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Found 8 papers, 7 papers with code
Coarse-grained and emergent distributed parameter systems from data
We explore the derivation of distributed parameter system evolution laws (and in particular, partial differential operators and associated partial differential equations, PDEs) from spatiotemporal data.
Particles to Partial Differential Equations Parsimoniously
Equations governing physico-chemical processes are usually known at microscopic spatial scales, yet one suspects that there exist equations, e. g. in the form of Partial Differential Equations (PDEs), that can explain the system evolution at much coarser, meso- or macroscopic length scales.
Linking Machine Learning with Multiscale Numerics: Data-Driven Discovery of Homogenized Equations
Training deep neural networks to learn such data-driven partial differential operators requires extensive spatiotemporal data.
Numerical Analysis Numerical Analysis Computational Physics 35B27
Generative stochastic modeling of strongly nonlinear flows with non-Gaussian statistics
As such, this framework represents the chaotic time series as the evolution of a stochastic system observed through the lens of a nonlinear map.
Dynamical Systems Chaotic Dynamics 62G32, 76F20, 49Q22, 60G10
Spectral analysis of mixing in 2D high-Reynolds flows
We use spectral analysis of Eulerian and Lagrangian dynamics to study the advective mixing in an incompressible 2D bounded cavity flow.
Fluid Dynamics 76F25, 37A25
A data-driven Koopman model predictive control framework for nonlinear flows
The Koopman operator theory is an increasingly popular formalism of dynamical systems theory which enables analysis and prediction of the nonlinear dynamics from measurement data.
Fluid Dynamics 76B75, 35Q93, 76D55, 76N25
Study of dynamics in post-transient flows using Koopman mode decomposition
We observe that KMD outperforms the Proper Orthogonal Decomposition in reconstruction of the flows with strong quasi-periodic components. c features are present in the flow.
Fluid Dynamics 37N10
Ergodic theory, Dynamic Mode Decomposition and Computation of Spectral Properties of the Koopman operator
We establish the convergence of a class of numerical algorithms, known as Dynamic Mode Decomposition (DMD), for computation of the eigenvalues and eigenfunctions of the infinite-dimensional Koopman operator.
Dynamical Systems 37M10, 37A30, 65P99, 37N10
