometric regions of different dynamical regimes, and thus…

Because the Navier-Stokes equations are dissipative, the long-time dynamics of a flow in state space are expected to collapse onto a manifold whose dimension may be much lower than the dimension required for a resolved simulation. On this…

Invariant manifolds facilitate the understanding of nonlinear stochastic dynamics. When an invariant manifold is represented approximately by a graph for example, the whole stochastic dynamical system may be reduced or restricted to this…

This article establishes the foundation for a new theory of invariant/integral manifolds for non-autonomous dynamical systems. Current rigorous support for dimensional reduction modelling of slow-fast systems is limited by the rare events…

We develop a data-driven framework for learning and correcting non-autonomous vehicle dynamics. Physics-based vehicle models are often simplified for tractability and therefore exhibit inherent model-form uncertainty, motivating the need…

Complex chaotic dynamics, seen in natural and industrial systems like turbulent flows and weather patterns, often span vast spatial domains with interactions across scales. Accurately capturing these features requires a high-dimensional…

With the growing number of wind farms over the last decades and the availability of large datasets, research in wind-farm flow modeling - one of the key components in optimizing the design and operation of wind farms - is shifting towards…

Data-driven reduced-order models of the dynamics of complex flows are important for tasks related to design, understanding, prediction, and control. Many flows obey symmetries, and the present work illustrates how these can be exploited to…

Multivariate functional data can be intrinsically multivariate like movement trajectories in 2D or complementary like precipitation, temperature, and wind speeds over time at a given weather station. We propose a multivariate functional…

The complex dynamics of high-dimensional oscillatory flows can be simplified using phase-reduction analysis, providing a deeper understanding of the flow response to external perturbations. Although phase-based modeling and analysis have…

This paper introduces a novel data driven framework for constructing accurate and general equivariant models of multiscale phenomena which does not rely on specific assumptions about the underlying physics. This framework is illustrated…

In systems control, the dynamics of a system are governed by modulating its inputs to achieve a desired outcome. For example, to control the thrust of a quad-copter propeller the controller modulates its rotation rate, relying on a…

We propose to use a simulation driven inverse inference approach to model the dynamics of tree branches under manipulation. Learning branch dynamics and gaining the ability to manipulate deformable vegetation can help with occlusion-prone…

Model-free data-driven computational mechanics replaces phenomenological constitutive functions by numerical simulations based on data sets of representative samples in stress-strain space. The distance of strain and stress pairs from the…

To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…

Control invariant set is critical for guaranteeing safe control and the problem of computing control invariant set for linear discrete-time system is revisited in this paper by using a data-driven approach. Specifically, sample points on…

The dynamics of flexible filaments entrained in flow, important for understanding many biological and industrial processes, are computationally expensive to model with full-physics simulations. This work describes a data-driven technique to…

Shape-constrained functional data encompass a wide array of application fields, such as activity profiling, growth curves, healthcare and mortality. Most existing methods for general functional data analysis often ignore that such data are…

Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…

We propose a hybrid physics-informed machine learning framework to approximate invariant manifolds (IMs) of discrete-time dynamical systems driven by exogenous autonomous dynamics (exosystems). Such systems appear in applications ranging…