Related papers: Data-driven prediction of large-scale spatiotempor…
This paper extends the subjects dicussed in the Data Analysis and Dynamical Systems courses by looking at the subject of modelling data. This task is nontrivial as the underlying process could be non-linear. In the paper some common…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
We show how the recent extension of spectral submanifold (SSM) theory to delay differential equations (DDEs) enables data-driven model reduction of nonlinear delay systems. First, using a scalar DDE with a single discrete delay, we compare…
Data-driven emulation of nonlinear dynamics is challenging due to long-range skill decay that often produces physically unrealistic outputs. Recent advances in generative modeling aim to address these issues by providing uncertainty…
In this article, we present data-driven reduced-order modeling for nonautonomous dynamical systems in multiscale media using Koopman operators. Different from the case of autonomous dynamical systems, the Koopman operator family of…
Many unsteady flows exhibiting complex dynamics are nevertheless characterized by emergent large-scale coherence in space and time. Reduced-order models based on Galerkin projection of the governing equations onto an orthogonal modal basis…
Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how observed neural activity relates to perception and behavior. Models of neural dynamics often focus on either…
The use of machine learning algorithms to predict behaviors of complex systems is booming. However, the key to an effective use of machine learning tools in multi-physics problems, including combustion, is to couple them to physical and…
A generic data-assisted control architecture within the port-Hamiltonian framework is proposed, introducing a physically meaningful observable that links conservative dynamics to all actuation, dissipation, and disturbance channels. A…
The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…
Among the most relevant processes in the Earth system for human habitability are quasi-periodic, ocean-driven multi-year events whose dynamics are currently incompletely characterized by physical models, and hence poorly predictable. This…
A complex system comprises multiple interacting entities whose interdependencies form a unified whole, exhibiting emergent behaviours not present in individual components. Examples include the human brain, living cells, soft matter, Earth's…
Chaotic systems are intrinsically sensitive to small errors, challenging efforts to construct predictive data-driven models of real-world dynamical systems such as fluid flows or neuronal activity. Prior efforts comprise either specialized…
Learning shared structure across environments facilitates rapid learning and adaptive behavior in neural systems. This has been widely demonstrated and applied in machine learning to train models that are capable of generalizing to novel…
Large collections of coupled, heterogeneous agents can manifest complex dynamical behavior presenting difficulties for simulation and analysis. However, if the collective dynamics lie on a low-dimensional manifold then the original…
An alternative data-driven modeling approach has been proposed and employed to gain fundamental insights into robot motion interaction with granular terrain at certain length scales. The approach is based on an integration of dimension…
We investigate whether a strongly turbulent flow with intermittent large-scale reorganizations admits a compact state-space description. As a representative high-dimensional chaotic system we consider two-dimensional Rayleigh--B\'enard…
Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. Having reliable uncertainty assessment of the forecast enables tools to be deployed to predict…
Shallow water equations are extensively considered in the domains of oceans, atmospheric modelling, and engineering research (Franca et al., 2022), which play significant roles in floods and tsunami governance. Nonetheless, the accurate…
Nonequilibrium statistical models of point vortex systems are constructed using an optimal closure method, and these models are employed to approximate the relaxation toward equilibrium of systems governed by the two-dimensional Euler…