19 citations · 35 across the 9 of their papers we have counts for
9 papers
On the relationship between Koopman operator approximations and neural ordinary differential equations for data-driven time-evolution predictions
Jake Buzhardt, C. Ricardo Constante-Amores, Michael D. Graham
This work explores the relationship between state space methods and Koopman operator-based methods for predicting the time-evolution of nonlinear dynamical systems. We demonstrate…
Data-driven prediction of large-scale spatiotemporal chaos with distributed low-dimensional models
C. Ricardo Constante-Amores, Alec J. Linot, Michael D. Graham
Complex chaotic dynamics, seen in natural and industrial systems like turbulent flows and weather patterns, often span vast spatial domains with interactions across scales. Accurat…
Elastoinertial turbulence: Data-driven reduced-order model based on manifold dynamics
Manish Kumar, C. Ricardo Constante-Amores, Michael D. Graham
Elastoinertial turbulence (EIT) is a chaotic state that emerges in the flows of dilute polymer solutions. Direct numerical simulation (DNS) of EIT is highly computationally expensi…
Dynamics of a Data-Driven Low-Dimensional Model of Turbulent Minimal Pipe Flow
C. Ricardo Constante-Amores, Alec J. Linot, Michael D. Graham
The simulation of turbulent flow requires many degrees of freedom to resolve all the relevant times and length scales. However, due to the dissipative nature of the Navier-Stokes e…
Data-driven Koopman operator predictions of turbulent dynamics in models of shear flows
C. Ricardo Constante-Amores, Andrew J. Fox, Carlos E. Pérez De Jesús +1
The Koopman operator enables the analysis of nonlinear dynamical systems through a linear perspective by describing time evolution in the infinite-dimensional space of observables.…
Data-driven low-dimensional model of a sedimenting flexible fiber
Andrew J Fox, Michael D. Graham
The dynamics of flexible filaments entrained in flow, important for understanding many biological and industrial processes, are computationally expensive to model with full-physics…
Building symmetries into data-driven manifold dynamics models for complex flows: application to two-dimensional Kolmogorov flow
Carlos E. Pérez De Jesús, Alec J. Linot, Michael D. Graham
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…
Data-driven state-space and Koopman operator models of coherent state dynamics on invariant manifolds
C. Ricardo Constante-Amores, Michael D. Graham
The accurate simulation of complex dynamics in fluid flows demands a substantial number of degrees of freedom, i.e. a high-dimensional state space. Nevertheless, the swift attenuat…
Enhancing Predictive Capabilities in Data-Driven Dynamical Modeling with Automatic Differentiation: Koopman and Neural ODE Approaches
C. Ricardo Constante-Amores, Alec J. Linot, Michael D. Graham
Data-driven approximations of the Koopman operator are promising for predicting the time evolution of systems characterized by complex dynamics. Among these methods, the approach k…