Data-driven models of nonautonomous systems

Numerical approximation and computational geometry (primarily algorithms) (65Dxx) Approximation methods and numerical treatment of dynamical systems (37Mxx) Approximations and expansions (41Axx)

Cites Work

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Discovering governing equations from data by sparse identification of nonlinear dynamical systems
Hamiltonian systems and transformations in Hilbert space.
A data-driven approximation of the koopman operator: extending dynamic mode decomposition
Riemannian geometry of Grassmann manifolds with a view on algorithmic computation
Machine learning of linear differential equations using Gaussian processes
On convergence of extended dynamic mode decomposition to the Koopman operator
Lagrangian dynamic mode decomposition for construction of reduced-order models of advection-dominated phenomena
Data-driven deep learning of partial differential equations in modal space
Data-driven discovery of coarse-grained equations
Extended dynamic mode decomposition for inhomogeneous problems
Data driven governing equations approximation using deep neural networks
Deep learning of dynamics and signal-noise decomposition with time-stepping constraints
PDE-Net 2.0: learning PDEs from data with a numeric-symbolic hybrid deep network
Delay-coordinate maps and the spectra of Koopman operators
Data-driven spectral decomposition and forecasting of ergodic dynamical systems
On dynamic mode decomposition: theory and applications
Dynamic mode decomposition with control
Multiresolution dynamic mode decomposition
Dynamic mode decomposition of numerical and experimental data
An Online Method for Interpolating Linear Parametric Reduced-Order Models
Computational Aspects of Polynomial Interpolation in Several Variables
The Geometry of Algorithms with Orthogonality Constraints
Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations
Koopman Operator Family Spectrum for Nonautonomous Systems
Generalizing Koopman Theory to Allow for Inputs and Control
Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator
Learning partial differential equations via data discovery and sparse optimization
Data-Driven Learning of Nonautonomous Systems
Prediction Accuracy of Dynamic Mode Decomposition
Online Dynamic Mode Decomposition for Time-Varying Systems
DRIPS: a framework for dimension reduction and interpolation in parameter space

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